A Solution to the Sign Problem Using a Sum of Controlled Few-Fermions

TL;DR

The paper introduces a Monte Carlo method to simulate certain quantum systems without the sign problem and proves that these systems can encode any BQP algorithm, implying BQP equals BPP.

Contribution

It presents a novel restricted path integral approach for simulating controlled few-fermions and establishes the universality of these systems for quantum computation.

Findings

Sign problem is avoided in the proposed simulation method.

Any BQP algorithm can be encoded into controlled few-fermions.

BQP is shown to be equivalent to BPP using these systems.

Abstract

A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is proven to assert that any bounded-error quantum polynomial time (BQP) algorithm can be encoded into a sum of controlled few-fermions and simulated efficiently using classical Monte Carlo. Therefore, BQP is precisely the same as the class of bounded-error probabilistic polynomial time (BPP), namely, BPP = BQP.