• Open Access

Avoiding Barren Plateaus Using Classical Shadows

Stefan H. Sack, Raimel A. Medina, Alexios A. Michailidis, Richard Kueng, and Maksym Serbyn
PRX Quantum 3, 020365 – Published 29 June 2022

Abstract

Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients, which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBPs) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows WBPs to be avoided during the optimization process. This paves the way for efficient barren plateau-free optimization on near-term devices.

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  • Received 1 February 2022
  • Revised 12 April 2022
  • Accepted 20 May 2022

DOI:https://doi.org/10.1103/PRXQuantum.3.020365

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Stefan H. Sack1,*,‡, Raimel A. Medina1,†,‡, Alexios A. Michailidis1,2, Richard Kueng3, and Maksym Serbyn1

  • 1IST Austria, Am Campus 1, Klosterneuburg 3400, Austria
  • 2Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, Geneva 1211, Switzerland
  • 3Institute for Integrated Circuits, Johannes Kepler University Linz, Altenberger Straße 69, Austria

  • *stefan.sack@ist.ac.at
  • raimel.medina@ist.ac.at
  • These authors contributed equally.

Popular Summary

Variational quantum algorithms provide a promising route for achieving quantum advantage on near-term devices. Their objective is to minimize a cost function, which encodes the solution of a hard problem. This is achieved by varying the parameters of a quantum circuit encoded in the quantum device. However, the optimization landscape is often dominated by large regions of vanishing gradients known as barren plateaus (BPs), which prevent optimization. The avoidance of BPs during optimization is crucial for the future success of variational algorithms.

Our work is motivated by the relation of BPs to entanglement entropy and information scrambling. In particular, we introduce a notion of weak barren plateau (WBP) that probes a locally scrambled state and acts as a precursor to a BP. In contrast to BPs, WBPs can be efficiently measured in current quantum devices using the recently introduced classical shadow protocol. Therefore, our work provides a tool for the avoidance of BPs, both at the initialization state and during the optimization process, that can be directly applied to current quantum algorithms. We propose a simple modification to the common variational quantum algorithm, capable of avoiding BPs and implementable on available devices.

Our work paves the way for efficient barren plateau-free optimization on near-term devices. In addition, the intricate connections between BPs and dynamics of entanglement entropy, as outlined by our work, indicates strong connection between the fields of quantum optimization and out-of-equilibrium quantum physics that is yet to be fully explored.

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Vol. 3, Iss. 2 — June - August 2022

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