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Quantum Information and Computation

Quantum algorithmic differentiation

Giuseppe Colucci, Francesco Giacosa

Published Feb 1, 2021• 2 citations
Publisher

Abstract

In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid approach). Since the implementation of elementary functions is already possible on quantum computers, the scheme that we propose can be easily applied. Moreover, since some steps (such as the CNOT operator) can (or will be) faster on a quantum computer than on a classical one, our procedure may ultimately emonstrate that quantum algorithmic differentiation has an advantage relative to its classical counterpart.

DOI
10.26421/qic21.1-2-5

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In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid approach). Since the implementation of elementary functions is already possible on quantum computers, the scheme that we propose can be easily applied. Moreover, since some steps (such as the CNOT operator) can (or will be) faster on a quantum computer than on a classical one, our procedure may ultimately emonstrate that quantum algorithmic differentiation has an advantage relative to its classical counterpart.
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The coming era of quantum computing promises to revolutionize computation, but, given the efficiency of many classical routines as well as quantum hardware limitations, calls to quantum devices are and will continue to be used as subroutines in larger, hybrid quantum-classical algorithms. This Perspective explores the essential differences between pure and hybrid quantum algorithms, discusses some examples, and frames the future of hybrid quantum-classical algorithms in its natural context of classical heterotic computing.
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Abstract A new method of eliminating the finite‐time‐step error inherent in diffusion quantum Monte Carlo is presented, utilizing an improved version of the existing differential techniques. An implementation is described and results of several small but representative calculations are discussed. The pertinent computation requirements on these systems were reduced by up to a factor of five by the new algorithm. It is speculated that this method may be easily applied to other quantum Monte Carlo and discretized path integral Monte Carlo techniques having related finite step‐size errors with a possibility of obtaining similar good results.