The Heisenberg representation of quantum computers

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Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. ... continued below

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20 p.

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Gottesman, D. June 24, 1998.

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Description

Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.

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20 p.

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OSTI as DE99001840

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  • Group theoretical methods in physics, Hobart (Australia), 13-17 Jul 1998

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  • Other: DE99001840
  • Report No.: LA-UR--98-2848
  • Report No.: CONF-980788--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 319738
  • Archival Resource Key: ark:/67531/metadc685467

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  • June 24, 1998

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  • July 25, 2015, 2:20 a.m.

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  • May 20, 2016, 2:52 p.m.

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Gottesman, D. The Heisenberg representation of quantum computers, article, June 24, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc685467/: accessed September 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.