Simulation of single-qubit open quantum systems

Ryan Sweke, Ilya Sinayskiy, and Francesco Petruccione
Phys. Rev. A 90, 022331 – Published 27 August 2014; Erratum Phys. Rev. A 95, 069905 (2017)

Abstract

A quantum algorithm is presented for the simulation of arbitrary Markovian dynamics of a qubit, described by a semigroup of single-qubit quantum channels {Tt} specified by a generator L. This algorithm requires only single-qubit and controlled-not gates and approximates the channel Tt=etL up to the chosen accuracy ε, with a slightly superlinear cost O((L(11)t)1+1/2k/ε1/2k) for any integer k. Inspired by developments in Hamiltonian simulation, a decomposition and recombination technique is utilized which allows for the exploitation of recently developed methods for the approximation of arbitrary single-qubit channels. In particular, as a result of these methods the algorithm requires only a single ancilla qubit, the minimal possible dilation for a nonunitary single-qubit quantum channel.

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  • Received 26 May 2014

DOI:https://doi.org/10.1103/PhysRevA.90.022331

©2014 American Physical Society

Erratum

Erratum: Simulation of single-qubit open quantum systems [Phys. Rev. A 90, 022331 (2014)]

Ryan Sweke, Ilya Sinayskiy, and Francesco Petruccione
Phys. Rev. A 95, 069905 (2017)

Authors & Affiliations

Ryan Sweke*

  • Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4001, South Africa

Ilya Sinayskiy and Francesco Petruccione

  • Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4001, South Africa and National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, South Africa

  • *rsweke@gmail.com
  • sinayskiy@ukzn.ac.za
  • petruccione@ukzn.ac.za

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Issue

Vol. 90, Iss. 2 — August 2014

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