Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers

Abstract

Simulating properties of quantum materials is one of the most promising applications of quantum computation, both near- and long-term. While real-time dynamics can be straightforwardly implemented, the finite temperature ensemble involves non-unitary operators that render an implementation on a near-term quantum computer extremely challenging. Recently, [Lu, Bañuls and Cirac, PRX Quantum 2, 020321 (2021)] suggested a "time-series quantum Monte Carlo method" which circumvents this problem by extracting finite temperature properties from real-time simulations via Wick's rotation and Monte Carlo sampling of easily preparable states. In this paper, we address the challenges associated with the practical applications of this method, using the two-dimensional transverse field Ising model as a testbed. We demonstrate that estimating Boltzmann weights via Wick's rotation is very sensitive to time-domain truncation and statistical shot noise. To alleviate this problem, we introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. In addition, we show how to reduce the statistical errors of Monte Carlo sampling via a reweighted version of the Wolff cluster algorithm. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.

arXiv comment16 pages, 22 figures

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• Observation of a finite-energy phase transition in a one-dimensional quantum simulator
• Phase-Sensitive Quantum Measurement without Controlled Operations
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
• Heisenberg-limited metrology with perturbing interactions
• Energy-filtered quantum states and the emergence of non-local correlations
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians
• Lindblad engineering for quantum Gibbs state preparation under the eigenstate thermalization hypothesis