Lower bounds on the complexity of simulating quantum gates

Andrew M. Childs; Henry L. Haselgrove; Michael A. Nielsen

doi:10.1103/PhysRevA.68.052311

Lower bounds on the complexity of simulating quantum gates

Andrew M. Childs, Henry L. Haselgrove, and Michael A. Nielsen

Phys. Rev. A 68, 052311 – Published 18 November 2003

Abstract

We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates.

Received 4 August 2003

DOI:https://doi.org/10.1103/PhysRevA.68.052311

Authors & Affiliations

Andrew M. Childs^1,*, Henry L. Haselgrove^2,3,†, and Michael A. Nielsen^2,4,5,‡

¹Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²School of Physical Sciences, The University of Queensland, Brisbane QLD 4072, Australia
³Information Sciences Laboratory, Defence Science and Technology Organisation, Edinburgh 5111, Australia
⁴School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane QLD 4072, Australia
⁵Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA

^*Electronic address: amchilds@mit.edu
^†Electronic address: hlh@physics.uq.edu.au
^‡Electronic address: nielsen@physics.uq.edu.au; www.qinfo.org/people/nielsen

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Vol. 68, Iss. 5 — November 2003

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