Preparing low-variance states using a distributed quantum algorithm

Quantum, vol. 9, pp. 1838

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.

Authors 3

1. Xiaoyu Liu Aachen $\langle aQa ^L\rangle $ Applied Quantum Algorithms Instituut-Lorentz

   Leiden University

   Affiliation as printed

   $\langle aQa ^L\rangle $ Applied Quantum Algorithms, Universiteit Leiden

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

2. Benjamin F. Schiffer

   Max Planck Institute of Quantum Optics

   Affiliation as printed

   Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany

3. Jordi Tura Aachen $\langle aQa ^L\rangle $ Applied Quantum Algorithms Instituut-Lorentz

   Leiden University

   Affiliation as printed

   $\langle aQa ^L\rangle $ Applied Quantum Algorithms, Universiteit Leiden

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands