This document discusses quantum computers from a mathematical perspective by comparing them to Turing machines. It proposes that a quantum computer can be modeled as a Turing machine with an infinite tape of "qubits" rather than bits. This raises philosophical questions about the relationship between mathematical models and reality when dealing with infinity. The document also explores how concepts like information, choice, and measurement are understood differently in quantum as opposed to classical computation.
1) Amdahl's Law describes the theoretical speedup from parallel processors based on the proportion of a program that can be parallelized (1-B) versus the portion that must run serially (B).
2) The speedup formula is: Speedup = 1 / (B + (1-B)/Number of Processors). This shows diminishing returns as more processors are added.
3) A speedup curve based on Amdahl's Law will always be below the ideal linear speedup (S=N) line, showing the limits on parallelization from the serial components of a program.
This document discusses parallel programming and algorithm design. It covers principles of parallel algorithms like decomposing computations into simultaneous tasks. It describes task decomposition techniques like data, recursive, exploratory and speculative decomposition. It also discusses mapping techniques to distribute tasks across processes, characteristics of tasks, and parallel algorithm models like data-parallel, task graph, work pool, master-slave, and producer-consumer. Finally, it briefly introduces GPU computing and references.
Using prior knowledge to initialize the hypothesis,kbannswapnac12
1) The KBANN algorithm uses a domain theory represented as Horn clauses to initialize an artificial neural network before training it with examples. This helps the network generalize better than random initialization when training data is limited.
2) KBANN constructs a network matching the domain theory's predictions exactly, then refines it with backpropagation to fit examples. This balances theory and data when they disagree.
3) In experiments on promoter recognition, KBANN achieved a 4% error rate compared to 8% for backpropagation alone, showing the benefit of prior knowledge.
This document contains the student's responses to 7 questions about operating system concepts related to process synchronization and concurrency control. The questions cover topics like the critical section problem, Peterson's solution, semaphores, monitors, and classical synchronization problems like the bounded buffer problem and readers-writers problem. The student provides definitions and explanations of the key concepts and how they can be implemented using constructs like mutexes, condition variables, load-locked and store-conditional instructions. Specific examples of how synchronization applies in areas like process management and bounded buffers are also discussed.
An introduction to quantum machine learning.pptxColleen Farrelly
Very basic introduction to quantum computing given at Indaba Malawi 2022. Overviews some basic hardware in classical and quantum computing, as well as a few quantum machine learning algorithms in use today. Resources for self-study provided.
An explicitly parallel program must specify concurrency and interaction between concurrent subtasks.
The former is sometimes also referred to as the control structure and the latter as the communication model.
Critical section problem in operating system.MOHIT DADU
The critical section problem refers to ensuring that at most one process can execute its critical section, a code segment that accesses shared resources, at any given time. There are three requirements for a correct solution: mutual exclusion, meaning no two processes can be in their critical section simultaneously; progress, ensuring a process can enter its critical section if it wants; and bounded waiting, placing a limit on how long a process may wait to enter the critical section. Early attempts to solve this using flags or a turn variable were incorrect as they did not guarantee all three requirements.
1) Amdahl's Law describes the theoretical speedup from parallel processors based on the proportion of a program that can be parallelized (1-B) versus the portion that must run serially (B).
2) The speedup formula is: Speedup = 1 / (B + (1-B)/Number of Processors). This shows diminishing returns as more processors are added.
3) A speedup curve based on Amdahl's Law will always be below the ideal linear speedup (S=N) line, showing the limits on parallelization from the serial components of a program.
This document discusses parallel programming and algorithm design. It covers principles of parallel algorithms like decomposing computations into simultaneous tasks. It describes task decomposition techniques like data, recursive, exploratory and speculative decomposition. It also discusses mapping techniques to distribute tasks across processes, characteristics of tasks, and parallel algorithm models like data-parallel, task graph, work pool, master-slave, and producer-consumer. Finally, it briefly introduces GPU computing and references.
Using prior knowledge to initialize the hypothesis,kbannswapnac12
1) The KBANN algorithm uses a domain theory represented as Horn clauses to initialize an artificial neural network before training it with examples. This helps the network generalize better than random initialization when training data is limited.
2) KBANN constructs a network matching the domain theory's predictions exactly, then refines it with backpropagation to fit examples. This balances theory and data when they disagree.
3) In experiments on promoter recognition, KBANN achieved a 4% error rate compared to 8% for backpropagation alone, showing the benefit of prior knowledge.
This document contains the student's responses to 7 questions about operating system concepts related to process synchronization and concurrency control. The questions cover topics like the critical section problem, Peterson's solution, semaphores, monitors, and classical synchronization problems like the bounded buffer problem and readers-writers problem. The student provides definitions and explanations of the key concepts and how they can be implemented using constructs like mutexes, condition variables, load-locked and store-conditional instructions. Specific examples of how synchronization applies in areas like process management and bounded buffers are also discussed.
An introduction to quantum machine learning.pptxColleen Farrelly
Very basic introduction to quantum computing given at Indaba Malawi 2022. Overviews some basic hardware in classical and quantum computing, as well as a few quantum machine learning algorithms in use today. Resources for self-study provided.
An explicitly parallel program must specify concurrency and interaction between concurrent subtasks.
The former is sometimes also referred to as the control structure and the latter as the communication model.
Critical section problem in operating system.MOHIT DADU
The critical section problem refers to ensuring that at most one process can execute its critical section, a code segment that accesses shared resources, at any given time. There are three requirements for a correct solution: mutual exclusion, meaning no two processes can be in their critical section simultaneously; progress, ensuring a process can enter its critical section if it wants; and bounded waiting, placing a limit on how long a process may wait to enter the critical section. Early attempts to solve this using flags or a turn variable were incorrect as they did not guarantee all three requirements.
In the last decades, a new model of computation based on quantum mechanics has gained attention in the computer science community. We give an introduction to this model starting from the basics, with no prerequisites. Then, with the help of some simple examples, we see why quantum computers outperform standard ones in certain tasks. We then move to the topic of quantum entanglement and show how sharing quantum information can create a strong provable correlation among distant parties. With this basic understanding of quantum computation and quantum entanglement, we can already illustrate two interesting cryptographic protocols: quantum key distribution and position verification. Both perform classically impossible tasks: the first allows to detect an intruder intercepting a secret communication, while the second allows certifying somebody's GPS location.
This document discusses hybrid intelligent systems that combine different technologies such as neural networks, fuzzy systems, and expert systems. It provides examples of neural expert systems, which combine neural networks and rule-based expert systems, and neuro-fuzzy systems, which integrate neural networks with fuzzy logic systems. The key benefits of these hybrid systems include gaining the learning and parallel processing abilities of neural networks as well as the transparency and human-like knowledge representation of fuzzy and expert systems.
This document discusses defuzzification in fuzzy logic. It defines defuzzification as the process of converting fuzzy quantities into crisp quantities. There are several reasons for and applications of defuzzification, such as converting fuzzy controller outputs into crisp values for applications. The document outlines the defuzzification process and several common defuzzification methods, including the centroid method, weighted average method, and max membership principle. It also discusses the lambda-cut and alpha-cut methods for deriving crisp values from fuzzy sets and relations.
This document provides an introduction to finite automata. It defines key concepts like alphabets, strings, languages, and finite state machines. It also describes the different types of automata, specifically deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs). DFAs have a single transition between states for each input, while NFAs can have multiple transitions. NFAs are generally easier to construct than DFAs. The next class will focus on deterministic finite automata in more detail.
The document discusses planning and problem solving in artificial intelligence. It describes planning problems as finding a sequence of actions to achieve a given goal state from an initial state. Common assumptions in planning include atomic time steps, deterministic actions, and a closed world. Blocks world examples are provided to illustrate planning domains and representations using states, goals, and operators. Classical planning approaches like STRIPS are summarized.
The document provides an overview of Truth Maintenance Systems (TMS) in artificial intelligence. It discusses key aspects of TMS including:
1. Enforcing logical relations among beliefs by maintaining and updating relations when assumptions change.
2. Generating explanations for conclusions by using cached inferences to avoid re-deriving inferences.
3. Finding solutions to search problems by representing problems as sets of variables, domains, and constraints.
The document also covers justification-based and assumption-based TMS, and how a TMS interacts with a problem solver to add and retract assumptions, detect contradictions, and perform belief revision.
This document discusses parallel processing concepts including:
1. Parallel computing involves simultaneously using multiple processing elements to solve problems faster than a single processor. Common parallel platforms include shared-memory and message-passing architectures.
2. Key considerations for parallel platforms include the control structure for specifying parallel tasks, communication models, and physical organization including interconnection networks.
3. Scalable design principles for parallel systems include avoiding single points of failure, pushing work away from the core, and designing for maintenance and automation. Common parallel architectures include N-wide superscalar, which can dispatch N instructions per cycle, and multi-core which places multiple cores on a single processor socket.
Deep learning lecture - part 1 (basics, CNN)SungminYou
This presentation is a lecture with the Deep Learning book. (Bengio, Yoshua, Ian Goodfellow, and Aaron Courville. MIT press, 2017) It contains the basics of deep learning and theories about the convolutional neural network.
The document provides information on solving the sum of subsets problem using backtracking. It discusses two formulations - one where solutions are represented by tuples indicating which numbers are included, and another where each position indicates if the corresponding number is included or not. It shows the state space tree that represents all possible solutions for each formulation. The tree is traversed depth-first to find all solutions where the sum of the included numbers equals the target sum. Pruning techniques are used to avoid exploring non-promising paths.
Memory system, and not processor speed, is often the bottleneck for many applications.
Memory system performance is largely captured by two parameters, latency and bandwidth.
Latency is the time from the issue of a memory request to the time the data is available at the processor.
Bandwidth is the rate at which data can be pumped to the processor by the memory system.
Lecture 4 principles of parallel algorithm design updatedVajira Thambawita
The main principles of parallel algorithm design are discussed here. For more information: visit, https://sites.google.com/view/vajira-thambawita/leaning-materials
A situated planning agent treats planning and acting as a single process rather than separate processes. It uses conditional planning to construct plans that account for possible contingencies by including sensing actions. The agent resolves any flaws in the conditional plan before executing actions when their conditions are met. When facing uncertainty, the agent must have preferences between outcomes to make decisions using utility theory and represent probabilities using a joint probability distribution over variables in the domain.
The document discusses various search algorithms used in artificial intelligence including uninformed and informed search methods. It provides details on breadth-first search, depth-first search, uniform cost search, and heuristic search approaches like hill climbing, greedy best-first search, and A* search. It also covers general problem solving techniques and evaluating search performance based on completeness, time complexity, space complexity, and optimality.
A brief introduction to Process synchronization in Operating Systems with classical examples and solutions using semaphores. A good starting tutorial for beginners.
Genetic Algorithm in Artificial IntelligenceSinbad Konick
Genetic algorithms are a heuristic search technique inspired by biological evolution to find optimized solutions to problems. The workflow involves initially generating a random population which is then evaluated based on a fitness function. Individuals are selected from the population based on their fitness for reproduction, with crossover and mutation occurring to create a new generation. This process is repeated until an optimal solution is found. Genetic algorithms have applications in fields like robotics, medicine, and computer gaming. They provide advantages like not requiring derivatives and being able to optimize both continuous and discrete functions, but also have limitations such as computational expense and not guaranteeing optimal solutions.
A process needs to be in the memory to be executed.
A process can be swapped temporarily out of memory to a backing store, and then brought back into memory for continued execution
Total physical memory space of processes can exceed physical memory
Backing store – fast disk large enough to accommodate copies of all memory images for all users; must provide direct access to these memory images
Abstract: This PDSG workship introduces basic concepts on using Hill Climbing for Local Search. Concepts covered are global and local maximum, shoulder/flat, value functions, local beam search, and stochastic variant.
Level: Fundamental
Requirements: Should have prior familiarity with Graph Search. No prior programming knowledge is required.
This document provides an overview of quantum computing and common algorithms used on different types of quantum computers. It discusses how quantum computers work using qubits or qumodes and the existing gate-based and quantum annealing-based architectures. Some examples of algorithms that could run on these quantum computers are presented, including for supervised and unsupervised machine learning tasks as well as graph and network analysis problems. Researchers can access existing quantum computers through the cloud or simulate circuits classically.
This document discusses several search strategies including uninformed search, breadth-first search, depth-first search, uniform cost search, iterative deepening search, and bi-directional search. It provides algorithms and examples to explain how each strategy works. Key points include: breadth-first search visits nodes by level of depth; depth-first search generates nodes along the largest depth first before moving up; uniform cost search expands the lowest cost node; and iterative deepening search avoids infinite depth by searching each level iteratively and increasing the depth limit.
Quantum information as the information of infinite series Vasil Penchev
Quantum information is equivalent to that generalization of the classical information from finite to infinite series or collections
The quantity of information is the quantity of choices measured in the units of elementary choice
The qubit is that generalization of bit, which is a choice among a continuum of alternatives
The axiom of choice is necessary for quantum information: The coherent state is transformed into a well-ordered series of results in time after measurement
The quantity of quantum information is the ordinal corresponding to the infinity series in question
Quantum Computer: Quantum Model and RealityVasil Penchev
1. The document discusses several philosophical questions about interpreting quantum computers and quantum mechanics. It argues that unlike classical models, a quantum model can coincide with reality.
2. Reality can be interpreted as a quantum computer, and physical processes can be understood as computations of a quantum computer. Quantum information is proposed as the fundamental basis of the world.
3. The conception of a quantum computer is said to unify physics and mathematics by allowing models and reality to coincide. A quantum computer is also described as a non-Turing machine that can perform infinite computations in a finite time.
In the last decades, a new model of computation based on quantum mechanics has gained attention in the computer science community. We give an introduction to this model starting from the basics, with no prerequisites. Then, with the help of some simple examples, we see why quantum computers outperform standard ones in certain tasks. We then move to the topic of quantum entanglement and show how sharing quantum information can create a strong provable correlation among distant parties. With this basic understanding of quantum computation and quantum entanglement, we can already illustrate two interesting cryptographic protocols: quantum key distribution and position verification. Both perform classically impossible tasks: the first allows to detect an intruder intercepting a secret communication, while the second allows certifying somebody's GPS location.
This document discusses hybrid intelligent systems that combine different technologies such as neural networks, fuzzy systems, and expert systems. It provides examples of neural expert systems, which combine neural networks and rule-based expert systems, and neuro-fuzzy systems, which integrate neural networks with fuzzy logic systems. The key benefits of these hybrid systems include gaining the learning and parallel processing abilities of neural networks as well as the transparency and human-like knowledge representation of fuzzy and expert systems.
This document discusses defuzzification in fuzzy logic. It defines defuzzification as the process of converting fuzzy quantities into crisp quantities. There are several reasons for and applications of defuzzification, such as converting fuzzy controller outputs into crisp values for applications. The document outlines the defuzzification process and several common defuzzification methods, including the centroid method, weighted average method, and max membership principle. It also discusses the lambda-cut and alpha-cut methods for deriving crisp values from fuzzy sets and relations.
This document provides an introduction to finite automata. It defines key concepts like alphabets, strings, languages, and finite state machines. It also describes the different types of automata, specifically deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs). DFAs have a single transition between states for each input, while NFAs can have multiple transitions. NFAs are generally easier to construct than DFAs. The next class will focus on deterministic finite automata in more detail.
The document discusses planning and problem solving in artificial intelligence. It describes planning problems as finding a sequence of actions to achieve a given goal state from an initial state. Common assumptions in planning include atomic time steps, deterministic actions, and a closed world. Blocks world examples are provided to illustrate planning domains and representations using states, goals, and operators. Classical planning approaches like STRIPS are summarized.
The document provides an overview of Truth Maintenance Systems (TMS) in artificial intelligence. It discusses key aspects of TMS including:
1. Enforcing logical relations among beliefs by maintaining and updating relations when assumptions change.
2. Generating explanations for conclusions by using cached inferences to avoid re-deriving inferences.
3. Finding solutions to search problems by representing problems as sets of variables, domains, and constraints.
The document also covers justification-based and assumption-based TMS, and how a TMS interacts with a problem solver to add and retract assumptions, detect contradictions, and perform belief revision.
This document discusses parallel processing concepts including:
1. Parallel computing involves simultaneously using multiple processing elements to solve problems faster than a single processor. Common parallel platforms include shared-memory and message-passing architectures.
2. Key considerations for parallel platforms include the control structure for specifying parallel tasks, communication models, and physical organization including interconnection networks.
3. Scalable design principles for parallel systems include avoiding single points of failure, pushing work away from the core, and designing for maintenance and automation. Common parallel architectures include N-wide superscalar, which can dispatch N instructions per cycle, and multi-core which places multiple cores on a single processor socket.
Deep learning lecture - part 1 (basics, CNN)SungminYou
This presentation is a lecture with the Deep Learning book. (Bengio, Yoshua, Ian Goodfellow, and Aaron Courville. MIT press, 2017) It contains the basics of deep learning and theories about the convolutional neural network.
The document provides information on solving the sum of subsets problem using backtracking. It discusses two formulations - one where solutions are represented by tuples indicating which numbers are included, and another where each position indicates if the corresponding number is included or not. It shows the state space tree that represents all possible solutions for each formulation. The tree is traversed depth-first to find all solutions where the sum of the included numbers equals the target sum. Pruning techniques are used to avoid exploring non-promising paths.
Memory system, and not processor speed, is often the bottleneck for many applications.
Memory system performance is largely captured by two parameters, latency and bandwidth.
Latency is the time from the issue of a memory request to the time the data is available at the processor.
Bandwidth is the rate at which data can be pumped to the processor by the memory system.
Lecture 4 principles of parallel algorithm design updatedVajira Thambawita
The main principles of parallel algorithm design are discussed here. For more information: visit, https://sites.google.com/view/vajira-thambawita/leaning-materials
A situated planning agent treats planning and acting as a single process rather than separate processes. It uses conditional planning to construct plans that account for possible contingencies by including sensing actions. The agent resolves any flaws in the conditional plan before executing actions when their conditions are met. When facing uncertainty, the agent must have preferences between outcomes to make decisions using utility theory and represent probabilities using a joint probability distribution over variables in the domain.
The document discusses various search algorithms used in artificial intelligence including uninformed and informed search methods. It provides details on breadth-first search, depth-first search, uniform cost search, and heuristic search approaches like hill climbing, greedy best-first search, and A* search. It also covers general problem solving techniques and evaluating search performance based on completeness, time complexity, space complexity, and optimality.
A brief introduction to Process synchronization in Operating Systems with classical examples and solutions using semaphores. A good starting tutorial for beginners.
Genetic Algorithm in Artificial IntelligenceSinbad Konick
Genetic algorithms are a heuristic search technique inspired by biological evolution to find optimized solutions to problems. The workflow involves initially generating a random population which is then evaluated based on a fitness function. Individuals are selected from the population based on their fitness for reproduction, with crossover and mutation occurring to create a new generation. This process is repeated until an optimal solution is found. Genetic algorithms have applications in fields like robotics, medicine, and computer gaming. They provide advantages like not requiring derivatives and being able to optimize both continuous and discrete functions, but also have limitations such as computational expense and not guaranteeing optimal solutions.
A process needs to be in the memory to be executed.
A process can be swapped temporarily out of memory to a backing store, and then brought back into memory for continued execution
Total physical memory space of processes can exceed physical memory
Backing store – fast disk large enough to accommodate copies of all memory images for all users; must provide direct access to these memory images
Abstract: This PDSG workship introduces basic concepts on using Hill Climbing for Local Search. Concepts covered are global and local maximum, shoulder/flat, value functions, local beam search, and stochastic variant.
Level: Fundamental
Requirements: Should have prior familiarity with Graph Search. No prior programming knowledge is required.
This document provides an overview of quantum computing and common algorithms used on different types of quantum computers. It discusses how quantum computers work using qubits or qumodes and the existing gate-based and quantum annealing-based architectures. Some examples of algorithms that could run on these quantum computers are presented, including for supervised and unsupervised machine learning tasks as well as graph and network analysis problems. Researchers can access existing quantum computers through the cloud or simulate circuits classically.
This document discusses several search strategies including uninformed search, breadth-first search, depth-first search, uniform cost search, iterative deepening search, and bi-directional search. It provides algorithms and examples to explain how each strategy works. Key points include: breadth-first search visits nodes by level of depth; depth-first search generates nodes along the largest depth first before moving up; uniform cost search expands the lowest cost node; and iterative deepening search avoids infinite depth by searching each level iteratively and increasing the depth limit.
Quantum information as the information of infinite series Vasil Penchev
Quantum information is equivalent to that generalization of the classical information from finite to infinite series or collections
The quantity of information is the quantity of choices measured in the units of elementary choice
The qubit is that generalization of bit, which is a choice among a continuum of alternatives
The axiom of choice is necessary for quantum information: The coherent state is transformed into a well-ordered series of results in time after measurement
The quantity of quantum information is the ordinal corresponding to the infinity series in question
Quantum Computer: Quantum Model and RealityVasil Penchev
1. The document discusses several philosophical questions about interpreting quantum computers and quantum mechanics. It argues that unlike classical models, a quantum model can coincide with reality.
2. Reality can be interpreted as a quantum computer, and physical processes can be understood as computations of a quantum computer. Quantum information is proposed as the fundamental basis of the world.
3. The conception of a quantum computer is said to unify physics and mathematics by allowing models and reality to coincide. A quantum computer is also described as a non-Turing machine that can perform infinite computations in a finite time.
quantum computing basics roll no 15.pptxtoget48099
The document discusses quantum computing, providing an overview of classical computers and their evolution. It then introduces quantum computers, explaining key concepts like quantum superposition, entanglement, and teleportation. Quantum computers could solve problems like factorization exponentially faster than classical computers. While promising for applications like encryption, simulation, and optimization, quantum computing faces challenges like difficulty controlling qubits and requiring isolated environments. The document envisions future work developing silicon-based quantum computers, new algorithms, and using quantum computers to simulate other quantum systems.
Quantum Information as the Substance of the WorldVasil Penchev
The concept of matter in physics can be considered as a generalized form of information, that of quantum information involved by quantum mechanics
Even more, quantum information is a generalization of classical information: So, information either classical or quantum is the universal foundation of all in the world
In particular, the ideal or abstract objects also share information (the classical one) in their common base
Matter as Information. Quantum Information as MatterVasil Penchev
This document discusses interpreting matter and mass in physics as a form of quantum information. It argues that the concept of mass can be seen as a quantity of quantum information, with energy and matter interpreted as amounts of quantum information involved in infinite collections. Seeing mass and energy as quantum information helps unify the concepts of concrete and abstract objects by generalizing information from finite to infinite sets. This allows information to be viewed as a universal substance that subsumes the notions of mass and energy.
This research paper gives an overview of quantum computers – description of their operation, differences between quantum and silicon computers, major construction problems of a quantum computer and many other basic aspects. No special scientific knowledge is necessary for the reader.
This document provides an overview of quantum computing, including its history, key concepts, differences from classical computing, applications, advantages, and challenges. Quantum computing uses quantum bits that can exist in superposition and entanglement, allowing massive parallelism. Some potential applications include factoring, simulation, optimization, and secure communication. However, challenges include difficulty controlling quantum states and building reliable quantum hardware. Future work may focus on developing silicon-based designs and new algorithms to better exploit quantum computing.
A Technical Seminar on Quantum Computers By SAIKIRAN PANJALASaikiran Panjala
A quantum computer harnesses the power of atoms and molecules to perform calculations exponentially faster than classical computers by exploiting quantum mechanical phenomena like superposition and entanglement. While theoretical quantum algorithms could solve problems like integer factorization that are intractable on classical computers, building a large-scale, practical quantum computer remains a significant technological challenge due to issues like qubit coherence. Researchers are working towards developing quantum computers using technologies like superconductors, trapped ions, and optical lattices.
Both classical and quantum information [autosaved]Vasil Penchev
Information can be considered a the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information. particularly by their units, bit and qubit, correspond and unify the finite and infinite:
As classical information is relevant to finite series and sets, as quantum information, to infinite ones. The separable complex Hilbert space of quantum mechanics can be represented equivalently as “qubit space”) as quantum information and doubled dually or “complimentary” by Hilbert arithmetic (classical information).
Pulse Compression Sequence (PCS) are widely used in radar to increase the range resolution. Binary sequence has the limitation that the compression ratio is small. Ternary code is suggested as an alternative. The design of ternary sequence with good Discriminating Factor (DF) and merit factor can be considered as a nonlinear multivariable optimization problem which is difficult to solve. In this paper, we proposed a new method for designing ternary sequence by using Modified Simulated Annealing Algorithm (MSAA). The general features such as global convergence and robustness of the statistical algorithm are revealed.
Quantum computers is a machine that performs calculations based on the laws of quantum mechanics which is the behaviour of particles at the subatomic level.
This document summarizes the key differences between classical and quantum computing. Classical computing uses binary bits that are either 1 or 0, while quantum computing uses quantum bits (qubits) that can be 1, 0, or both at the same time due to quantum superposition. The document explains how qubits are based on properties of electrons and their spin, and how quantum gates manipulate qubit states. It discusses how quantum entanglement allows qubits to influence each other in a way that could solve complex problems more efficiently than classical computing. However, the document notes that quantum computing is still in development and some dispute claims about its current capabilities.
Quantum computing uses quantum bits (qubits) that can exist in superpositions of states rather than just 1s and 0s. This allows quantum computers to perform exponentially more calculations in parallel than classical computers. Some of the main challenges to building quantum computers are preventing qubit decoherence from environmental interference, developing effective error correction methods, and observing outputs without corrupting data. Quantum computers may one day be able to break current encryption methods and solve optimization problems much faster than classical computers.
Quantum computing is a rapidly emerging technology that uses principles of quantum mechanics like superposition and entanglement to perform operations on quantum bits (qubits) and solve complex problems. It has the potential to vastly outperform classical computers for certain problems. The document discusses key aspects of quantum computing including how it differs from classical computing, what qubits are, how quantum computers work using elements like superconductors and Josephson junctions, and potential applications in areas like artificial intelligence, drug development, weather forecasting, and cybersecurity. It also covers advantages like speed and ability to solve complex problems, as well as current disadvantages like difficulty to build and susceptibility to errors.
Quantum computing provides an alternative computational model based on quantum mechanics. It utilizes quantum phenomena such as superposition and entanglement to perform computations using quantum logic gates on qubits. This allows quantum computers to potentially solve certain problems exponentially faster than classical computers. However, building large-scale quantum computers remains a challenge. In the meantime, smaller quantum systems are being developed and quantum algorithms are being experimentally tested on these devices. Researchers are also working on methods to efficiently simulate quantum computations on classical computers.
Quantum computers are still theoretical but could perform certain calculations much faster than classical computers. They use quantum bits that can exist in superposition and entanglement, allowing them to represent multiple states simultaneously. Current quantum computers have only manipulated a few qubits, but applications could include factoring large numbers and rapidly searching large databases. Significant challenges remain in developing practical quantum computers that can maintain quantum states long enough to perform useful computations.
This presentation is about quantum computing.which going to be new technological concept for computer operating system.In this subject the research is going on.
Quantum computers are incredibly powerful machines that take a new approach to processing information. Built on the principles of quantum mechanics, they exploit complex and fascinating laws of nature that are always there, but usually remain hidden from view. By harnessing such natural behavior, quantum computing can run new types of algorithms to process information more holistically. They may one day lead to revolutionary breakthroughs in materials and drug discovery, the optimization of complex manmade systems, and artificial intelligence. We expect them to open doors that we once thought would remain locked indefinitely. Acquaint yourself with the strange and exciting world of quantum computing.
1. The document discusses entanglement generation and state transfer in a Heisenberg spin-1/2 chain under an external magnetic field.
2. It analyzes the fidelity and concurrence of the system over time and temperature using the density matrix and Hamiltonian equations for a 2-qubit system.
3. The results show that maximally entangled states are difficult to achieve but desirable for quantum computation applications like quantum teleportation.
Similar to Quantum Computer on a Turing Machine (20)
The generalization of the Periodic table. The "Periodic table" of "dark matter"Vasil Penchev
The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum systems. In other words, an atom of any chemical element and as a quantum system, i.e. as a wave function, should be represented as a non-orthogonal in general (i.e. entangled) subspace of the separable complex Hilbert space relevant to the system to which the atom at issue is related as a true part of it. The paper follows previous publications of mine stating that “dark matter” and “dark energy” are projections of arbitrarily entangled states on the cognitive “screen” of Einstein’s “Mach’s principle” in general relativity postulating that gravitational field can be generated only by mass or energy.
Modal History versus Counterfactual History: History as IntentionVasil Penchev
The distinction of whether real or counterfactual history makes sense only post factum. However, modal history is to be defined only as ones’ intention and thus, ex-ante. Modal history is probable history, and its probability is subjective. One needs phenomenological “epoché” in relation to its reality (respectively, counterfactuality). Thus, modal history describes historical “phenomena” in Husserl’s sense and would need a specific application of phenomenological reduction, which can be called historical reduction. Modal history doubles history just as the recorded history of historiography does it. That doubling is a necessary condition of historical objectivity including one’s subjectivity: whether actors’, ex-anteor historians’ post factum. The objectivity doubled by ones’ subjectivity constitute “hermeneutical circle”.
A CLASS OF EXEMPLES DEMONSTRATING THAT “푃푃≠푁푁푁 ” IN THE “P VS NP” PROBLEMVasil Penchev
The CMI Millennium “P vs NP Problem” can be resolved e.g. if one shows at least one counterexample to the “P=NP” conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the hypothesis “P=NP” for any conditions satisfying the formulation of the problem. Thus, the solution “P≠NP” of the problem in general is proved. The class of counterexamples can be interpreted as any quantum superposition of any finite set of quantum states. The Kochen-Specker theorem is involved. Any fundamentally random choice among a finite set of alternatives belong to “NP’ but not to “P”. The conjecture that the set complement of “P” to “NP” can be described by that kind of choice exhaustively is formulated.
FERMAT’S LAST THEOREM PROVED BY INDUCTION (accompanied by a philosophical com...Vasil Penchev
A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n=3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. The infinite descent is linked to induction starting from n=3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n=4, one can suggest that the proof for n≥4 was accessible to him.
An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995), and would justify Fermat’s claim (1637) for its proof. The inspiration for a simple proof would contradict to Descartes’s dualism for appealing to merge “mind” and “body”, “words” and “things”, “terms” and “propositions”, all orders of logic. A counterfactual course of history of mathematics and philosophy may be admitted. The bifurcation happened in Descartes and Fermat’s age. FLT is exceptionally difficult to be proved in our real branch rather than in the counterfactual one.
The space-time interpretation of Poincare’s conjecture proved by G. Perelman Vasil Penchev
This document discusses the generalization of Poincaré's conjecture to higher dimensions and its interpretation in terms of special relativity. It proposes that Poincaré's conjecture can be generalized to state that any 4-dimensional ball is topologically equivalent to 3D Euclidean space. This generalization has a physical interpretation in which our 3D space can be viewed as a "4-ball" closed in a fourth dimension. The document also outlines ideas for how one might prove this generalization by "unfolding" the problem into topological equivalences between Euclidean spaces.
FROM THE PRINCIPLE OF LEAST ACTION TO THE CONSERVATION OF QUANTUM INFORMATION...Vasil Penchev
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to
the quantum leaps as if accomplished in all possible trajectories (according to Feynman’s interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change.The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the ge eralization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem). The problem: If any quantum change is accomplished in al possible “variations (i.e. “violations) of energy conservation” (by different probabilities),
what (if any) is conserved? An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.
From the principle of least action to the conservation of quantum information...Vasil Penchev
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918):any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (e.g. according to Feynman’s viewpoint) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change.
The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem).
The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations) of energy conservation” (by different probabilities), what (if any) is conserved?
An answer: quantum information is what is conserved. Indeed it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. (An illustration: if observers in arbitrarily accelerated reference frames exchange light signals about the course of a single chemical reaction observed by all of them, the universal viewpoint shareаble by all is that of quantum information).
That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements necessary conserving quantum information rather than energy: thus it can be called “alchemical periodic table”.
Poincaré’s conjecture proved by G. Perelman by the isomorphism of Minkowski s...Vasil Penchev
- The document discusses the relationship between separable complex Hilbert spaces (H) and sets of ordinals (H) and how they should not be equated if natural numbers are identified as finite.
- It presents two interpretations of H: as vectors in n-dimensional complex space or as squarely integrable functions, and discusses how the latter adds unitarity from energy conservation.
- It argues that Η rather than H should be used when not involving energy conservation, and discusses how the relation between H and HH generates spheres representing areas and can be interpreted physically in terms of energy and force.
Why anything rather than nothing? The answer of quantum mechnaicsVasil Penchev
Many researchers determine the question “Why anything
rather than nothing?” to be the most ancient and fundamental philosophical problem. It is closely related to the idea of Creation shared by religion, science, and philosophy, for example in the shape of the “Big Bang”, the doctrine of first cause or causa sui, the Creation in six days in the Bible, etc. Thus, the solution of quantum mechanics, being scientific in essence, can also be interpreted philosophically, and even religiously. This paper will only discuss the philosophical interpretation. The essence of the answer of quantum mechanics is: 1.) Creation is necessary in a rigorously mathematical sense. Thus, it does not need any hoice, free will, subject, God, etc. to appear. The world exists by virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4; and 2.) Being is less than nothing rather than ore than nothing. Thus creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation to nothing. Time and its “arrow” form the road from that diminishment or incompleteness to nothing.
The Square of Opposition & The Concept of Infinity: The shared information s...Vasil Penchev
The power of the square of opposition has been proved during millennia, It supplies logic by the ontological language of infinity for describing anything...
6th WORLD CONGRESS ON THE SQUARE OF OPPOSITION
http://www.square-of-opposition.org/square2018.html
Mamardashvili, an Observer of the Totality. About “Symbol and Consciousness”,...Vasil Penchev
The paper discusses a few tensions “crucifying” the works and even personality of the great Georgian philosopher Merab Mamardashvili: East and West; human being and thought, symbol and consciousness, infinity and finiteness, similarity and differences. The observer can be involved as the correlative counterpart of the totality: An observer opposed to the totality externalizes an internal part outside. Thus the phenomena of an observer and the totality turn out to converge to each other or to be one and the same. In other words, the phenomenon of an observer includes the singularity of the solipsistic Self, which (or “who”) is the same as that of the totality. Furthermore, observation can be thought as that primary and initial action underlain by the phenomenon of an observer. That action of observation consists in the externalization of the solipsistic Self outside as some external reality. It is both a zero action and the singularity of the phenomenon of action. The main conclusions are: Mamardashvili’s philosophy can be thought both as the suffering effort to be a human being again and again as well as the philosophical reflection on the genesis of thought from itself by the same effort. Thus it can be recognized as a powerful tension between signs anа symbol, between conscious structures and consciousness, between the syncretism of the East and the discursiveness of the West crucifying spiritually Georgia
Completeness: From henkin's Proposition to Quantum ComputerVasil Penchev
This document discusses how Leon Henkin's proposition relates to concepts in logic, set theory, information theory, and quantum mechanics. It argues that Henkin's proposition, which states the provability of a statement within a formal system, is equivalent to an internal and consistent position regarding infinity. The document then explores how this connects to Martin Lob's theorem, the Einstein-Podolsky-Rosen paradox in quantum mechanics, theorems about the absence of hidden variables, entanglement, quantum information, and ultimately quantum computers.
Why anything rather than nothing? The answer of quantum mechanicsVasil Penchev
This document discusses the philosophical question of why there is something rather than nothing from the perspective of quantum mechanics. It argues that quantum mechanics provides a solution where creation is permanent and due to the irreversibility of time. The creation in quantum mechanics represents a necessary loss of information as alternatives are rejected in the course of time, rather than being due to some external cause like God's will. This permanent creation process makes the universe mathematically necessary rather than requiring an initial singular event like the Big Bang.
The outlined approach allows a common philosophical viewpoint to the physical world, language and some mathematical structures therefore calling for the universe to be understood as a joint physical, linguistic and mathematical universum, in which physical motion and metaphor are one and the same rather than only similar in a sense.
Hilbert Space and pseudo-Riemannian Space: The Common Base of Quantum Informa...Vasil Penchev
Hilbert space underlying quantum mechanics and pseudo-Riemannian space underlying general relativity share a common base of quantum information. Hilbert space can be interpreted as the free variable of quantum information, and any point in it, being equivalent to a wave function (and thus, to a state of a quantum system), as a value of that variable of quantum information. In turn, pseudo-Riemannian space can be interpreted as the interaction of two or more quantities of quantum information and thus, as two or more entangled quantum systems. Consequently, one can distinguish local physical interactions describable by a single Hilbert space (or by any factorizable tensor product of such ones) and non-local physical interactions describable only by means by that Hilbert space, which cannot be factorized as any tensor product of the Hilbert spaces, by means of which one can describe the interacting quantum subsystems separately. Any interaction, which can be exhaustedly described in a single Hilbert space, such as the weak, strong, and electromagnetic one, is local in terms of quantum information. Any interaction, which cannot be described thus, is nonlocal in terms of quantum information. Any interaction, which is exhaustedly describable by pseudo-Riemannian space, such as gravity, is nonlocal in this sense. Consequently all known physical interaction can be described by a single geometrical base interpreting it in terms of quantum information.
This document discusses using Richard Feynman's interpretation of quantum mechanics as a way to formally summarize different explanations of quantum mechanics given to hypothetical children. It proposes that each child's understanding could be seen as one "pathway" or explanation, with the total set of explanations forming a distribution. The document then suggests that quantum mechanics itself could provide a meta-explanation that encompasses all the children's perspectives by describing phenomena probabilistically rather than deterministically. Finally, it gives some examples of how this approach could allow defining and experimentally studying the concept of God through quantum mechanics.
This document discusses whether artificial intelligence can have a soul from both scientific and religious perspectives. It begins by acknowledging that "soul" is a religious concept while AI is a scientific one. The document then examines how Christianity views creativity as a criterion for having a soul. It proposes formal scientific definitions of creativity involving learning rates and probabilities. An example is given comparing a master's creativity to an apprentice's. The document argues science can describe God's infinite creativity and human's finite creativity uniformly. It analyzes whether criteria for creativity can apply to AI like a Turing machine. Hypothetical examples involving infinite algorithms and self-learning machines are discussed.
Analogia entis as analogy universalized and formalized rigorously and mathema...Vasil Penchev
THE SECOND WORLD CONGRESS ON ANALOGY, POZNAŃ, MAY 24-26, 2017
(The Venue: Sala Lubrańskiego (Lubrański’s Hall at the Collegium Minus), Adam Mickiewicz University, Address: ul. Wieniawskiego 1) The presentation: 24 May, 15:30
Ontology as a formal one. The language of ontology as the ontology itself: th...Vasil Penchev
“Formal ontology” is introduced first to programing languages in different ways. The most relevant one as to philosophy is as a generalization of “nth-order logic” and “nth-level language” for n=0. Then, the “zero-level language” is a theoretical reflection on the naïve attitude to the world: the “things and words” coincide by themselves. That approach corresponds directly to the philosophical phenomenology of Husserl or fundamental ontology of Heidegger. Ontology as the 0-level language may be researched as a formal ontology
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
3. Quantum computer: mathematical
model or technical realization?
The term of “quantum computer” means both:
1. A mathematical model like a Turing machine,
which is the general model of any usual
computer we use, and:
2. Any concrete technical realization involving
the laws of quantum mechanics to implement
computations
4. Mathematical models: quantum
computer and Turing machine
• Only the mathematical model is meant here and
in comparison with that of a standard computer,
namely a Turing machine (Turing 1937)
• That mathematical model raises a series of
philosophical questions about model and
quantum model, quantum model and reality,
infinity and even actual infinity as a physical
entity, computational and physical process,
information and quantum information,
information and its carrier, etc.
5. Quantum Turing Machine
• The quantum Turing machine (Deutsch 1985)
is an abstract model computationally
equivalent (Yao 1993) to the quantum circuit
(Deutsch 1989) and can represent all features
of quantum computer without entanglement
• Deitsch (1985) did not use the notion of
‘qubit’ to define ‘quantum Turing machine’
6. Quantum computer in terms of
‘Turing machine’
• Another way to generalize the Turing machine to
the quantum computer is by replacing all bits or
cells of a Turing tape with “quantum bits” or
“qubits”
• Then all admissible operations on a cell of the
quantum tape are generalized to those two:
“write/ read a value of a qubit” just as “write/ read
a value of a bit” on the tape of a classical Turing
machine
• There are not other generalizations from a Turing
machine to a quantum one in that model: All the
rest is the same
7. A “classical” Turing machine
A quantum Turing machine
1 ... n n+1 ...
The
last
cell
A classical Turing
tape of bits:
A quantum Turing
tape of qubits:
1 ... n n+1 ...
The
/No
last
cell
The list of all
operations on a cell:
1. Write!
2. Read!
3. Next!
4. Stop!
8. A possible objection about reversibility
• All quantum computations are reversible
unlike the classical ones
• However the input/ output of a value in a
qubit is irreversible
• Thus a quantum Turing machine is not
reversible just as a classical one
• Quantum reversibility is “bracketed” and
“hidden” by the non-constructiveness of the
choice of a value for the axiom of choice
9. For what can and for what cannot
that model serve?
That model is intended:
- For elucidating the most general mathematical
and philosophical properties of quantum computer
or computation
- For their comparison with those of a classical
computer or computation
That model cannot serve to design any technical
realization of quantum computer just as the true
machine of Turing cannot as to a standard
computer
14. Bit vs. qubit
• Then if any bit is an elementary binary choice
between two disjunctive options usually
designated by “0” and “1”, any qubit is a choice
between a continuum of disjunctive options as
many as the points of the surface of the unit ball:
• Thus the concept of choice is the core of
computation and information. It is what can unify
the classical and quantum case, and the
demarcation between them is the bound between
a finite vs. infinite number of the alternatives of
the corresponding choice
15. 0
1
0
1
One bit (a finite choice)
One qubit (an infinite choice)
Choice Well-ordering
16. Qubit & the axiom of choice
• That visualization allows of highlighting the
fundamental difference between the Turing
machine and quantum computer: the choice
of an element of an uncountable set
necessarily requiring the axiom of choice
• The axiom of choice being non-constructive is
the relevant reference frame to the concept of
quantum algorithm to involve a constructive
process of solving or computation having an
infinite and even uncountable number of
steps
17. Choice and information
• The concept of information can be interpreted as
the quantity of the number of primary choices
• Furthermore the Turing machine either classical
or quantum as a model links computation to
information directly:
• The quantity of information can be thought as the
sum of the change bit by bit or qubit by qubit, i.e.
as the change of number written by two or
infinitely many digits
• Thus: a cell of a (quantum) Turing tape =
a choice of (quantum) information = a “digit”
18. Much Many
Information A choice
Finite
(binary)
Infinite
A cell Values
0
1
...
... ...
Turing tapes = well orderings:
19. Algorithm and information
• Furthermore the fundamental concept of
choice connects the algorithm to the
information:
• Any algorithm either classical or quantum is a
well-ordered series of choices:
• The quantity of information either classical or
quantum is the quantity of those choices in
units of primary choices: either bits or qubits
• In general the quantity of information does
not require the set of choices to be well-
ordered
20. Information and quantum information
• The generalization from information to
quantum information can be interpreted as
the corresponding generalization of ‘choice’:
from the choice between two (or any finite
number of) disjunctive alternatives to
infinitely many alternatives
• Thus the distinction between the classical and
quantum case can be limited within any cell of
an algorithm or (qu)bit of information
21. Quantum algorithm and quantum
information
• Obviously the concept of quantum algorithm
should involve infinity unlike the classical one
• Furthermore that infinity should be actual since
quantum algorithm can process an infinite
number of alternatives per a finite period of time
unlike a classical one needing an infinite time for
that aim
• Nevertheless the quantity of quantum
information in a quantum algorithm can have a
finite value being measured in qubits, i.e. in
“units of infinity” (figuratively said)
22. Turing machine and information
• The Turing machine as a general model of
calculation postulates the processing of
information bit by bit serially
• The processing is restricted to a few, exactly
defined operations stereotyped on any cell
(bit)
• Thus the Turing machine is designed to
represent any algorithm as the serial
processing of the primary units of
information: Information underlies algorithm
by that model
23. Quantum Turing machine and
quantum information
• The quantum Turing machine processes
quantum information correspondingly qubit
by qubit serially but in parallel within any
qubit, and the axiom of choice formalizes that
parallel processing as the choice of the result
• Even the operations on a qubit can be the
same as on a bit. The only difference is for
“write/ read”: to be a value of either a binary
(finite) or an infinite set
24. Information and information carrier
What is the relation between information and
its carrier, e.g. between an empty cell of the
tape and the written on it?
The classical notion of information or algorithm
separates them disjunctively from their
corresponding carriers.
The Turing machine model represents that
distinction by an empty cell, on the one
hand, and the set of values, which can be
written on it, or a given written value, on the
other hand
25. The “material” The “ideal”
The carrier of
information
The information
as a given and
conventional form
of that carrier
0
1
An empty cell
26. The classical disjunction of
information from information carrier
The classical concept of information divides
unconditionally information from its carrier and
excludes information without some energetic or
material carrier:
Information obeys the carrier: no information
without its carrier: Information needs something
with nonzero energy, on which is written or from
which is read. Otherwise it cannot exist
OK, but all this refers to the classical
information, not to the quantum one. One can call
the latter emancipated information
27. The classical disjunction of potential
and actual choice
• Furthermore it separates disjunctively the option
of choice (the set of possible values) from the
chosen alternative of choice (e.g. either “0” or
“1”) and thus the possible or potential from
the real or actual
• The act of choice is the demarcation between
“virtuality” and reality. That act is irreversible.
Thus it creates a well-ordering of successive
choices just because of irreveresibility
29. The coincidence of quantum information
and quantum-information carrier
All those classical demarcations are removed in
quantum information:
It coincides with its carrier
Potential and actual choice merge
The empty cells and the written on them are
interchangeable (as a basis and as a vector in an
orthonormal vector space like Hilbert space)
However all this contradicts our prejudices
borrowed from “common sense”: so much the
worse for the prejudices ...
30. The quantum case The classical case
The particle “carries”
the information of all its
properties and quantities:
That is: the set of them
is ‘particle’ or the ‘carrier
of information’
Space
Time A trajectory
‘Particle’= ‘Carrier’
The ‘particle’ is split into
two complementary sets
of properties, each of
which can be as if the
carrier of the other. Their
interchange is identical
...
...
...
...
Energy-
momentum
Position
33. Quantity in quantum mechanics and quan-
tum computation: a process and a result
• Thus any quantity in quantum mechanics can be
interpreted as a quantity of quantum information
and as quantum computation, and its value as the
result of that computation
• Indeed (in more detail, see Slide 10), any point in
Hilbert space (= a wave function) is equivalent to a
quantum Turing state, and the selfadjoint operator
is what conserves the sequence of qubits changing
their values. Thus the action of a selfadjoint
operator is equivalent to the change of the
quantum Turing state, i.e. to a quantum
computation
34. The “tape” of a quantum Turing machine
• As an illustration, the tape of quantum Turing
machine coincides with the written on it: Any
quantum Turing machine calculating should create
itself in a sense
• More exactly, if one transforms one qubit dually
(i.e. one empty cell from the basis and its value
interchange their positions), it will coincide with
the initial one: Any quantum Turing cell and the
written on it are one and the same in this sense of
invariance to interchange
35. Two dual, complementary qubits
Each one can be considered as the “carrier” of the
other: The “carrier” and information are identical
36. The concept of quantum invariance
• The term of “quantum invariance” can be coined
to outline the important role assigned to the
axiom of choice in the theory of quantum
computer and inherited from quantum
mechanics:
• Quantum invariance means the following principle
as to quantum computation:
The result chosen by the axiom of choice is the
same as the result of the corresponding quantum
algorithm. Or: the non-constructive choice and
the quantum-constructive choice coincide and can
be accepted as one and same
37. The justification of quantum invariance
That principle of quantum invariance is quite not
obvious and even contradicts “common sense”: It can
obtain relevant foundation from quantum mechanics
and quantum measurement:
Quantum measure underlies quantum measurement:
It is a fundamentally new kind of measure, which
transfers Skolem’s “relativity of ‘set’” (1922 *1970+)
into the theory of measure as that measure, to which
a “much” and a “many” are relative and can share it
and thus measured jointly
The justification of quantum invariance is as follows:
38. Quantum measurement and well-
ordering
• The theorems about the absence of hidden
variables in quantum mechanics (Neumann
1932; Kochen, Specker 1968) exclude any well-
ordering before measurement
• However the results of the measurements are
always well-ordered and thus any quantum
model implies the well-ordering theorem
equivalent to the axiom of choice
39. Quantum reality vs. orderablity
• Furthermore quantum reality according to the
cited theorems is not well-orderable in principle
• So if one measures the unorderable quantum
reality, one needs quantum measure to be able
to unify the measured and the results of
measurement:
• Quantum reality is always a “much” versus the
“many” of the measured results: Quantum
measure is only what can unify them and
underlies quantum invariance about all
measurable by it
40. Quantum model vs. quantum reality:
the axiom of choice
• Thus the relation between quantum model
and quantum reality requires correspondingly
the axiom of choice and its absence, or the
coined quantum invariance, to designate that
extraordinary relation between model and
reality specific to quantum mechanics and
trough it, to the theory of quantum computer:
• Quantum computation coincides with physical
process and thus with reality
41. Quantum invariance and Skolem’s
“paradox”
• That quantum invariance is well known in
mathematics in the form of Skolem’s paradox
(Skolem 1922 [1970]: ), who has introduced the
notion of “relativity” as to set theory discussing
infinity
• He even spoke that the notions of finite and infinite
set are relative and interchangeable (ibid.: [143-
144]) and the so-called “paradox” of Skolem can
comprise finite sets, too. Thus he is the immediate
predecessor of the concept of quantum measure
42. Quantum invariance: quantum
computer on a Turing machine
• Quantum invariance as to quantum computer can
be exhaustedly described by the mapping of
quantum computer on a Turing machine having an
infinite tape in general
• That mapping is always possible to be one-to-one
just because of the axiom of choice
• Quantum invariance means for that mapping to be
one-to-one
• Furthermore the unit of quantum measure can be
defined as that “one-to-one” of two heterogeneous
quantities like a “much” and a “many”
44. A single qubit by a Turing machine
• Any qubit of it being a choice of one between
a continuum of disjunctive options can be
replaced by a Turing machine (possibly with a
tape consisting of infinitely many cells)
utilizing the axiom of choice for replacing
• However the qubit itself as the unit of
quantum measure can be considered as any
one-to-one mapping of anything into a bit of
information
• Thus quantum information can mean the
equivalent mapping of anything into classical
information
45. Quantum computation: infinite but
convergent
• Given all that, any quantum computational
process can by defined in terms of a standard
one on a Turing machine as infinite but
convergent
• Consequently ‘quantum computer’ is that
extension of ‘Turing machine’, which
comprises infinite computational
processes, which are only infinite “loops” for a
Turing machine without any result
46. The result of quantum computation
The limit, to which it converges, is the result of
this quantum computation
That definition raises two questions:
• Does any series representing a quantum
computation converge and thus: Is the
existence of a limit point always guaranteed?
• Is that generalization of computation to
comprise infinite ones is only possible? Or in
other words: Is quantum and infinite
computation one and the same and does they
map to each other one-to-one?
47. Quantum computation and actual infinity
Quantum computation involves the notion of actual
infinity since the computational series is both
infinite and considered as a completed whole by
dint of its limit
Furthermore quantum computation unifies both
definitions of ‘function”:
• That as a constructive and thus computational
process
• That as a mapping of a set into another under
condition of a single image in the latter
That unifying cannot be obtained without involving
actual infinity
48. Quantum algorithm & quantum result
• As the model of a Turing machine unifies the
utilized algorithm with the result obtained by
it, quantum computer can be interpreted both as
a convergently advanced algorithm and a
convergently improved result for the former
• Quantum computer extends that equivalence of
algorithm and calculation to the
interchangeability of an “atom” of data (a qubit)
and the “atomic” operations on it:
• This is due to the interchangeability of quantum
information and its carrier as well as that of
computational and physical process
49. The coincidence of reality and
quantum computation
• If its objectivity is to model a concrete reality by
the computed ultimate result, it coincides with
reality unlike any standard Turing machine which
has to be finite and thus there is always a finite
difference between the computed reality and any
completed result of a Turing computation
• Quantum epistemology should be defined as
studying the discrete or computational hypostasis
of reality rather than the relation of cognition and
reality after cognition and reality have coincide
50. The coincidence of quantum model
and reality
• One can state that quantum computer
calculates reality or that quantum model and
reality coincide
• All classical epistemology assumes that there
is an irremovable essential difference between
any model and reality: No model can coincide
with reality and epistemology is that science,
which studies that difference. Consequently
that mismatch is the subject of classical
epistemology enabling it
51. The most general case of infinitely
many limit points
The offered model of quantum computer on a Turing
machine as a convergent and infinite process
comprises the more general case where that infinite
process does not converge and even has infinitely
many limit points
This is due to quantum invariance, which allows of two
equivalent “hypostases” of quantum computation:
The one is expanded, without the axiom of choice
being unorderable in principle
The other is compacted, well-ordered by the axiom
of choice and thus converging
52. The axiom of choice and the limit points
One can use the granted above axiom of choice to
order the limit points even being infinitely many as
a monotonic series, which necessarily converges if
it is a subset of any finite interval, and to accept
this last limit as the ultimate result of the quantum
computer
Consequently quantum invariance underlain by all
quantum mechanics is what guarantees that any
quantum computation has a single result, and thus
it unlike a Turing machines in general is complete
53. The physical and philosophical meaning
of Hilbert space by the axiom of choice
• The axiom of choice can be used in another
way to give the same result thus elucidating
the physical and even philosophical meaning
of Hilbert space, the basic mathematical
structure of quantum mechanics:
• Hilbert space is that common space where all
measured by quantum measure can be in one
place together co-existing: It allows of any
unorderable quantum “much” and its image
of a “many” to be seen as one and the same
54. Qubit as a limit point of a Turing machine
Any qubit represents equivalently a limit point
of the “tape” of the Turing machine, on which
the quantum computer is modeled
That qubit or that limit point can be expanded
into a series of qubits (i.e. a subspace of Hilbert
space) or to a series, which converges to this
limit point
The axiom of choice implies that “reverse
action” as above: Indeed, given the set of all
series converging to a limit point, it enables a
series to be chosen from it
55. The “axes” of Hilbert space as qubits
If those limit points are even infinitely many, they
can be represented equivalently by a point in
Hilbert space where any “axis” of it corresponds
one-to-one to a qubit ant thus to a limit point of the
quantum computational process (see Slide 10)
So any limit point corresponds one-to-one to a
subspace of Hilbert space, and any that one can be
compacted into a single qubit by the axiom of
choice. The same compacting as to a series means
to be chosen its limit point to represent all series
56. ... ... ... ...
Limit point m
Qubit m
Limit point n
Qubit n
Limit point p
Qubit p
A series with infinitely many limit points
... ... ......
The ultimate result of any quantum
computation exists always!
57. Wave function as quantum
computation
• Then obviously any change of the state of any
quantum system being a wave function and a
point in Hilbert space can be interpreted as a
quantum calculative process, and the physical
world as a whole as an immense quantum
computer
• The concept of computation and physical
reality converge to each other at the point
visible from quantum mechanics
58. The axiom of choice on a bounded
set of limit points
Using the axiom of choice, one can always reorder
monotonically a bounded set of limit points to
converge or represent a point in Hilbert space as a
single qubit by the Banach-Tarski paradox (Banach,
Tarski 1924):
Both are only different images of one and the same
quantum computation:
The one is compacted into a qubit or reordered as a
converging series
The other is expanded as Hilbert space (a converging
vector in it) or as an arbitrary series non-converging,
non-reordered, but reorderable in principle
59. Quantum vs. standard computer
• The model of quantum computer on a Turing
machine allows of clarifying the sense and
meaning of a quantum computation in terms
of a usual computer equivalent to some finite
Turing machine:
• It generalizes the notion from finite to infinite
and even to actual infinite computation.
Furthermore it allows of comparing between a
standard and a quantum computer on the
distinction of the finite/ infinite
60. Quantum vs. standard computer:
tendency & image vs. result as a value
• While the standard computer gives a result,
the quantum computer offers a tendency
comprising a potentially infinite sequence of
converging algorithms and results as well as
the limit of this tendency both as an ultimate
algorithm-result coinciding with reality and as
an image (“Gestalt”) of the tendency as a
completed whole
• Thus quantum computation generalizes the
finite calculation in a way close to human
understanding and interpretation
61. Quantum computer and human
understanding and interpretation
• The transition from the result of a usual
computer to the ultimate result of a quantum
computer is a leap comparable with human
understanding and interpretation to restore the
true reality on the base of a finite set of sensual
or experimental data
• One can rise the question whether that
comparison is only a metaphor or it reveals a
deeper link between quantum computation and
the human understanding and interpretation of
reality
63. References:
Banach, Stefan, Alfred Tarski 1924. “Sur la decomposition des ensembles de points en
parties respectivement congruentes.” Fundamenta Mathematicae. 6, (1): 244-277.
Deutsch, David 1985. “Quantum theory, the Church-Turing principle and the universal
quantum computer,” Proceedings of the Royal Society of London A. 400: 97-117.
Deutsch, David 1989. “Quantum computational networks,” Proceedings of the Royal
Society of London. Volume A 425 73-90
Kochen, Simon and Ernst Specker 1968. “The problem of hidden variables in quantum
mechanics,” Journal of Mathematics and Mechanics. 17 (1): 59-87.
Neumann, Johan von 1932. Mathematische Grundlagen der Quantenmechanik, Berlin:
Verlag von Julius Springer.
Skolem, Thoralf 1922. “Einige Bemerkungen zur axiomatischen Begründung der
Mengenlehre. ‒ In: T. Skolem,” in Selected works in logic (ed. E. Fenstad), Oslo:
Univforlaget (1970).
Turing, Allen 1937. “On computable numbers, with an application to the
Entscheidungsproblem,” Proceedings of London Mathematical Society, series 2. 42 (1):
230-265
Andrew Yao (1993). "Quantum circuit complexity". Proceedings of the 34th Annual
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