Enhanced Convergence of Quantum Typicality using a Randomized Low-Rank Approximation

• URL: http://arxiv.org/abs/2102.02293v2
• Date: Wed, 17 Feb 2021 18:21:04 GMT
• Title: Enhanced Convergence of Quantum Typicality using a Randomized Low-Rank Approximation
• Authors: Phillip Weinberg
• Abstract summary: We present a method to reduce the variance of trace estimators used in quantum typicality (QT) methods via a randomized low-rank approximation. The trace can be evaluated with higher accuracy in the low-rank subspace while using the QT estimator to approximate the trace in the complementary subspace.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a method to reduce the variance of stochastic trace estimators used in quantum typicality (QT) methods via a randomized low-rank approximation of the finite-temperature density matrix $e^{-\beta H}$. The trace can be evaluated with higher accuracy in the low-rank subspace while using the QT estimator to approximate the trace in the complementary subspace. We present two variants of the trace estimator and demonstrate their efficacy using numerical experiments. The experiments show that the low-rank approximation outperforms the standard QT trace estimator for moderate- to low-temperature. We argue this is due to the low-rank approximation accurately represent the density matrix at low temperatures, allowing for accurate results for the trace.

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