2021/02/03 by Phillip Weinberg, Weinberg, Phillip
Computer Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Stochastic Gradient Optimization Techniques #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2102.02293
openalex publication_date 2021/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-βH. 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.