Error-correcting codes for adiabatic quantum computation

Stephen P. Jordan, Edward Farhi, and Peter W. Shor
Phys. Rev. A 74, 052322 – Published 14 November 2006

Abstract

Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent resistance to noise. It is now known that universal quantum computation can be achieved adiabatically using two-local Hamiltonians. The energy gap in these Hamiltonians scales as an inverse polynomial in the number of quantum gates being simulated. Here we present stabilizer codes which can be used to produce a constant energy gap against one-local and two-local noise. The corresponding fault-tolerant universal Hamiltonians are four-local and six-local, respectively, which are the optimal result achievable within this framework.

  • Received 20 March 2006

DOI:https://doi.org/10.1103/PhysRevA.74.052322

©2006 American Physical Society

Authors & Affiliations

Stephen P. Jordan1,*, Edward Farhi1, and Peter W. Shor2

  • 1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Mathematics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *Electronic address: sjordan@mit.edu

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Issue

Vol. 74, Iss. 5 — November 2006

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