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Quantum Computing

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

Quantum computing is computing that follows the logic of quantummechanics. The first part of this subject is well‐specified after the hundred‐odd years of developmentof quantum theory. Definitions of computing are fuzzier, and argued over by philosophers: for the purposes of thisarticle we will leave such nuances aside in favor of exploring what is possible when the constraints of classicallogic are put aside, but the limitations of the physical world are kept firmly in hand.

Quantum computing is not simply computing that involves quantum effects, that would be too broad to beuseful. Since transitors and lasers exploit quantum properties of matter and light, most classical computers wouldthus be included. Yet it is worth remembering that definitions are never as clearcut as we would like. Figuringout which quantum systems can be simulated efficiently by classical computers is an active area of currentresearch, and pinning down the boundary between quantum and...

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Abbreviations

Bit:

A  two state classical system used to represent a binary digit, zero or one.

Bose–Einstein particles:

Integer spin quantum particles like to be together: any number can occupy the same quantum state.

Classical computing:

What we can compute within the laws of classical physics.

Error correction:

In a quantum context, fixing errors without disturbing the quantum superposition.

Entanglement:

Quantum states can be more highly correlated than classical systems: the extra correlations are known as entanglement.

Fermi–Dirac particles:

Half‐integer spin quantum particles like to be alone: only one such particle can occupy each quantum state.

Quantum communications:

Using quantum mechanics can gain an advantage when transmitting information.

Quantum dense coding:

Classical bits can be encoded two for one into qubits for communications purposes.

Quantum key distribution:

Quantum mechanics allows for secure key distribution in the presence of eavesdroppers and noisy environments. The keys can then be used for encrypted communication.

Quantum teleportation:

A method to transmit an unknown quantum state using only classical communications plus shared entanglement.

Quantum computing:

Computation based on the laws of quantum mechanics for the allowed logical operations.

Qubit:

A two state quantum system such as the spin of an electron or the polarization of a photon. More complex quantum particles (such as atoms) can be used as qubits if just two of their available states are chosen to represent the qubit.

Qubus:

A quantum version of a computer bus, the fast communications linking memory and processing registers. Can be implemented using a coherent light source (such as a laser).

Scalable:

A computer architecture designed from modular units that can be efficiently expanded to an arbitrary size.

Squeezing:

With a pair of complementary quantum observables, making one uncertain so that the other can be measured more precisely.

Threshold result:

In the context of quantum computation, this results says that error correction can work if the error rate is low enough.

Tunneling:

Quantum particles can get through barriers that classical particles remain stuck behind. If the barrier is not infinitely high, there is a some probability for the quantum particle to be the other side of it even though it doesn't on average have enough energy to jump over the top.

Unitary operations:

How to control quantum systems while preserving quantum properties. Quantum systems evolving without any influence from environmental disturbance follow unitary dynamical evolution.

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Further Reading

  1. For those who seriously want to learn the quantitative details of quantum computing, this is still the best textbook: Nielsen MA, Chuang IL (2000) Quantum Computation and Quantum Information. CUP, Cambs

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  2. For lighter browsing but still with all the technical details, there are several quantum wikis developed by the scientists doing the research:

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  3. Quantiki http://www.quantiki.org/wiki/index.php/Main_Page specifically quantum information

  4. Qwiki http://qwiki.stanford.edu/wiki/Main_Page covers wider quantum theory and experiments

  5. For those still struggling with the concepts (which probably means most people without a physics degree or other formal study of quantum theory), there are plenty of popular science books and articles. Please dive in, it's the way the world we all live in works, and there is no reason not dig in deep enough to marvel at the way it fits together and puzzle with the best of us about the bits we can't yet fathom.

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Author information

Authors and Affiliations

  1. School of Physics and Astronomy, University of Leeds, Leeds, UK

    Viv Kendon

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  1. Viv Kendon
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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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Kendon, V. (2009). Quantum Computing. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_429

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