Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation

TL;DR

This paper presents a classical algorithm that efficiently computes expectation values in certain continuous variable quantum circuits by leveraging an epistemic restriction in phase space, challenging the notion that Wigner negativity alone enables quantum speedup.

Contribution

The authors introduce a novel classical simulation method for a specific class of quantum circuits using an epistemic restriction in phase space, providing new insights into quantum-classical boundaries.

Findings

Classical algorithm efficiently computes expectation values in certain quantum circuits.

Wigner negativity is not sufficient for quantum speedup in the studied class.

Epistemic restrictions can serve as a conceptual tool for understanding quantum versus classical computation.

Abstract

We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the circuits | is at most second order in momentum. The classical computational algorithm exploits a specific epistemic restriction in classical phase space which directly captures the quantum uncertainty relation, to transform the quantum circuits in the complex Hilbert space into classical albeit unconventional stochastic processes in the phase space. The resulting multidimensional integral is then evaluated using the Monte Carlo sampling method. The work shows that for the specific class of computational schemes, Wigner negativity is not a sufficient resource for quantum speedup. It highlights the potential role of the epistemic restriction as an intuitive conceptual tool which may be used to study the boundary between quantum and classical computations.