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arXiv:quant-ph/0302125 · Journal of Modern Optics

Requirement for quantum computation

Stephen D. Bartlett, Barry C. Sanders

Published Jan 1, 2003• 27 citations
arXivHTMLPDF

Abstract

We identify ‘proper quantum computation’ with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish no-go theorems for classes of quantum optical experiments that cannot yield proper quantum computation, and we identify requirements for optical proper quantum computation that correspond to violations of assumptions underpinning the no-go theorems.

DOI
10.1080/09500340308233564

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We identify ‘proper quantum computation’ with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish no-go theorems for classes of quantum optical experiments that cannot yield proper quantum computation, and we identify requirements for optical proper quantum computation that correspond to violations of assumptions underpinning the no-go theorems.
In this paper we review the content of the Quantum Computer Condition, which is a rigorously specified criterion that provides a set of mathematical constraints that must be satisfied by a physical system if we intend to use that system as a quantum computing machine, and we discuss an important consequence of it known as the Quantum Computing No-Go Theorem, which establishes a bound for decoherence and dissipation beyond which quantum computation is not possible. In connection with this theorem, we explicitly calculate a universal critical damping value for fault-tolerant quantum computation. We also discuss a relevant class of time-dependent generalizations of the Lindblad equation.
The rapid development in hardware for quantum computing and simulation has led to much interest in problems where these devices can exceed the capabilities of existing classical computers and known methods. Approaching this for problems that go beyond testing the performance of a quantum device is an important step, and quantum simulation of many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum simulators with neutral atoms in optical lattices and trapped ions. Considering the primary sources of error in analogue devices and how they propagate after a quench in studies of the Hubbard or long-range transverse field Ising model, we identify the level of error expected in quantities we extract from experiments. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators. We also identify the hardware requirements to reach the same level of accuracy with future fault-tolerant digital quantum simulation. Verification techniques are already available to test the assumptions we make here, and demonstrating these in experiments will be an important next step.