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Deterministic quantum computation with one-clean-qubit model as an open quantum system

Jake Xuereb1,2,3,*, Steve Campbell2,4, John Goold3, and André Xuereb1

  • 1Department of Physics, University of Malta, Msida MSD 2080, Malta
  • 2School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
  • 3School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
  • 4Centre for Quantum Engineering, Science, and Technology, University College Dublin, Belfield, Dublin 4, Ireland

  • *jqed.xuereb@gmail.com
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Phys. Rev. A 107, 042222 – Published 28 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042222

Abstract

The deterministic quantum computation with one-clean-qubit model (DQC1) complexity class, or power-of-one qubit model, is examined as an open quantum system. We study the dynamics of a register of qubits carrying out a DQC1 algorithm and show that, for any algorithm in the complexity class, the evolution of the logical qubit can be described as an open quantum system undergoing a dynamics which is unital. Unital quantum channels respect the Tasaki-Crooks fluctuation theorem, and we demonstrate how this is captured by the thermodynamics of the logical qubit. As an application, we investigate the equilibrium and nonequilibrium thermodynamics of the DQC1 trace estimation algorithm. We show that different computational inputs, i.e., different traces being estimated, lead to different energetic exchanges across the register of qubits and that the temperature of the logical qubit impacts the magnitude of fluctuations experienced and quality of the algorithm.

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Outline

Information

Phys. Rev. A 107, 042222– Published 28 April, 2023
  • Received 21 October 2022
  • Accepted 28 March 2023
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