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 computers perform calculations using quantum mechanics and qubits that can represent superpositions of states. While classical computers use bits that are either 0 or 1, qubits can be both 0 and 1 simultaneously. This allows quantum computers to massively parallelize computations. Some potential applications include simulating molecular interactions for drug development, breaking encryption standards, and optimizing machine learning models. Several companies are working to develop quantum computers, but building large-scale, reliable versions remains a challenge due to the difficulty of controlling qubits.
The Presentation is about the quantum computers and quantum computing describing the quantum phenomena which makes the future computers 1000 times more powerful than the current computers .Also include an Artificial intelligence to tell the difference of computing power between the a conventional computer computing and a quantum computer computing.Quantum computers are still under research and development and not available for common peoples and businesses but major organization are investing highly on these future machine hardware especially U.S is spending billions of Dollars to make it happened for their future security purposes.
This document provides an overview of quantum computers, including their history, workings, applications, and comparisons to classical computers. It discusses how quantum computers can perform computations using superposition and entanglement to analyze multiple states simultaneously. The document traces the origins of quantum computing to proposals by Yuri Manin in 1980 and Richard Feynman in 1981. It explains that while a 2-bit classical computer can only analyze one state at a time, a 2-qubit quantum computer can analyze all 4 possible states simultaneously. The document suggests quantum computers may be able to solve currently intractable problems involving enormous data more efficiently, with examples including finding distant planets, earlier disease detection, and improved drug development.
-It is a good ppt for a beginner to learn about Quantum
Computer.
-Quantum computer a solution for every present day computing
problems.
-Quantum computer a best solution for AI making
The new emerging technology which is under research but when will come into practice, it will change the era of computing.
Its is based on changing the concept of inputs received by the machine.
till now the machine works with 0 and 1,however it will implement an input b/w 0 and 1 i.e 1/2.
The speed of processing will raise up-to 8 times and things will be beyond our expectations.
This document discusses quantum computers, which harness quantum phenomena like superposition and entanglement to perform operations. A qubit, the basic unit of information in a quantum computer, can exist in multiple states simultaneously. While this allows massive parallelism and an exponential increase in computational power over classical computers, building large-scale quantum computers faces challenges in maintaining coherence. Potential applications include cryptography, optimization problems, and software testing due to quantum computers' probabilistic solving approach.
Quantum computers have the potential to vastly outperform classical computers for certain problems. They make use of quantum bits (qubits) that can exist in superpositions of states and become entangled with each other. This allows quantum computers to perform calculations on all possible combinations of inputs simultaneously. However, building large-scale quantum computers faces challenges such as maintaining quantum coherence long enough to perform useful computations. Researchers are working to develop quantum algorithms and overcome issues like decoherence. If successful, quantum computers could solve problems in domains like cryptography, simulation, and machine learning that are intractable for classical computers.
Quantum computers perform calculations using quantum mechanics and qubits that can represent superpositions of states. While classical computers use bits that are either 0 or 1, qubits can be both 0 and 1 simultaneously. This allows quantum computers to massively parallelize computations. Some potential applications include simulating molecular interactions for drug development, breaking encryption standards, and optimizing machine learning models. Several companies are working to develop quantum computers, but building large-scale, reliable versions remains a challenge due to the difficulty of controlling qubits.
The Presentation is about the quantum computers and quantum computing describing the quantum phenomena which makes the future computers 1000 times more powerful than the current computers .Also include an Artificial intelligence to tell the difference of computing power between the a conventional computer computing and a quantum computer computing.Quantum computers are still under research and development and not available for common peoples and businesses but major organization are investing highly on these future machine hardware especially U.S is spending billions of Dollars to make it happened for their future security purposes.
This document provides an overview of quantum computers, including their history, workings, applications, and comparisons to classical computers. It discusses how quantum computers can perform computations using superposition and entanglement to analyze multiple states simultaneously. The document traces the origins of quantum computing to proposals by Yuri Manin in 1980 and Richard Feynman in 1981. It explains that while a 2-bit classical computer can only analyze one state at a time, a 2-qubit quantum computer can analyze all 4 possible states simultaneously. The document suggests quantum computers may be able to solve currently intractable problems involving enormous data more efficiently, with examples including finding distant planets, earlier disease detection, and improved drug development.
-It is a good ppt for a beginner to learn about Quantum
Computer.
-Quantum computer a solution for every present day computing
problems.
-Quantum computer a best solution for AI making
The new emerging technology which is under research but when will come into practice, it will change the era of computing.
Its is based on changing the concept of inputs received by the machine.
till now the machine works with 0 and 1,however it will implement an input b/w 0 and 1 i.e 1/2.
The speed of processing will raise up-to 8 times and things will be beyond our expectations.
This document discusses quantum computers, which harness quantum phenomena like superposition and entanglement to perform operations. A qubit, the basic unit of information in a quantum computer, can exist in multiple states simultaneously. While this allows massive parallelism and an exponential increase in computational power over classical computers, building large-scale quantum computers faces challenges in maintaining coherence. Potential applications include cryptography, optimization problems, and software testing due to quantum computers' probabilistic solving approach.
Quantum computers have the potential to vastly outperform classical computers for certain problems. They make use of quantum bits (qubits) that can exist in superpositions of states and become entangled with each other. This allows quantum computers to perform calculations on all possible combinations of inputs simultaneously. However, building large-scale quantum computers faces challenges such as maintaining quantum coherence long enough to perform useful computations. Researchers are working to develop quantum algorithms and overcome issues like decoherence. If successful, quantum computers could solve problems in domains like cryptography, simulation, and machine learning that are intractable for classical computers.
The document discusses the basics of quantum computing. It explains that quantum computers use qubits that can represent 0, 1, or both values simultaneously. Operations are performed using quantum logic gates to manipulate the qubits. Several important developments in quantum computing are mentioned, such as Feynman's proposal of a quantum computer in 1981, Deutsch developing the quantum Turing machine in 1985, and Shor creating an algorithm for integer factorization in 1994. Potential applications of quantum computing include factoring, simulations, encryption, and artificial intelligence. However, challenges remain such as quantum decoherence and error correction.
This document provides an overview of quantum computing, including basic quantum theory, the operation of quantum computers, and potential applications. It discusses how electrons can exist in a state of superposition with multiple possible values until measured. Quantum computers utilize this superposition property to perform operations in parallel on multiple potential values at once. One example given is Shor's algorithm for factoring large numbers, which could have applications in cryptography but would be difficult for classical computers. Specific quantum logic gates like the square root of NOT are also introduced, as is the concept of quantum entanglement where the states of multiple particles are linked.
This document provides an overview of quantum computing. It defines quantum as the smallest possible unit of physical properties like energy or matter. Quantum computers use quantum phenomena like superposition and entanglement to perform operations on quantum bits (qubits). Qubits can exist in multiple states simultaneously, unlike classical computer bits which are either 0 or 1. The document outlines how quantum computers work based on quantum principles and can solve certain problems exponentially faster than classical computers. It also compares classical computers to quantum computers and discusses potential applications of quantum computing in areas like artificial intelligence, cryptography, and molecular modeling.
This document provides an overview of quantum computers. It begins by explaining that quantum physics must be understood first as quantum computers are based on quantum mechanical principles rather than classical physics. It then defines a quantum computer as a machine that performs calculations based on the laws of quantum mechanics. The document goes on to discuss key quantum properties like superposition and entanglement that quantum computers exploit. It also covers qubits, quantum gates, applications, advantages, challenges, and concludes by stating that quantum computers will require a new way of looking at computing.
A quantum computer performs calculations using quantum mechanics and quantum properties like superposition and entanglement. It uses quantum bits (qubits) that can exist in superpositions of states unlike classical computer bits. A quantum computer could solve some problems, like factoring large numbers, much faster than classical computers. The document discusses the history of computing generations and quantum computing, how quantum computers work using qubits, superpositions and entanglement, and potential applications like encryption cracking and simulation.
This slide starts from a basic explanation between Bit and Qubit. It then follows with a brief history behind Quantum Computer, current trends, and update with concerns to make the quantum computer practically useful.
This document provides an introduction to quantum computing. It discusses how quantum computers work using quantum bits (qubits) that can exist in superpositions of states unlike classical bits. Qubits can become entangled so that operations on one qubit affect others. Implementing qubits requires isolating quantum systems to avoid decoherence. Challenges include controlling decoherence, but research continues on algorithms, hardware, and bringing theoretical quantum computers to practical use. Quantum computers may solve problems intractable for classical computers.
This document discusses quantum computing, including:
- Quantum computers use quantum phenomena like entanglement and superposition to perform calculations based on quantum mechanics.
- A qubit can represent a 1, 0, or superposition of both, allowing quantum computers to exponentially increase their processing power compared to classical computers.
- Researchers have made progress developing quantum computers, entangling up to 14 qubits and performing calculations with two qubits, but large-scale quantum computers able to solve important problems much faster than classical computers are still a future goal expected to be achieved within 10 years.
This document provides an overview of quantum computing, including its history, basic concepts, applications, advantages, difficulties, and future directions. It discusses how quantum computing originated in the 1980s with the goal of building a computer that is millions of times faster than classical computers and theoretically uses no energy. The basic concepts covered include quantum mechanics, superpositioning, qubits, quantum gates, and how quantum computers could perform calculations that are intractable on classical computers, such as factoring large numbers. The document also outlines some of the challenges facing quantum computing as well as potential future advances in the field.
The document provides an overview of fundamental concepts in quantum computing, including quantum properties like superposition, entanglement, and uncertainty principle. It discusses how quantum bits can represent more than classical bits by being in superpositions of states. Basic quantum gates like Hadamard, Pauli X, and phase shift gates are also introduced, along with pioneers in the field like Feynman, Deutsch, Shor, and Grover. Potential applications of quantum computing are listed.
Quantum computing is a type of computation that harnesses the collective properties of quantum states, such as superposition, interference, and entanglement, to perform calculations.
This presentation is designed to elucidate about the Quantum Computing - History - Principles - QUBITS - Quantum Computing Models - Applications - Advantages and Disadvantages.
1) Quantum computers operate using quantum bits (qubits) that can exist in superpositions of states rather than just 1s and 0s like classical bits.
2) Keeping qubits coherent and isolated from the external environment is extremely challenging as interaction causes decoherence within nanoseconds to seconds.
3) While prototypes of 5-7 qubit quantum computers exist, scaling them up to practical sizes of 50-100 qubits or more to outperform classical computers remains an outstanding challenge due to decoherence issues.
This seminar presentation provides an introduction to quantum computing, including its history, why it is important, how it works, potential applications, challenges, and conclusions. Specifically, it discusses how quantum computers use quantum mechanics principles like qubits and superposition to perform calculations. The history includes early proposals in 1982 and key algorithms developed in the 1990s. Applications that could benefit from quantum computing are mentioned like cryptography, artificial intelligence, and communication. Issues like error correction, decoherence, and cost are also presented. In conclusion, quantum computers may be able to simulate physical systems and even develop artificial intelligence.
A quantum computer harnesses the power of atoms and molecules to perform calculations billions of times faster than silicon-based computers. Unlike classical bits that are either 0 or 1, quantum bits or qubits can be in a superposition of both states simultaneously. While current quantum computers have only manipulated a few qubits, their potential applications include efficiently solving problems like integer factorization that are intractable for classical computers. Significant challenges remain to controlling quantum phenomena necessary for building useful quantum computers.
Quantum computing uses quantum mechanics phenomena like superposition, entanglement, and interference to perform computation. Quantum computers are improving at an exponential rate according to Neven's Law, doubling their processing power exponentially faster than classical computers. The basic unit of quantum information is the qubit, which can exist in superposition and represent a '1' and '0' simultaneously. This allows quantum computers to explore all computational paths at once, greatly increasing their processing speed over classical computers for certain problems.
A file on Quantum Computing for people with least knowledge about physics, electronics, computers and programming. Perfect for people with management backgrounds. Covers understandable details about the topic.
Quantum Computers are the future and this manual explains the topic in the best possible way.
Quantum computers use principles of quantum mechanics rather than classical binary logic. They have qubits that can represent superpositions of 0 and 1, allowing massive parallelism. Key effects like superposition, entanglement, and tunneling give them advantages over classical computers for problems like factoring and searching. Early quantum computers have been built with up to a few hundred qubits, and algorithms like Shor's show promise for cryptography applications. However, challenges remain around error correction and controlling quantum states as quantum computers scale up. D-Wave has produced commercial quantum annealing systems with over 1000 qubits, but debate continues on whether these demonstrate quantum advantage. Overall, quantum computing could transform fields like AI, simulation, and optimization if challenges around building reliable large-scale quantum
Presents an overview of quantum computing including its history, key concepts like qubits and superposition, applications like factoring large numbers and solving optimization problems, and advantages like speed and security compared to classical computers. Some challenges to building quantum computers are maintaining stability due to sensitivity to interference and requiring very cold temperatures.
I will explain why quantum computing is interesting, how it works and what you actually need to build a working quantum computer. I will use the superconducting two-qubit quantum processor I built during my PhD as an example to explain its basic building blocks. I will show how we used this processor to achieve so-called quantum speed-up for a search algorithm that we ran on it. Finally, I will give a short overview of the current state of superconducting quantum computing and Google's recently announced effort to build a working quantum computer in cooperation with one of the leading research groups in this field.
Quantum computers have the potential to solve certain problems much faster than classical computers by exploiting principles of quantum mechanics, such as superposition and entanglement. However, building large-scale, reliable quantum computers faces challenges related to decoherence and controlling quantum systems. Current research aims to develop quantum algorithms and overcome issues in scaling up quantum hardware to perform more complex computations than today's most powerful supercomputers.
The document discusses the basics of quantum computing. It explains that quantum computers use qubits that can represent 0, 1, or both values simultaneously. Operations are performed using quantum logic gates to manipulate the qubits. Several important developments in quantum computing are mentioned, such as Feynman's proposal of a quantum computer in 1981, Deutsch developing the quantum Turing machine in 1985, and Shor creating an algorithm for integer factorization in 1994. Potential applications of quantum computing include factoring, simulations, encryption, and artificial intelligence. However, challenges remain such as quantum decoherence and error correction.
This document provides an overview of quantum computing, including basic quantum theory, the operation of quantum computers, and potential applications. It discusses how electrons can exist in a state of superposition with multiple possible values until measured. Quantum computers utilize this superposition property to perform operations in parallel on multiple potential values at once. One example given is Shor's algorithm for factoring large numbers, which could have applications in cryptography but would be difficult for classical computers. Specific quantum logic gates like the square root of NOT are also introduced, as is the concept of quantum entanglement where the states of multiple particles are linked.
This document provides an overview of quantum computing. It defines quantum as the smallest possible unit of physical properties like energy or matter. Quantum computers use quantum phenomena like superposition and entanglement to perform operations on quantum bits (qubits). Qubits can exist in multiple states simultaneously, unlike classical computer bits which are either 0 or 1. The document outlines how quantum computers work based on quantum principles and can solve certain problems exponentially faster than classical computers. It also compares classical computers to quantum computers and discusses potential applications of quantum computing in areas like artificial intelligence, cryptography, and molecular modeling.
This document provides an overview of quantum computers. It begins by explaining that quantum physics must be understood first as quantum computers are based on quantum mechanical principles rather than classical physics. It then defines a quantum computer as a machine that performs calculations based on the laws of quantum mechanics. The document goes on to discuss key quantum properties like superposition and entanglement that quantum computers exploit. It also covers qubits, quantum gates, applications, advantages, challenges, and concludes by stating that quantum computers will require a new way of looking at computing.
A quantum computer performs calculations using quantum mechanics and quantum properties like superposition and entanglement. It uses quantum bits (qubits) that can exist in superpositions of states unlike classical computer bits. A quantum computer could solve some problems, like factoring large numbers, much faster than classical computers. The document discusses the history of computing generations and quantum computing, how quantum computers work using qubits, superpositions and entanglement, and potential applications like encryption cracking and simulation.
This slide starts from a basic explanation between Bit and Qubit. It then follows with a brief history behind Quantum Computer, current trends, and update with concerns to make the quantum computer practically useful.
This document provides an introduction to quantum computing. It discusses how quantum computers work using quantum bits (qubits) that can exist in superpositions of states unlike classical bits. Qubits can become entangled so that operations on one qubit affect others. Implementing qubits requires isolating quantum systems to avoid decoherence. Challenges include controlling decoherence, but research continues on algorithms, hardware, and bringing theoretical quantum computers to practical use. Quantum computers may solve problems intractable for classical computers.
This document discusses quantum computing, including:
- Quantum computers use quantum phenomena like entanglement and superposition to perform calculations based on quantum mechanics.
- A qubit can represent a 1, 0, or superposition of both, allowing quantum computers to exponentially increase their processing power compared to classical computers.
- Researchers have made progress developing quantum computers, entangling up to 14 qubits and performing calculations with two qubits, but large-scale quantum computers able to solve important problems much faster than classical computers are still a future goal expected to be achieved within 10 years.
This document provides an overview of quantum computing, including its history, basic concepts, applications, advantages, difficulties, and future directions. It discusses how quantum computing originated in the 1980s with the goal of building a computer that is millions of times faster than classical computers and theoretically uses no energy. The basic concepts covered include quantum mechanics, superpositioning, qubits, quantum gates, and how quantum computers could perform calculations that are intractable on classical computers, such as factoring large numbers. The document also outlines some of the challenges facing quantum computing as well as potential future advances in the field.
The document provides an overview of fundamental concepts in quantum computing, including quantum properties like superposition, entanglement, and uncertainty principle. It discusses how quantum bits can represent more than classical bits by being in superpositions of states. Basic quantum gates like Hadamard, Pauli X, and phase shift gates are also introduced, along with pioneers in the field like Feynman, Deutsch, Shor, and Grover. Potential applications of quantum computing are listed.
Quantum computing is a type of computation that harnesses the collective properties of quantum states, such as superposition, interference, and entanglement, to perform calculations.
This presentation is designed to elucidate about the Quantum Computing - History - Principles - QUBITS - Quantum Computing Models - Applications - Advantages and Disadvantages.
1) Quantum computers operate using quantum bits (qubits) that can exist in superpositions of states rather than just 1s and 0s like classical bits.
2) Keeping qubits coherent and isolated from the external environment is extremely challenging as interaction causes decoherence within nanoseconds to seconds.
3) While prototypes of 5-7 qubit quantum computers exist, scaling them up to practical sizes of 50-100 qubits or more to outperform classical computers remains an outstanding challenge due to decoherence issues.
This seminar presentation provides an introduction to quantum computing, including its history, why it is important, how it works, potential applications, challenges, and conclusions. Specifically, it discusses how quantum computers use quantum mechanics principles like qubits and superposition to perform calculations. The history includes early proposals in 1982 and key algorithms developed in the 1990s. Applications that could benefit from quantum computing are mentioned like cryptography, artificial intelligence, and communication. Issues like error correction, decoherence, and cost are also presented. In conclusion, quantum computers may be able to simulate physical systems and even develop artificial intelligence.
A quantum computer harnesses the power of atoms and molecules to perform calculations billions of times faster than silicon-based computers. Unlike classical bits that are either 0 or 1, quantum bits or qubits can be in a superposition of both states simultaneously. While current quantum computers have only manipulated a few qubits, their potential applications include efficiently solving problems like integer factorization that are intractable for classical computers. Significant challenges remain to controlling quantum phenomena necessary for building useful quantum computers.
Quantum computing uses quantum mechanics phenomena like superposition, entanglement, and interference to perform computation. Quantum computers are improving at an exponential rate according to Neven's Law, doubling their processing power exponentially faster than classical computers. The basic unit of quantum information is the qubit, which can exist in superposition and represent a '1' and '0' simultaneously. This allows quantum computers to explore all computational paths at once, greatly increasing their processing speed over classical computers for certain problems.
A file on Quantum Computing for people with least knowledge about physics, electronics, computers and programming. Perfect for people with management backgrounds. Covers understandable details about the topic.
Quantum Computers are the future and this manual explains the topic in the best possible way.
Quantum computers use principles of quantum mechanics rather than classical binary logic. They have qubits that can represent superpositions of 0 and 1, allowing massive parallelism. Key effects like superposition, entanglement, and tunneling give them advantages over classical computers for problems like factoring and searching. Early quantum computers have been built with up to a few hundred qubits, and algorithms like Shor's show promise for cryptography applications. However, challenges remain around error correction and controlling quantum states as quantum computers scale up. D-Wave has produced commercial quantum annealing systems with over 1000 qubits, but debate continues on whether these demonstrate quantum advantage. Overall, quantum computing could transform fields like AI, simulation, and optimization if challenges around building reliable large-scale quantum
Presents an overview of quantum computing including its history, key concepts like qubits and superposition, applications like factoring large numbers and solving optimization problems, and advantages like speed and security compared to classical computers. Some challenges to building quantum computers are maintaining stability due to sensitivity to interference and requiring very cold temperatures.
I will explain why quantum computing is interesting, how it works and what you actually need to build a working quantum computer. I will use the superconducting two-qubit quantum processor I built during my PhD as an example to explain its basic building blocks. I will show how we used this processor to achieve so-called quantum speed-up for a search algorithm that we ran on it. Finally, I will give a short overview of the current state of superconducting quantum computing and Google's recently announced effort to build a working quantum computer in cooperation with one of the leading research groups in this field.
Quantum computers have the potential to solve certain problems much faster than classical computers by exploiting principles of quantum mechanics, such as superposition and entanglement. However, building large-scale, reliable quantum computers faces challenges related to decoherence and controlling quantum systems. Current research aims to develop quantum algorithms and overcome issues in scaling up quantum hardware to perform more complex computations than today's most powerful supercomputers.
This document presents an overview of quantum computers. It begins with an introduction and brief outline, then discusses the history of quantum computing from 1982 onwards. It explains that quantum computers use quantum mechanics principles like qubits and superposition to potentially solve problems beyond the capabilities of classical computers. Some applications mentioned include cryptography, artificial intelligence, and teleportation. Challenges like decoherence and error correction are also noted. The conclusion states that if successfully built, quantum computers could revolutionize society.
Representation & Realityby Language (How to make a home quantum computer) Vasil Penchev
Reality as if is doubled in relation to language
We will model this doubling by two Turing machines (i.e. by usual computers) in a kind of “dialog”: the one for reality, the other for its image in language
The two ones have to reach the state of equilibrium to each other
At last, one can demonstrate that the pair of them is equivalent to a quantum computer
One can construct a model of two independent Turing machines allowing of a series of relevant interpretations:
Language
Quantum computer
Representation and metaphor
Reality and ontology
In turn that model is based on the concepts of choice and information
The document discusses quantum mechanics and three interpretations of its formalism: the Copenhagen interpretation, the many-worlds interpretation, and the transactional interpretation. It describes four quantum paradoxes around non-locality, wave-particle duality, and wave function collapse. Each interpretation aims to resolve these paradoxes while linking the mathematical formalism to physical phenomena.
This document provides an overview of DNA microarrays (DNA chips). It discusses that DNA chips allow scientists to simultaneously measure gene expression levels or genotype multiple genomic regions. It describes the principle technologies used in DNA chips, including attaching cDNA or oligonucleotide probes to glass or silicon surfaces. The document also provides background on DNA and microarrays, their history, applications in gene expression analysis and disease research, and principle of hybridization. It discusses alternative bead-based array technologies and how microarrays enabled large-scale genomic experiments.
With the introduction of quantum computing on the horizon, computer security organizations are stepping up research and development to defend against a new kind of computer power. Quantum computers pose a very real threat to the global information technology infrastructure of today. Many security implementations in use based on the difficulty for modern-day computers to perform large integer factorization. Utilizing a specialized algorithm such as mathematician Peter Shor’s, a quantum computer can compute large integer factoring in polynomial time versus classical computing’s sub-exponential time. This theoretical exponential increase in computing speed has prompted computer security experts around the world to begin preparing by devising new and improved cryptography methods. If the proper measures are not in place by the time full-scale quantum computers produced, the world’s governments and major enterprises could suffer from security breaches and the loss of massive amounts of encrypted data
This document discusses the history and future of quantum computing. It explains how quantum computers work using principles of quantum mechanics like superposition and entanglement. Quantum computers can perform multiple computations simultaneously by exploiting the ability of qubits to exist in superposition. Current research involves building larger quantum registers with more qubits and performing calculations with 2 qubits. The future of quantum computing may enable solving certain problems much faster than classical computers, with desktop quantum computers potentially arriving within 10 years.
Quantum Computing: Welcome to the FutureVernBrownell
Vern Brownell, CEO at D-Wave Systems, shares his thoughts on Quantum Computing in this presentation, which he delivered at Compute Midwest in November 2014. He addresses big questions that include: What is a quantum computer? How do you build one? Why does it matter? What does the future hold for quantum computing?
This document provides an overview of DNA microarrays, also known as DNA chips. It discusses the principles and techniques used to prepare DNA microarrays, including photolithography. There are two main types of DNA chips: cDNA-based chips and oligonucleotide-based chips. DNA microarrays have various applications, including gene expression profiling, drug discovery, and diagnostics. They provide the advantage of analyzing thousands of genes simultaneously but also have disadvantages such as high costs and complex data analysis.
This document summarizes a seminar on Gi-Fi technology. It discusses currently used wireless technologies like Wi-Fi and Bluetooth. It then introduces Gi-Fi, explaining that it uses light waves to transmit data wirelessly over short distances at high speeds. The document outlines Gi-Fi's architecture, features like high speed data transfer and low power consumption. It also lists some applications and concludes that Gi-Fi is expected to become the dominant wireless networking technology within five years, bringing wireless broadband to both homes and offices.
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).
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.
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
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.
Quantum Mechanics as a Measure Theory: The Theory of Quantum MeasureVasil Penchev
This document discusses representing quantum mechanics as a measure theory, with the key points being:
1. Quantum measure can unify the measurement of discrete and continuous quantities by treating them as "much" and "many".
2. The unit of quantum measure is the qubit, allowing it to jointly measure probability, quantity, order, and disorder.
3. All physical processes can be interpreted as computations of a quantum computer, with the universal substance being quantum information.
4. Quantum measure can provide a nonlocal explanation for the Aharonov-Bohm effect by linking it to the electromagnetic nature of space-time itself.
Quantum information as the information of infinite seriesVasil Penchev
The quantum information introduced by quantum mechanics 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, can be interpreted as 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 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
This document provides an introduction to quantum computing, including its history, key concepts, applications, and current challenges. Some of the main points covered include:
- Quantum computing uses quantum phenomena like superposition and entanglement to perform operations on quantum bits (qubits).
- Important quantum computing concepts include qubits, quantum information, superposition, entanglement, teleportation, and parallelism.
- Potential applications include quantum networking, secure communications, artificial intelligence, and molecular simulations.
- Current challenges to developing quantum computers include limited qubit numbers and physical machine size. Further development could revolutionize computation for certain problems.
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.
The Quantum computing has become a buzzword now a days, however it has not been the favorite of the researchers until recent times.
Let's follow about
What's Quantum Computing?
It's Evolution
Primary Focus
Future
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
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 computers is a machine that performs calculations based on the laws of quantum mechanics which is the behaviour of particles at the subatomic level.
“No hidden variables!”: From Neumann’s to Kochen and Specker’s theorem in qua...Vasil Penchev
The talk addresses a philosophical comparison and thus interpretation of both theorems having one and the same subject:
The absence of the “other half” of variables, called “hidden” for that, to the analogical set of variables in classical mechanics:
These theorems are:
John’s von Neumann’s (1932)
Simon Kochen and Ernst Specker’s (1968)
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.
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.
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.
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.
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.
Similar to Quantum Computer: Quantum Model and Reality (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
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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.
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.
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
Both necessity and arbitrariness of the sign: informationVasil Penchev
There is a fundamental contradiction or rather tension in Sausure’d Course: between the necessity of the sign within itself and its arbitrariness within a system of signs. That tension penetrates the entire Course and generates its “plot”. It can be expressed by the quantity of information generalized to quantum information by quantum mechanics. Then the problem is how a bit to be expressed by a qubit or vice versa. The structure of the main problem of quantum mechanics is isomorphic. Thus its solution, namely the set of solutions of the Schrödinger equation, implies the solution of the above contradictionor tension.
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Overview
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Key Topics Covered
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10. Configuring Camel K Integrations for Data Pipelines
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11. What is a Jupyter Notebook?
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12. Jupyter Notebooks with Code Examples
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3. Eight questions
• There are a few most essential questions
about the philosophical interpretation of
quantum computer, which are enumerated on
the next slide
• They refer to the fundamental problems in
ontology and epistemology rather than
philosophy of science, of information and
computation
• The contemporary development of quantum
mechanics and the theory of quantum
information generates them
4. • 1. Can a quantum model unlike a classical model coincide
with reality?
• 2. Is reality interpretable as a quantum computer?
• 3. Can physical processes be understood better and more
generally as computations of quantum computer?
• 4. Is quantum information the real fundament of the
world?
• 5. Does the conception of quantum computer unify
physics and mathematics and thus the material and the
ideal world?
• 6. Is quantum computer a non-Turing machine in
principle?
• 7. Can a quantum computation be interpreted as an
infinite classical computational process of a Turing
machine?
• 8. Does quantum computer introduce the notion of
“actually infinite computational process”?
5. 1. Can a quantum model unlike a
classical model coincide with reality?
• There is a “central dogma” in epistemology about
the irremovable difference between reality and
knowledge, because of which cognition is an infinite
process of the representation of reality by better and
better models. Thus any model can coincide with
reality is excluded in principle
• Furthermore any classical model corroborates that
postulate: The model is always something simpler
and less perfect than reality. Any quantity representing the difference between reality and any
model should be neither zero nor converging to zero
6. 1.1. Quantum model
Quantum model can be defined as some subset
in Hilbert space representing some part of
reality:
• The simplest non-trivial example of a quantum
model is a wave function (i.e. a point in Hilbert
space) which represents a state of a quantum
system
• That state can be interpreted both as a
coherent superposition of all possible states of
the system and as a statistical ensemble of all
measurements of it.
7. 1.2. An option of the model and
reality to coincide with each other
Quantum model realizes that option being as
complementary as identical to the
corresponding reality rather paradoxically:
• Any classical model is always neither
complementary nor identical to the
corresponding reality
• One can say that the cost of that coincidence
is quantum complementarity being the
necessity condition for it
8. 1.3. Infinity as the condition of
coincidence of a model and reality
• Hilbert space is infinitely dimensional, but
even the finitely dimensional subspaces of it
involve infinity by virtue of the “Banach –
Tarski paradox”
• Indeed only an infinite set can be divided into
two parts such that there exists three one-toone mappings between any two of them
accordingly
• The opposite is also true: that division of a set
means that it is infinite
9. 2. Is reality interpretable as a
quantum computer?
• To answer that question, one should define a
quantum computer and utilizing the
coincidence of a quantum model and reality
as above, show how a quantum computer can
process a quantum model
• Furthermore, any physical quantity or its
change both defined as a self-adjoint operator
in Hilbert space according to quantum
mechanics can be represented as a
corresponding computation of a quantum
computer
10. 2.1. Quantum computer
• Quantum computer can be defined as that
computer, all possible states of which are
coherent states of a quantum system
• Thus all of them can be described by
corresponding wave functions
• As all wave functions are points in Hilbert
space, the quantum computer can be
equivalently defined as a series of successive
transformations (operators) of Hilbert space
into itself: Thus a single quantum computation
is any of those transformations (operators)
12. A “classical” Turing machine
A classical Turing
tape of bits:
1
...
1
n+1
...
...
The
/No
last
cell
1. Write!
2. Read!
3. Next!
4. Stop!
The list of all
operations on a cell:
A quantum Turing
tape of qubits:
n
The
last
cell
...
n
n+1
A quantum Turing machine
16. 2.3. Physical process as a quantum
computation
• Quantum computer can be equivalently
represented by a quantum Turing machine
• A quantum Turing machine is equivalent to
Hilbert space
• Quantum mechanics states that any physical state
or it change is a self-adjoint operator in Hilbert
space as any physical system can be considered as
a quantum one
• Consequently all physical process can be
interpreted as the calculation of a single
computer and thus the universe being as it
17. 3. Can physical processes be understood
better and more generally as
computations of quantum computer?
• Yes, they can, as being computations, they
should share a common informational
fundament, which is hidden from any other
viewpoint to the physical processes
• However that fundament cannot be that of
the information defined classically (e.g. in
Shannon) but it should be generalized as a
new kind of information: quantum
information
18. 3.1. A wave function as a value of
quantum information
• Any wave function can be represented as an
ordered series of qubits enumerated by the
positive integers
• Just as an ordering of bits can represent a
value of classical information, that series of
qubits, equivalent to a wave function
represents a value of quantum information
• One can think of the qubits of the series as a
special kind of digits: infinite digits. As a binary
digit can accept two values, that infinite digit
should accept infinite values
19. 3.2. Physical quantity and computation
• Any physical quantity according to quantum
mechanics corresponds to a self-adjoint
operator and thus to a certain change of a
wave function
• Any wave function represents a state of a
quantum computer
• Consequently, any physical quantity should
correspond to a quantum computation
defined as the change the state of a quantum
computer
20. 3.3. All physical processes as
informational ones
• Quantum mechanics is the universal doctrine
about the physical world and any physical
process can be interpreted as a quantum one:
• Any quantum process is informational in
terms of a generalized kind of information:
quantum information
• Consequently, all physical processes are
informational in the above sense
21. 4. Is quantum information the real
fundament of the world?
• All physical states in the world are wave
functions and thus they are different values of
quantum information
• All physical quantities in the world are a
certain kind of changes of wave functions and
thus of quantum information
• Consequently, one can certainly state that the
physical world consists of only quantum
information: It is the substance of the physical
world, its “matter”
22. 4.1. Quantum information
Quantum information can be defined in a few
equivalent ways:
As the information in Hilbert space
As the information measured in quantum bits
(qubits)
As the information concerning infinite sets
As the information in a wave function
As the information in any quantum state or
process
23. 4.2. Quantum information vs. classical
information
• If classical information refers only to finite
sets, quantum information is defined
immediately only as to infinite sets
• Quantum information can be discussed both
as the counterpart of classical information to
the infinite sets and as the generalization of
classical information including both the finite
and infinite sets
• The latter requires the axiom of choice, the
former does not
24. 4.3. Information and choice
• Information either classical or quantum can be
defined as the quantity of the units of choice in a
entity:
• The unit of classical information is a choice
between a given finite number of equiprobable
alternatives, e.g. a bit is a choice among two
equiprobable alternatives usually designated by
“0” and “1”
• Analogically the unit of quantum information, a
qubit is a choice among infinite equiprobable
alternatives therefore requiring the axiom of choice
in general
25. 5. Does the conception of quantum
computer unify physics and mathematics
and thus the material and the ideal world?
• As information is a dimensionless quantity
equally well referring both to a physical entity
or to a mathematical class, it can serve as a
“bridge” between physics and mathematics and
thus between the material and ideal world
• In fact quantum information being a generalized
kind of information is just what allows of the
physical and mathematical to be considered as
two interpretations of the underlying quantum
information
26. 5.1. Physics as a branch of mathematics
• Classical physics and science distinguish
fundamentally the mathematically models from
the modeled reality and thus there is a “strong
interface” between mathematics and physics
• However quantum mechanics, erasing that
boundary, therefore understands physics newly:
as a special branch of mathematics, in which
two kinds of models coincide in principle:
• Then reality (and therefore physics) turns out to
be defined within mathematics as the one kinds
of models
27. 5.2. The quantum pathway between
physics and mathematics
• The bridge between physics and mathematics, built
by quantum mechanics necessarily utilizes the
concept of infinity
• Mathematics has introduced that concept in its
fundament since the end of the 19th century by set
theory
• Quantum mechanics is the only experimental
science about reality, which has forced also to
involve infinity in its ground to describe uniformly
quantum (leap-like) and smooth (continuous)
motion since the first half of the 20th century
29. 6. Is quantum computer a non-Turing
machine in principle?
• The concept of infinity allows of distinguishing
a quantum computer from a Turing machine
• A Turing machine should end its computation
in a finite number of steps and in a finite time
as any step is accomplished in a finite but
nonzero time
• A quantum computer can finish making an
infinite number of steps necessity of a Turing
machine as a whole by a leap in a finite time
even zero theoretically
30. 6.1. Turing machine
• One can restrict the set of Turing machines to
that subset of them, which have finished the
work with a result
• That subset is equivalent to the set of all
finite positive integers (e.g. represented
binarily)
• For a quantum computer not to be equivalent
to any Turing machine, it should not belong to
the above set, which is enumerable
31. 6.2. Quantum Turing machine
• A quantum Turing machine being equivalent to a
quantum computer can be defined as a Turing
machine, in which all bits are replaced by qubits
as above
• Any qubit is a choice among an uncountable set
such as the points of a 3D unit sphere
• Consequently a quantum computer is not a
Turing machine in general as all its possible states
are an uncountable set unlike a Turing machine
32. 6.3. Quantum computation is infinite
on a Turing machine
However a quantum computation can be
represented as an infinite, but converging series of
Turing machines finished the work with a partial
result
Thus all possible states of a Turing machine and
those of a quantum computer are related to each
other as a set of rational numbers to that of
irrational ones within any finite interval or area
Consequently a quantum computation on a Turing
machine will require infinitely many steps and
cannot ever end
33. 7. Can a quantum computation be
interpreted as an infinite classical
computational process of a Turing machine?
• Consequently a quantum computation can be
interpreted so:
• However a quantum computer can accomplish
that computation ending with a finite result in
a finite time making a quantum jump to the
limit of the process
• While a Turing machine cannot do that leap
and cannot stop ever yielding the result
34. 7.1. The axiom of choice in quantum
computation
• Any quantum computation in general makes a
jump and thus it chooses the result in a nonconstructive way therefore requiring the axiom of
choice
• Quantum computation is grounded both on
infinity and the axiom of choice
• However the quantum computation is invariant to
the axiom of choice in a sense for the result is
single and necessary and thus no choice is made.
Only the non-constructiveness of the quantum
computation is only what remains from it
35. 7.2. The equivalence of a single qubit
and arbitrarily many qubits
• As an infinite set has the same power as the
set of arbitrarily many sets, each of the same
power, the choice of a point among a qubit is
equivalent to the choice of arbitrarily many
points, each from a qubit
• The same can be deduced from the so-called
Banach-Tarski (1924) paradox for a qubit is
isomorphic to a the choice of a point among
those of a 3D sphere
36. 7.3. Quantum computation as
converging
• Being infinite, a quantum computation must be
converging to a finite limit
• This is guaranteed as any qubit is limited and the
axiom of choice always allows of reordering any
series to a monotonic one. (Any limited monotonic
series has necessarily a limit.)
• However there are in general two monotonic
reordering for any series: either ascending or
descending implying two complementary limits as
any reordering excludes the other
37. 8. Does quantum computer introduce the
notion of “actually infinite computational
process”?
• In fact quantum computer requires for the
computational processes to be actually infinite in
general:
• Indeed the existing of a limit of a series means
that it should be taken as completed whole (the
limit is possible not to belong to the sequence at
all)
• Thus the concept of actual infinity involves
implicitly a pair of an infinite series and a limit, to
which the series should converge in principle
38. 8.1. The limit of an infinite computation
• Rather paradoxically, the concept of actual infinity
unlike that of potential infinity implies Skolem’s
relativity (1922) of the sets by mediation of the
axiom of choice
• Thus the limit of an infinite computation can be
considered as the finite and complementary,
quantum counterpart of the corresponding infinite
series of the computation
• Max Born’s “interpretation” (1926) of quantum
mechanics implies the same statement and thus the
infinite series and its limit are the two
complementary representations of a quantum state
interpreted as a quantum computation
39. 8.2. The limit of a computation as
actual infinity
In fact the concept of ‘limit’ of an infinite series has
already introduced that of ‘actual infinity’ as:
There is an infinite set, that of the members of
the series in question
That set must be considered as a completed
whole in the limit of the series, which can be as
finite as infinite, as a member of the series, as not
such a one
Thus the limit represents the infinite series as a
singularity
40. 8.3. Quantum computation as an
infinite computation
• Quantum computation can be represented as
an infinite series of partial results or “Turing
machines” necessarily converging to a limit
• Consequently, it is an infinite computation if it is
modeled on a set of Turing machines
• The transition to the limit is always a leap from
any partial result:
• Thus that jump being just quantum in fact
cannot be accomplished by any Turing machine
41. Conclusions:
• A quantum model unlike a classical model can
coincide with reality
• Reality can be interpreted as a quantum
computer
• The physical processes represent
computations of the quantum computer
• Quantum information is the real fundament of
the world
42. Conclusions:
• The conception of quantum computer unifies
physics and mathematics and thus the
material and the ideal world
• Quantum computer is a non-Turing machine in
principle
• Any quantum computing can be interpreted as
an infinite classical computational process of a
Turing machine
• Quantum computer introduces the notion of
“actually infinite computational process”
43. References:
• Banach, S. and Tarski, A. (1924). On the decomposition of sets of points
into parts respectively congruent [Sur la decomposition des ensembles de
points en parties respectivement congruentes]. Fundamenta
Mathematicae, 6 (1), 244-277.
• Born M. (1926a). On the quantum mechanics of shock events [Zur
Quantenmechanik der Stoβvorgänge]. Zeitschrift für Physik, 37,(12/
December), 863-867.
• Born, M. (1926b). The quantum mechanics of shock events
[Quantenmechanik der Stoβvorgänge]. Zeitschrift für Physik, 38 (11-12/
November), 803-827.
• Kochen, S. and Specker, E. (1968). “The problem of hidden variables in
quantum mechanics,” Journal of Mathematics and Mechanics. 17 (1): 5987.
• Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik,
Berlin: Verlag von Julius Springer.
• Skolem, T. (1922). A few notes to the axiomatic foundation of set theory
[Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre].
Matematikerkongressen i Helsingrofs den 4-7 Juli 1922, Den femte
skandinaviska matematikerkongressen, Redogörelse, Helsinki: AkademiskaBokhandeln, 1923, pp. 217-232.