Preparing low-variance states using a distributed quantum algorithm

TL;DR

This paper introduces a distributed quantum algorithm inspired by iterative phase estimation to efficiently prepare low-variance eigenstates, leveraging multiple devices and postselection to outperform single-device methods.

Contribution

The work presents a novel distributed quantum algorithm that reduces energy variance faster than traditional single-device approaches, suitable for near-term quantum devices.

Findings

Distributed algorithm outperforms single-device methods in variance reduction

Uses minimal auxiliary qubits per device for control

Heralds successful runs via joint measurement and postselection

Abstract

Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The routine then acts as an effective filtering operation, reducing the energy variance of the initial state. In this work, we present a distributed quantum algorithm inspired by iterative phase estimation to prepare low-variance states. Our method uses a single auxiliary qubit per quantum device, which controls its dynamics, and a postselection strategy for a joint quantum measurement on such auxiliary qubits. In the multi-device case, the result of this measurement heralds the successful runs of the protocol. This allows us to demonstrate that our distributed algorithm reduces the energy variance faster compared to single-device implementations, thereby highlighting the potential of distributed algorithms for near-term and early fault-tolerant devices.