# Quantum Computation And Quantum Information Chuang Pdf

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*Not a MyNAP member yet? Register for a free account to start saving and receiving special member only perks. Quantum mechanics, the subfield of physics that describes the behavior of very small particles, provides the basis for a new paradigm of computing.*

- Michael Nielsen's articles on arXiv
- CMSC/PHYS 457: Introduction to quantum computing (Spring 2019)
- Quantum Information Theory (Spring 2019)

## Michael Nielsen's articles on arXiv

Not a MyNAP member yet? Register for a free account to start saving and receiving special member only perks. Quantum mechanics, the subfield of physics that describes the behavior of very small particles, provides the basis for a new paradigm of computing.

While these results were very exciting in the s, they were only of theoretical interest: no one knew of a method to build a computer out of quantum systems. Quantum computers are the only known computing technology that violates this thesis. Nielsen, Michael A. An introduction to quantum computing. Oxford University Press, This work has reinvigorated the field and led to significant private sector investment.

A classical computer uses bits to represent the values it is operating on; a quantum computer uses quantum bits, or qubits. While the state of a classical computer is determined by the binary values of a collection of bits, at any single point in time the state of a quantum computer with the same number of quantum bits can span all possible states of the corresponding classical computer, and thus works in an exponentially larger problem space.

Many innovations over the past 25 years have enabled researchers to build physical systems that are starting to provide the needed isolation and control for quantum computing. Even if one is able to make very high quality qubits, creating and making use of these quantum computers QCs brings a new set of challenges.

They use a different set of operations than those of classical computers, requiring new algorithms, software, control technologies, and hardware abstractions. One of the major differences between a classical computer and a quantum computer is in how it handles small unwanted variations, or noise, in the system. Since a classical bit is either one or zero, even if the value is slightly off some noise in the system it is easy for the operations on that signal to remove that noise.

Because a qubit can be any combination of one and zero, qubits and quantum gates cannot readily reject small errors noise that occur in physical circuits.

As a result, small errors in creating the desired quantum operations, or any stray signals that couple into the physical system, can eventually lead to wrong outputs appearing in the computation. Thus, one of the most important design parameters for systems that operate on physical qubits is their error rate.

Low error rates have been difficult to achieve; even in mid, the error rates for 2-qubit operations on systems with 5 or more qubits are more than a few percent. Better error rates have been demonstrated in smaller systems, and this improved operation fidelity needs to move to larger qubit systems for quantum computing to be successful see Section 2. While QECs will be essential to create error-free quantum computers in the future, they are too resource intensive to be used in the short term: quantum computers in the near term are likely to have errors.

This class of machines is referred to as noisy intermediate-scale quantum NISQ computers see Section 3. While a quantum computer can use a small number of qubits to represent an exponentially larger amount of data, there is not currently a method to rapidly convert a large amount of classical data to a quantum state 2 this does not apply if the data can be generated algorithmically.

For problems that require large inputs, the amount of time needed to create the input quantum state would typically dominate the computation time, and greatly reduce the quantum advantage. This means that one can extract only the same amount of data from a quantum computer that one could from a classical computer of the same size. To reap the benefit of a quantum computer, quantum algorithms must leverage uniquely quantum features such as interference and entanglement to arrive at the final classical result.

Thus, achieving quantum speedup requires totally new kinds of algorithm design principles and very clever algorithm design. Quantum algorithm development is a critical aspect of the field see Chapter 3. As with all computers, building a useful device is much more complex than just creating the hardware—tools are needed to create and debug QC-specific software.

Since quantum programs are different from programs for classical computers, research and development is needed to further develop the software tool stack. Because these software tools drive the hardware, contemporaneous development of the hardware and software tool chain will shorten the development time for a useful quantum computer.

In fact, using early tools to complete the end-to-end design application design to final results helps elucidate hidden issues and drives toward designs with the best chance for overall success, an approach used in classical computer design see Section 6.

Methods to debug quantum hardware and software are of critical importance. Current debugging methods for classical computers rely on memory, and the reading of intermediate machine states. Neither is possible in a quantum computer. A quantum state cannot simply be copied per the so-called no-cloning theorem for later examination, and any measurement of a quantum state collapses it to a set of classical bits, bringing computation to a halt.

New approaches to debugging are essential for the development of large-scale quantum computers see Section 6. Predicting the future is always risky, but it can be attempted when the product of interest is an extrapolation of current devices that does not span too many orders of magnitude.

RSA encrypted message requires building a machine that is more than five orders of magnitude larger and has error rates that are about two orders of magnitude better than current machines, as well as developing the software development environment to support this machine. The progress required to bridge this gap makes it impossible to project the time frame for a large error-corrected quantum computer, and while significant progress in these areas continues, there is no guarantee that all of these challenges will be overcome.

The process of bridging this gap might expose unanticipated challenges, require techniques that are not yet invented, or shift owing to new results of foundational scientific research that change our understanding of the quantum world. Rather than speculating on a specific time frame, the committee identified factors that will affect the rate of technology innovation and proposed two metrics and several milestones for monitoring progress in the field moving forward see Section 7.

Given the unique characteristics and challenges of quantum computers, they are unlikely to be useful as a direct replacement for classical computers. In fact, they require a number of classical computers to control their operations and carry out computations needed to implement quantum error correction. Thus, they are currently being designed as special-purpose devices operating in a complementary fashion with classical processors, analogous to a co-processor or an accelerator see Section 5.

In rapidly advancing fields, where there are many unknowns and hard problems, the rate of overall development is set by the ability of the whole community to take advantage of new approaches and insights. Fields where research results are kept secret or proprietary progress much more slowly. Fortunately, many quantum computing researchers have been open about sharing advances to date, and the field will benefit greatly by continuing with this philosophy see Section 7.

Key Finding 9: An open ecosystem that enables cross-pollination of ideas and groups will accelerate rapid technology advancement. Chapter 7. In the absence of intermediate successes yielding commercial revenue, progress will depend on governmental agencies continuing to increase funding of this effort.

Even in this scenario, successful completion of intermediate milestones is likely to be essential see Section 1. While many interesting applications exist for large error-corrected quantum computers, practical applications for NISQ computers do not currently exist. Creating practical applications for NISQ computers is a relatively new area of research and will require work on new types of quantum algorithms.

Developing commercial NISQ computer applications by the early s will be essential to starting this virtuous cycle of investment see Section 3. Key Finding 3: Research and development into practical commercial applications of noisy intermediate-scale quantum NISQ computers is an issue of immediate urgency for the field. The results of this work will have a profound impact on the rate of development of large-scale quantum computers and on the size and robustness of a commercial market for quantum computers.

Quantum computers can be divided into three general categories or types. Examples of analog machines include quantum annealers, adiabatic quantum computers, and direct quantum simulators. Noise is present in both of these types of machine, which means that the quality measured by error rates and qubit coherence times will limit the complexity of the problems that these machines can solve.

The first milestones of progress in QC were the demonstration of simple proof-of-principle analog and digital systems. Small digital NISQ computers became available in , with tens of qubits with errors too. Work in quantum annealing began approximately a decade earlier using qubits built with a technology that had lower coherence times but that allowed them to scale more rapidly.

Thus, by experimental quantum annealers had grown to machines with around 2, qubits. From this starting point, progress can be identified with the achievement of one of several possible milestones. While several teams have been focused on this goal, it has not yet been demonstrated as of mid Another major milestone is creating a commercially useful quantum computer, which would require a QC that carries out at least one practical task more efficiently than any classical computer.

While this milestone is in theory harder than achieving quantum supremacy—since the application in question must be better and more useful than available classical approaches— proving quantum supremacy could be difficult, especially for analog QC.

Thus, it is possible that a useful application could arise before quantum supremacy is demonstrated. Deployment of QEC on a QC to create a logical qubit with a significant reduction in error rate is another major milestone and is the first step to creating fully error-corrected machines see Section 7. Progress in gate-based quantum computing can be monitored by tracking the key properties that define the quality of a quantum processor: the effective error rates of the single-qubit and two-qubit operations, the interqubit connectivity, and the number of qubits contained within a single hardware module.

Key Finding 4: Given the information available to the committee, it is still too early to be able to predict the time horizon for a scalable quantum computer. Instead, progress can be tracked in the near term by monitoring the scaling rate of physical qubits at constant average gate error rate , as evaluated using randomized benchmarking, and in the long term by monitoring the effective number of logical error-corrected qubits that a system represents.

Tracking the size and scaling rate for logical qubits will provide a better estimate on the timing of future milestones. Key Finding 5: The state of the field would be much easier to monitor if the research community adopted clear reporting conventions to enable comparison between devices and translation into metrics such as those. A set of benchmarking applications that enable comparison between different machines would help drive improvements in the efficiency of quantum software and the architecture of the underlying quantum hardware.

It is clear that efforts to develop quantum computers and other quantum technologies are under way around the world. It is expected that large, concerted research efforts entailing both foundational scientific advances and new strategies in engineering—spanning multiple traditional disciplines—will be required to build a successful QC.

Key Finding 8: While the United States has historically played a leading role in developing quantum technologies, quantum information science and technology is now a global field. Given the large resource commitment several non-U.

Furthermore, the private sector currently plays a large role in the U. Key Finding 2: If near-term quantum computers are not commercially successful, government funding may be essential to prevent a significant decline in quantum computing research and development.

Quantum computing will have a major impact on cryptography, which relies upon hard-to-compute problems to protect data. There is strong commercial interest in deploying post-quantum cryptography well before such a quantum computer has been built. Companies and governments cannot afford to have their now-private communications decrypted in the future, even if that future is 30 years away.

For this reason, there is a need to begin the transition to post-quantum cryptography as soon as possible, especially since it takes over a decade to make existing Web standards obsolete see Section 4.

Key Finding 1: Given the current state of quantum computing and recent rates of progress, it is highly unexpected that a quantum computer that can compromise RSA or comparable discrete logarithm-based public key cryptosystems will be built within the next decade. Key Finding Even if a quantum computer that can decrypt current cryptographic ciphers is more than a decade off, the hazard of such a machine is high enough—and the time frame for transitioning to a new security protocol is sufficiently long and uncertain—that prioritization of the development, standardization, and deployment of post-quantum cryptography is critical for minimizing the chance of a potential security and privacy disaster.

Given the large risk a quantum computer poses to current protocols, there is an active effort to develop post-quantum cryptography, asymmetric ciphers that a quantum computer cannot defeat. These are likely to be standardized in the s. Significant technical barriers remain before a practical QC can be achieved, and there is no guarantee that they will be overcome. Building and using QCs will require not only device engineering but also fundamental progress at the convergence of a host of scientific disciplines—from computer science and mathematics to physics, chemistry, and materials science.

Yet these efforts also offer potential benefits. As with all foundational scientific research, discoveries from this field could lead to transformative new knowledge and applications. The challenges to creating a large, error-corrected quantum computer are significant. Successful quantum computation will require unprecedented control of quantum coherence, pushing the boundaries of what is possible by refining existing tools and techniques—or perhaps even by developing new ones.

Related technologies, such as quantum sensing and quantum communication, that also rely upon quantum coherence control may also leverage these advances see Section 2.

Key Finding 7: Although the feasibility of a large-scale quantum computer is not yet certain, the benefits of the effort to develop a practical QC are likely to be large, and they may continue to spill over to other nearer-term applications of quantum information technology, such as qubit-based sensing.

## CMSC/PHYS 457: Introduction to quantum computing (Spring 2019)

This course is part of a three-course series that provides an introduction to the theory and practice of quantum computation. We cover: the physics of information processing quantum logic quantum algorithms including Shor's factoring algorithm and Grover's search algorithm quantum error correction quantum communication and key distribution. This course will help you establish a foundation of knowledge for understanding what quantum computers can do, how they work, and how you can contribute to discovering new things and solving problems in quantum information science and engineering. The three-course series comprises: 8. Prior knowledge of quantum mechanics is helpful but not required. This course has been authored by one or more members of the Faculty of the Massachusetts Institute of Technology.

See author identifier help for more information about arXiv author identifiers, please report any problems. We gratefully acknowledge support from the Simons Foundation and member institutions. Authors: Alexei Gilchrist , Nathan K. Langford , Michael A. Comments: 15 pages; this version in line with published version.

Formidable, mathematically rigorous, page textbook. Quite a treatment, considering that quantum computers might not ever be buildable. Michael Nielsen was born in Brisbane, Australia in , and was educated at the University of Queensland, obtaining postgraduate degrees in mathematics and physics, before being awarded his PhD in physics at the University of New Mexico in Isaac Chuang is a native of Louisville, KY. He received his doctorate in electrical engineering from Stanford University in , where he was a Hertz Foundation Fellow, and holds two bachelors degrees and one masters degree in physics and electrical engineering from the Massachusetts Institute of Technology.

## Quantum Information Theory (Spring 2019)

Homework for the week. Course description. Nielsen, Isaac L.

#### WHY BUILDING AND USING A QUANTUM COMPUTER IS CHALLENGING

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Nielsen and I. Nielsen , I. Chuang Published Physics.

Quantum Computation and Quantum Information is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang , regarded as a standard text on the subject. Peter Shor called the text "an excellent book". Lov Grover called it "the bible of the quantum information field". Scott Aaronson said about it, " 'Mike and Ike' as it's affectionately called, remains the quantum computing textbook to which all others are compared. From Wikipedia, the free encyclopedia. Textbook by scientists Michael Nielsen and Isaac Chuang.

This is the course homepage. See here for the course homepage for The MasterMath course page is the primary source for all course material. Thanks very much for attending our course — and good luck with the exam! With the birth of Quantum Mechanics a century ago, our understanding of the physical world has profoundly expanded, and so has our understanding of information. Quantum Information Theory studies the remarkable properties of this new type of information, ways of processing it, as well as its advantages and limitations.

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