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International Conference on Quantum Information

Quantum simulation and quantum analogue computation

Viv M. Kendon

Published Jan 1, 2011• 0 citations
Publisher

Abstract

Quantum simulation is expected to be one of the most important first applications of quantum computing. I motivate the use of continuous variable quantum computation (CVQC) for quantum simulation, and describe work investigating microwave frequency cavity QED systems as viable architectures for CVQC.
DOI
10.1364/icqi.2011.qwa2

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Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described by models which we cannot solve with sufficient accuracy, neither analytically nor numerically with classical computers. Using a quantum computer to simulate such quantum systems has been viewed as a key application of quantum computation from the very beginning of the field in the 1980s. Moreover, useful results beyond the reach of classical computation are expected to be accessible with fewer than a hundred qubits, making quantum simulation potentially one of the earliest practical applications of quantum computers. In this paper we survey the theoretical and experimental development of quantum simulation using quantum computers, from the first ideas to the intense research efforts currently underway.
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We formulate a continuous-variable quantum computing (CVQC) algorithm to study Berry's phase on photonic quantum computers. We demonstrate that CVQC allows the simulation of charged particles with orbital angular momentum under the influence of an adiabatically changing B⃗\vec{B}B field. Although formulated entirely in the CVQC setting, our construction uses only passive linear-optical operations (beam splitters and phase shifts), which act identically in single-photon photonic architectures. This enables experimental realisation on the Quandella Ascella platform, where we observe the Berry's phase phenomenon with interferometric measurement. We also generalise the framework to more rapid non-adiabatic evolution. By concatenating Aharonov-Anandan cycles for opposing magnetic fields we demonstrate that one can engineer a circuit in which dynamical phases and leading non-geometric errors cancel by symmetry, leaving the intrinsically robust geometric phase contribution.
Continuous-variable quantum computing (CVQC) is a computing paradigm in which measurements yield values over a continuous domain. CVQC is both a convenient computational framework for modeling physical quantum systems, and a good abstraction for hardware platforms based on quantum optics. Yet, the semantic foundations of CVQC remain underdeveloped. To address this gap, we develop a formal semantics for a core CV quantum programming language, and sound verification methods for program correctness. A main contribution of this work is to isolate a well-behaved quantitative predicate domain that achieves sufficient expressiveness to accommodate unbounded values as they arise in the infinite-dimensional, continuous setting. Specifically, we choose closed positive quadratic forms as semantic predicates, representing finite expectations, domains of finiteness, and infinite penalties in one ordered object. We validate our choice by establishing that our semantic predicates satisfy desirable closure properties including the definition of weakest preconditions. We validate our design with two case studies, including an example based on the celebrated GKP error-correcting code, for which we establish a second moment bound.