Abstract

Digital quantum simulation on quantum computers provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time evolution operator through a sequence of elementary quantum gates. A fundamental challenge in this context originates from experimental imperfections, which critically limits the number of attainable gates within a reasonable accuracy and therefore the achievable system sizes and simulation times. In this work, we introduce a reinforcement learning algorithm to systematically build optimized quantum circuits for digital quantum simulation upon imposing a strong constraint on the number of quantum gates. With this we consistently obtain quantum circuits that reproduce physical observables with as little as three entangling gates for long times and large system sizes up to 16 qubits. As concrete examples we apply our formalism to a long-range Ising chain and the lattice Schwinger model. Our method demonstrates that digital quantum simulation on noisy intermediate scale quantum devices can be pushed to much larger scale within the current experimental technology by a suitable engineering of quantum circuits using reinforcement learning.

Highlights

  • Introduction.—Digital quantum simulation (DQS) has emerged as one of the most promising applications of quantum computers

  • In this work we introduce a method based on reinforcement learning (RL) to systematically build DQSs constrained to a fixed low number of entangling gates

  • We apply our method to two models chosen because of their relevance for DQS: the long-range Ising (LRI) model, unsolvable analytically but inheriting a natural Trotter decomposition, and the lattice Schwinger model, a key model to be simulated digitally [8,17]

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Summary

Adrien Bolens and Markus Heyl

Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany (Received 3 July 2020; revised 9 May 2021; accepted 22 July 2021; published 9 September 2021). We introduce a reinforcement learning algorithm to systematically build optimized quantum circuits for digital quantum simulation upon imposing a strong constraint on the number of quantum gates. With this we consistently obtain quantum circuits that reproduce physical observables with as little as three entangling gates for long times and large system sizes up to 16 qubits. For the lattice Schwinger model, we build quantum circuits using only three entangling gates that correctly reproduce the dynamics of local observables and correlation functions for up to 16 qubits and for large times, reducing the number of entangling gates by one order of magnitude in comparison

Published by the American Physical Society
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