ULTRA-QMC: A Universal Quantum Monte Carlo Framework

Kaoru Ohno, Keivan Esfarjani, Yoshiyuki Kawazoe

Kaoru Ohno, Keivan Esfarjani, Yoshiyuki Kawazoe

Poetri Sonya Tarabunga, Yi-Ming Ding

Quantum Monte Carlo (QMC) methods are essential for the numerical study of large-scale quantum many-body systems, yet their utility has been significantly hampered by the difficulty in computing key quantities such as off-diagonal operators and entanglement. This Letter introduces Bell-QMC, a novel QMC framework leveraging Bell sampling, a two-copy measurement protocol in the transversal Bell basis. We demonstrate that Bell-QMC enables an efficient and unbiased estimation of both challenging classes of observables, offering a significant advantage over previous QMC approaches. Notably, the entanglement across all system partitions can be computed in a single Bell-QMC simulation. We implement this method within the stochastic series expansion, where we design an efficient update scheme for sampling the configurations in the Bell basis. We demonstrate our algorithm in the one-dimensional transverse-field Ising model and the two-dimensional Z 2 lattice gauge theory, extracting universal quantum features using only simple diagonal measurements. This Letter establishes Bell-QMC as a powerful framework that significantly expands the accessible quantum properties in QMC simulations, providing a substantial advantage over conventional QMC.

John M. Martyn, Joshua Lin, Neill C. Warrington +2 more

Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.

Poetri Sonya Tarabunga, Yi-Ming Ding

Quantum Monte Carlo (QMC) methods are essential for the numerical study of large-scale quantum many-body systems, yet their utility has been significantly hampered by the difficulty in computing key quantities such as off-diagonal operators and entanglement. This Letter introduces Bell-QMC, a novel QMC framework leveraging Bell sampling, a two-copy measurement protocol in the transversal Bell basis. We demonstrate that Bell-QMC enables an efficient and unbiased estimation of both challenging classes of observables, offering a significant advantage over previous QMC approaches. Notably, the entanglement across all system partitions can be computed in a single Bell-QMC simulation. We implement this method within the stochastic series expansion, where we design an efficient update scheme for sampling the configurations in the Bell basis. We demonstrate our algorithm in the one-dimensional transverse-field Ising model and the two-dimensional Z_{2} lattice gauge theory, extracting universal quantum features using only simple diagonal measurements. This Letter establishes Bell-QMC as a powerful framework that significantly expands the accessible quantum properties in QMC simulations, providing a substantial advantage over conventional QMC.

Shi Guo

North Carolina State University Theses Physics.