Quantum computing uses quantum mechanics principles to perform calculations. A qubit can represent a 1, 0, or superposition of both simultaneously. Operations are performed by reversible logic gates like CNOT. Shor's algorithm shows quantum computers can factor large numbers faster by using quantum parallelism and Fourier transforms to find the period of a function, revealing the factors. While progress is being made, challenges remain in building larger quantum computers and developing new algorithms to solve other hard problems.
Quantum computing - A Compilation of ConceptsGokul Alex
Excerpts of the Talk Delivered at the 'Bio-Inspired Computing' Workshop conducted by Department of Computational Biology and Bioinformatics, University of Kerala.
Shor's algorithm is for quantum computer. Using this algorithm any arbitrarily large number can be factored in polynomial time. which is not possible in classical computer
Quantum computing - A Compilation of ConceptsGokul Alex
Excerpts of the Talk Delivered at the 'Bio-Inspired Computing' Workshop conducted by Department of Computational Biology and Bioinformatics, University of Kerala.
Shor's algorithm is for quantum computer. Using this algorithm any arbitrarily large number can be factored in polynomial time. which is not possible in classical computer
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.
Cryptanalysis with a Quantum Computer - An Exposition on Shor's Factoring Alg...Daniel Hutama
Integer factorization is a problem that has been studied by mathematicians for centuries, but has yet to see an efficient classical solution. The apparent intractability of the factorization problem has become the cornerstone of several cryptosystems, such as the widely used RSA encryption scheme for securing financial transactions and communications.
In this presentation, we show an in-depth study of quantum circuit designs for a quantum computer running Shor's algorithm. In particular, we present a classical-based reversible quantum circuit design of Vedral et. al., and a Fourier space circuit designed by Draper and Beauregard. Included in the appendix are detailed descriptions of Shor's full algorithm and a fully worked (classically simulated) example for factoring a 5-bit semiprime number.
Readers should have a basic knowledge of quantum computing concepts, such as qubits, quantum logic gates, entanglement, and their mathematical descriptions.
This is my second version of the quantum notes collected as part of my study.
This organizes content from various open source for study and reference only.
a ppt on based on quantum computing and in very short manner and all the basic areas are covered
and Logical gates are also included
and observation and conclusion also
this will lead you to get a brief knowledge about quantum computers and its explanation
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Descripcion about IBM quantum experience. In this presentation I introduce the IBM Tools for quantum programming. Also it serves as a general introduction to Quantum Computing
Experimental realisation of Shor's quantum factoring algorithm using qubit r...XequeMateShannon
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N=21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.
The basics of quantum computing, associated mathematics, DJ algorithms and coding details are covered.
These slides are used in my videos https://youtu.be/6o2jh25lrmI, https://youtu.be/Wj73E4pObRk, https://youtu.be/OkFkSXfGawQ and https://youtu.be/OkFkSXfGawQ
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
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.
Cryptanalysis with a Quantum Computer - An Exposition on Shor's Factoring Alg...Daniel Hutama
Integer factorization is a problem that has been studied by mathematicians for centuries, but has yet to see an efficient classical solution. The apparent intractability of the factorization problem has become the cornerstone of several cryptosystems, such as the widely used RSA encryption scheme for securing financial transactions and communications.
In this presentation, we show an in-depth study of quantum circuit designs for a quantum computer running Shor's algorithm. In particular, we present a classical-based reversible quantum circuit design of Vedral et. al., and a Fourier space circuit designed by Draper and Beauregard. Included in the appendix are detailed descriptions of Shor's full algorithm and a fully worked (classically simulated) example for factoring a 5-bit semiprime number.
Readers should have a basic knowledge of quantum computing concepts, such as qubits, quantum logic gates, entanglement, and their mathematical descriptions.
This is my second version of the quantum notes collected as part of my study.
This organizes content from various open source for study and reference only.
a ppt on based on quantum computing and in very short manner and all the basic areas are covered
and Logical gates are also included
and observation and conclusion also
this will lead you to get a brief knowledge about quantum computers and its explanation
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Descripcion about IBM quantum experience. In this presentation I introduce the IBM Tools for quantum programming. Also it serves as a general introduction to Quantum Computing
Experimental realisation of Shor's quantum factoring algorithm using qubit r...XequeMateShannon
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N=21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.
The basics of quantum computing, associated mathematics, DJ algorithms and coding details are covered.
These slides are used in my videos https://youtu.be/6o2jh25lrmI, https://youtu.be/Wj73E4pObRk, https://youtu.be/OkFkSXfGawQ and https://youtu.be/OkFkSXfGawQ
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Generating a custom Ruby SDK for your web service or Rails API using Smithyg2nightmarescribd
Have you ever wanted a Ruby client API to communicate with your web service? Smithy is a protocol-agnostic language for defining services and SDKs. Smithy Ruby is an implementation of Smithy that generates a Ruby SDK using a Smithy model. In this talk, we will explore Smithy and Smithy Ruby to learn how to generate custom feature-rich SDKs that can communicate with any web service, such as a Rails JSON API.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
2. Overview
Introduction and History
Data Representation
Operations on Data
Shor’s Algorithm
Conclusion and Open Questions
3. Introduction
What is a quantum computer?
A quantum computer is a machine that performs
calculations based on the laws of quantum mechanics,
which is the behavior of particles at the sub-atomic
level.
4. Introduction
“I think I can safely say that nobody
understands quantum mechanics” - Feynman
1982 - Feynman proposed the idea of creating
machines based on the laws of quantum
mechanics instead of the laws of classical
physics.
1985 - David Deutsch developed the quantum turing
machine, showing that quantum circuits are universal.
1994 - Peter Shor came up with a quantum
algorithm to factor very large numbers in polynomial
time.
1997 - Lov Grover develops a quantum search
algorithm with O(√N) complexity
5. Overview
Introduction and History
Data Representation
Operations on Data
Shor’s Algorithm
Conclusion and Open Questions
6. Representation of Data - Qubits
A bit of data is represented by a single atom that is in one of
two states denoted by |0> and |1>. A single bit of this form is
known as a qubit
A physical implementation of a qubit could use the two energy
levels of an atom. An excited state representing |1> and a
ground state representing |0>.
Excited
State
Ground
State
Nucleus
Light pulse of
frequency for
time interval t
Electron
State |0> State |1>
7. Representation of Data - Superposition
A single qubit can be forced into a superposition of the two states
denoted by the addition of the state vectors:
|> = |0> + |1>
Where and are complex numbers and | | + | | = 1
1 2
1 2 1 2
2 2
A qubit in superposition is in both of the
states |1> and |0 at the same time
8. Representation of Data - Superposition
Light pulse of
frequency for time
interval t/2
State |0> State |0> + |1>
Consider a 3 bit qubit register. An equally weighted
superposition of all possible states would be denoted by:
|> = |000> + |001> + . . . + |111>
1
√8
1
√8
1
√8
9. Data Retrieval
In general, an n qubit register can represent the numbers 0
through 2^n-1 simultaneously.
Sound too good to be true?…It is!
If we attempt to retrieve the values represented within a
superposition, the superposition randomly collapses to
represent just one of the original values.
In our equation: |> = |0> + |1> , represents the
probability of the superposition collapsing to |0>. The ’s
are called probability amplitudes. In a balanced
superposition, = 1/√2 where n is the number of qubits.
1 2 1
n
10. Relationships among data - Entanglement
Entanglement is the ability of quantum systems to exhibit
correlations between states within a superposition.
Imagine two qubits, each in the state |0> + |1> (a superposition
of the 0 and 1.) We can entangle the two qubits such that the
measurement of one qubit is always correlated to the
measurement of the other qubit.
11. Overview
Introduction and History
Data Representation
Operations on Data
Shor’s Algorithm
Conclusion and Open Questions
12. Due to the nature of quantum physics, the destruction of
information in a gate will cause heat to be evolved which can
destroy the superposition of qubits.
Operations on Qubits - Reversible Logic
A B C
0 0 0
0 1 0
1 0 0
1 1 1
Input Output
A
B
C
In these 3 cases,
information is
being destroyed
Ex.
The AND Gate
This type of gate cannot be used. We must use
Quantum Gates.
13. Quantum Gates
Quantum Gates are similar to classical gates, but do not have
a degenerate output. i.e. their original input state can be derived
from their output state, uniquely. They must be reversible.
This means that a deterministic computation can be performed
on a quantum computer only if it is reversible. Luckily, it has
been shown that any deterministic computation can be made
reversible.(Charles Bennet, 1973)
14. Quantum Gates - Hadamard
Simplest gate involves one qubit and is called a Hadamard
Gate (also known as a square-root of NOT gate.) Used to put
qubits into superposition.
H
State
|0>
State
|0> + |1>
H
State
|1>
Note: Two Hadamard gates used in
succession can be used as a NOT gate
15. Quantum Gates - Controlled NOT
A gate which operates on two qubits is called a Controlled-
NOT (CN) Gate. If the bit on the control line is 1, invert
the bit on the target line.
A - Target
B - Control
A B A’ B’
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 1
Input Output
Note: The CN gate has a similar
behavior to the XOR gate with some
extra information to make it reversible.
A’
B’
16. Example Operation - Multiplication By 2
Carry Bit
Carry
Bit
Ones
Bit
Carry
Bit
Ones
Bit
0 0 0 0
0 1 1 0
Input Output
Ones Bit
We can build a reversible logic circuit to calculate multiplication
by 2 using CN gates arranged in the following manner:
0
H
17. Quantum Gates - Controlled Controlled NOT (CCN)
A - Target
B - Control 1
C - Control 2
A B C A’ B’ C’
0 0 0 0 0 0
0 0 1 0 0 1
0 1 0 0 1 0
0 1 1 1 1 1
1 0 0 1 0 0
1 0 1 1 0 1
1 1 0 1 1 0
1 1 1 0 1 1
Input Output
A’
B’
C’
A gate which operates on three qubits is called a
Controlled Controlled NOT (CCN) Gate. Iff the bits on
both of the control lines is 1,then the target bit is inverted.
18. A Universal Quantum Computer
The CCN gate has been shown to be a universal reversible
logic gate as it can be used as a NAND gate.
A - Target
B - Control 1
C - Control 2
A B C A’ B’ C’
0 0 0 0 0 0
0 0 1 0 0 1
0 1 0 0 1 0
0 1 1 1 1 1
1 0 0 1 0 0
1 0 1 1 0 1
1 1 0 1 1 0
1 1 1 0 1 1
Input Output
A’
B’
C’
When our target input is 1, our target
output is a result of a NAND of B and C.
19. Overview
Introduction and History
Data Representation
Operations on Data
Shor’s Algorithm
Conclusion and Open Questions
20. Shor’s Algorithm
Shor’s algorithm shows (in principle,) that a quantum
computer is capable of factoring very large numbers in
polynomial time.
The algorithm is dependant on
Modular Arithmetic
Quantum Parallelism
Quantum Fourier Transform
21. Shor’s Algorithm - Periodicity
Choose N = 15 and x = 7 and we get the following:
7 mod 15 = 1
7 mod 15 = 7
7 mod 15 = 4
7 mod 15 = 13
7 mod 15 = 1
0
1
2
3
4
An important result from Number Theory:
F(a) = x mod N is a periodic function
a
.
.
.
22. Shor’s Algorithm - In Depth Analysis
To Factor an odd integer N (Let’s choose 15) :
1. Choose an integer q such that N < q < 2N let’s pick 256
2. Choose a random integer x such that GCD(x, N) = 1 let’s pick 7
3. Create two quantum registers (these registers must also be
entangled so that the collapse of the input register corresponds to
the collapse of the output register)
• Input register: must contain enough qubits to represent
numbers as large as q-1. up to 255, so we need 8 qubits
• Output register: must contain enough qubits to represent
numbers as large as N-1. up to 14, so we need 4 qubits
2 2
23. Shor’s Algorithm - Preparing Data
4. Load the input register with an equally weighted
superposition of all integers from 0 to q-1. 0 to 255
5. Load the output register with all zeros.
The total state of the system at this point will be:
1
√256
∑ |a, 000>
a=0
255
Input
Register
Output
Register
Note: the comma here
denotes that the
registers are entangled
24. Shor’s Algorithm - Modular Arithmetic
6. Apply the transformation x mod N to each number in
the input register, storing the result of each computation
in the output register.
a
Input Register 7 Mod 15 Output Register
|0> 7 Mod 15 1
|1> 7 Mod 15 7
|2> 7 Mod 15 4
|3> 7 Mod 15 13
|4> 7 Mod 15 1
|5> 7 Mod 15 7
|6> 7 Mod 15 4
|7> 7 Mod 15 13
a
0
1
7
6
5
4
3
2
Note that we are using decimal
numbers here only for simplicity.
.
.
25. Shor’s Algorithm - Superposition Collapse
7. Now take a measurement on the output register. This will
collapse the superposition to represent just one of the results
of the transformation, let’s call this value c.
Our output register will collapse to represent one of
the following:
|1>, |4>, |7>, or |13
For sake of example, lets choose |1>
26. Shor’s Algorithm - Entanglement
8. Since the two registers are entangled, measuring the output
register will have the effect of partially collapsing the input
register into an equal superposition of each state between 0
and q-1 that yielded c (the value of the collapsed output
register.)
Now things really get interesting !
Since the output register collapsed to |1>, the input register
will partially collapse to:
|0> + |4> + |8> + |12>, . . .
The probabilities in this case are since our register is
now in an equal superposition of 64 values (0, 4, 8, . . . 252)
1
√64
1
√64
1
√64
1
√64
1
√64
27. Shor’s Algorithm - QFT
We now apply the Quantum Fourier transform on the
partially collapsed input register. The fourier transform has
the effect of taking a state |a> and transforming it into a
state given by:
1
√q
∑ |c> * e
c=0
q-1
2iac / q
28. Shor’s Algorithm - QFT
1
√256
∑ |c> * e
c=0
255
2iac / 256
1
√64
∑ |a> , |1>
a A
Note: A is the set of all values that 7 mod 15 yielded 1.
In our case A = {0, 4, 8, …, 252}
So the final state of the input register after the QFT is:
a
1
√64
∑ , |1>
a A
1
√256
∑ |c> * e
c=0
255
2iac / 256
29. Shor’s Algorithm - QFT
The QFT will essentially peak the probability amplitudes at
integer multiples of q/4 in our case 256/4, or 64.
|0>, |64>, |128>, |192>, …
So we no longer have an equal superposition of states, the
probability amplitudes of the above states are now higher
than the other states in our register. We measure the register,
and it will collapse with high probability to one of these
multiples of 64, let’s call this value p.
With our knowledge of q, and p, there are methods of
calculating the period (one method is the continuous fraction
expansion of the ratio between q and p.)
30. Shor’s Algorithm - The Factors :)
10. Now that we have the period, the factors of N can be
determined by taking the greatest common divisor of N
with respect to x ^ (P/2) + 1 and x ^ (P/2) - 1. The idea
here is that this computation will be done on a classical
computer.
We compute:
Gcd(7 + 1, 15) = 5
Gcd(7 - 1, 15) = 3
We have successfully factored 15!
4/2
4/2
31. Shor’s Algorithm - Problems
The QFT comes up short and reveals the wrong period. This
probability is actually dependant on your choice of q. The
larger the q, the higher the probability of finding the correct
probability.
The period of the series ends up being odd
If either of these cases occur, we go back to
the beginning and pick a new x.
32. Overview
Introduction and History
Data Representation
Operations on Data
Shor’s Algorithm
Conclusion and Open Questions
33. Conclusion
In 2001, a 7 qubit machine was built and programmed to run
Shor’s algorithm to successfully factor 15.
What algorithms will be discovered next?
Can quantum computers solve NP Complete problems in
polynomial time?