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Quantum Computation

Quantum Computation




instructor:-John Preskill







Course Description



The theory of quantum information and quantum computation. Overview of classical information theory, compression of quantum information, transmission of quantum information through noisy channels, quantum entanglement, quantum cryptography. Overview of classical complexity theory, quantum complexity, efficient quantum algorithms, quantum error-correcting codes, fault-tolerant quantum computation, physical implementations of quantum computation.

Prerequisites

The course material should be of interest to physicists, mathematicians, computer scientists, and engineers, so we hope to make the course accessible to people with a variety of backgrounds.
Certainly it would be useful to have had a previous course on quantum mechanics, though this may not be essential. It would also be useful to know something about (classical) information theory,  (classical) coding theory,  and (classical) complexity theory, since a central goal of the course will be generalize these topics to apply to quantum information. But we will review this material when we get to it, so you don't need to worry if you haven't seen it before. In the discussion of quantum coding, we will use some rudimentary group theory.




Course Overview

Information is something that can be encoded in the state of a physical system, and a computation is a task that can be performed with a physically realizable device. Therefore, since the physical world is fundamentally quantum mechanical, the foundations of information theory and computer science should be sought in quantum physics.
In fact, quantum information -- information stored in the quantum state of a physical system -- has weird properties that contrast sharply with the familiar properties of "classical" information. And a quantum computer -- a new type of machine that exploits the quantum properties of information -- could perform certain types of calculations far more efficiently than any foreseeable classical computer.
In this course, we will study the properties that distinguish quantum information from classical information. And we will see how these properties can be exploited in the design of quantum algorithms that solve certain problems faster than classical algorithms can.
A quantum computer will be much more vulnerable than a conventional digital computer to the effects of noise and of imperfections in the machine. Unavoidable interactions of the device with its surroundings will damage the quantum information that it encodes, a process known as decoherence. Schemes must be developed to overcome this difficulty if quantum computers are ever to become practical devices.
In this course, we will study quantum error-correcting codes that can be exploited to protect quantum information from decoherence and other potential sources of error. And we will see how coding can enable a quantum computer to perform reliably despite the inevitable effects of noise.
Building a quantum computer that really works will not be easy. Experimental physicists are now just beginning to build and operate hardware that can coherently process quantum information.
In this course, we will learn about the pioneering efforts to operate quantum computing hardware, using ion traps, cavity quantum electrodynamics, and nuclear magnetic resonance.

Lecture Notes

The first 6 chapters were originally prepared in 1997-98. They were last updated on 2 October 1998. Chapter 7 was added in 1999 and was last updated on 23 February 1999. (Sorry, the figures for Chapter 7 are not available.)  Chapter 8 (Fault-tolerant quantum computation) is not yet available. Chapter 9 was added in 2004. There is also an updated (though incomplete) version of Chapter 4, prepared in 2001.




Chapters 1-6 in one file,  321 pages (ps format)
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