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Quantum Information Processing

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Computational Complexity

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Article Outline

Glossary

Definition of the Subject

Introduction

Quantum Mechanics

Quantum Computation

Noise and Errors

Quantum Communication

Implications and Conclusions

Bibliography

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Abbreviations

Algorithm:

A systematic procedure for solving a problem, frequently implemented as a computer program.

Bit:

The fundamental unit of information, representing the distinction between two possible states, conventionally called 0 and 1. The word ‘bit’ is also used to refer to a physical system that registers a bit of information.

Boolean algebra:

The mathematics of manipulating bits using simple operations such as AND, OR, NOT, and COPY.

Communication channel:

A physical system that allows information to be transmitted from one place to another.

Computer:

A device for processing information. A digital computer uses Boolean algebra (q. v.) to processes information in the form of bits.

Cryptography:

The science and technique of encoding information in a secret form. The process of encoding is called encryption, and a system for encoding and decoding is called a cipher. A key is a piece of information used for encoding or decoding. Public‑key cryptography operates using a public key by which information is encrypted, and a separate private key by which the encrypted message is decoded.

Decoherence:

A peculiarly quantum form of noise that has no classical analog. Decoherence destroys quantum superpositions and is the most important and ubiquitous form of noise in quantum computers and quantum communication channels.

Error‐correcting code:

A technique for encoding information in a form that is resistant to errors. The syndrome is the part of the code that allows the error to be detected and that specifies how it should be corrected.

Entanglement:

A peculiarly quantum form of correlation that is responsible for many types of quantum weirdness. Entanglement arises when two or more quantum systems exist in a superposition of correlated states.

Entropy:

Information registered by the microscopic motion of atoms and molecules. The second law of thermodynamics (q. v.)states that entropy does not decrease over time.

Fault‐tolerant computation:

Computation that uses error‐correcting codes to perform algorithms faithfully in the presence of noise and errors. If the rate of errors falls below a certain threshold, then computations of any desired length can be performed in a fault‐tolerant fashion. Also known as robust computation.

Information:

When used in a broad sense, information is data, messages, meaning, knowledge, etc. Used in the more specific sense of information theory, information is a quantity that can be measured in bits.

Logic gate:

A physical system that performs the operations of Boolean algebra (q. v.) such as AND, OR, NOT, and COPY, on bits.

Moore's law:

The observation, first made by Gordon Moore, that the power of computers increases by a factor of two every year and a half or so.

Quantum algorithm:

An algorithm designed specifically to be performed by a quantum computer using quantum logic. Quantum algorithms exploit the phenomena of superposition and entanglement to solve problems more rapidly than classical computer algorithms can. Examples of quantum algorithms include Shor's algorithm for factoring large numbers and breaking public‑key cryptosystems, Grover's algorithm for searching databases, quantum simulation, the adiabatic algorithm, etc.

Quantum bit:

A bit registered by a quantum‐mechanical system such as an atom, photon, or nuclear spin. A quantum bit, or ‘qubit’, has the property that it can exist in a quantum superposition of the states 0 and 1.

Qubit:

A quantum bit.

Quantum communication channel:

A communication channel that transmits quantum bits. The most common communication channel is the bosonic channel, which transmits information using light, sound, or other substances whose elementary excitations consist of bosons (photons for light, phonons for sound).

Quantum computer:

A computer that operates on quantum bits to perform quantum algorithms. Quantum computers have the feature that they can preserve quantum superpositions and entanglement.

Quantum cryptography:

A cryptographic technique that encodes information on quantum bits. Quantum cryptography uses the fact that measuring quantum systems typically disturbs them to implement cryptosystems whose security is guaranteed by the laws of physics. Quantum key distribution (QKD) is a quantum cryptographic technique for distributing secret keys.

Quantum error‐correcting code:

An error‐correcting code that corrects for the effects of noise on quantum bits. Quantum error‐correcting codes can correct for the effect of decoherence (q. v.) as well as for conventional bit‑flip errors.

Quantum information:

Information that is stored on qubits rather than on classical bits.

Quantum mechanics:

The branch of physics that describes how matter and energy behave at their most fundamental scales. Quantum mechanics is famously weird and counterintuitive.

Quantum weirdness:

A catch‑all term for the strange and counterintuitive aspects of quantum mechanics. Well‑known instances of quantum weirdness include Schrödinger's cat (q. v.), the Einstein–Podolsky–Rosen thought experiment, violations of Bell's inequalities, and the Greenberger–Horne–Zeilinger experiment.

Reversible logic:

Logical operations that do not discard information. Quantum computers operate using reversible logic.

Schrödinger's cat:

A famous example of quantum weirdness. A thought experiment proposed by Erwin Schrödinger, in which a cat is put in a quantum superposition of being alive and being dead. Not sanctioned by the Society for Prevention of Cruelty to Animals.

Second law of thermodynamics:

The second law of thermodynamics states that entropy does not increase. An alternative formulation of the second law states that it is not possible to build an eternal motion machine.

Superposition:

The defining feature of quantum mechanics which allows particles such as electrons to exist in two or more places at once. Quantum bits can exist in superpositions of 0 and 1 simultaneously.

Teleportation:

A form of quantum communication that uses pre‑existing entanglement and classical communication to send quantum bits from one place to another.

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Authors and Affiliations

  1. W.M. Keck Center for Extreme Quantum Information Processing (xQIT), MIT, Cambridge, USA

    Seth Lloyd

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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Lloyd, S. (2012). Quantum Information Processing . In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_153

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