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Simulating properties of quantum materials is one of the most promisingapplications of quantum computation, both near- and long-term. While real-timedynamics can be straightforwardly implemented, the finite temperature ensembleinvolves non-unitary operators that render an implementation on a near-termquantum computer extremely challenging. Recently, [Lu, Ba\~nuls and Cirac, PRXQuantum 2, 020321 (2021)] suggested a "time-series quantum Monte Carlo method"which circumvents this problem by extracting finite temperature properties fromreal-time simulations via Wick's rotation and Monte Carlo sampling of easilypreparable states. In this paper, we address the challenges associated with thepractical applications of this method, using the two-dimensional transversefield Ising model as a testbed. We demonstrate that estimating Boltzmannweights via Wick's rotation is very sensitive to time-domain truncation andstatistical shot noise. To alleviate this problem, we introduce a techniquethat imposes constraints on the density of states, most notably itsnon-negativity, and show that this way, we can reliably extract Boltzmannweights from noisy time series. In addition, we show how to reduce thestatistical errors of Monte Carlo sampling via a reweighted version of theWolff cluster algorithm. Our work enables the implementation of the time-seriesalgorithm on present-day quantum computers to study finite temperatureproperties of many-body quantum systems.

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