Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9703050 · Mathematics and Computers in Simulation

Monte Carlo simulation of quantum computation

Nicolas J. Cerf, S. E. Koonin

Published Aug 1, 1998• 17 citations
arXivHTMLPDF
DOI
10.1016/s0378-4754(98)00099-8

Related papers

Utilization of Quantum Monte Carlo Algorithm for Uncertainty Quantification

Rochisha Agarwal, Ferdin Sagai Don Bosco, Ramesh Kolluru +4 more

Efficient and robust uncertainty quantification (UQ) is essential in aerospace systems, as emphasized by both NASA’s CFD Vision 2030 and Certification by Analysis (CbA) 2040 initiatives. However, the extensive computational resources required by traditional UQ methods, especially when coupled with high-fidelity computational fluid dynamics (CFD) simulations, pose significant barriers. Quantum computing (QC) has been identified by the CFD Vision 2030 study as a promising technology to address these challenges, but has not yet been extensively explored in the context of UQ. In this study, a Quantum Computing-based Monte Carlo (QCMC) algorithm is implemented using a Qiskit simulator. This method utilizes Quantum Amplitude Estimation (QAE), specifically tailored for near-term Noisy Intermediate-Scale Quantum (NISQ) computers. The QCMC method demonstrates comparable accuracy to classical Monte Carlo (MC) methods on a two-dimensional heat diffusion problem while reducing the required number of samples (oracle calls) by ∼8X. By substantially lowering the computational overhead of UQ, this quantum computing-based algorithm could be a promising tool required to enable robust uncertainty-informed aerospace design.

AIAA AVIATION Forum•Jul 16, 2025•1 citation

From Monte Carlo to quantum computation

Stefan Heinrich

Mathematics and Computers in Simulation•Mar 1, 2003•22 citations

Eliminating Redundant Computation in Noisy Quantum Computing Simulation

Gushu Li, Yufei Ding, Yuan Xie

Noisy Quantum Computing (QC) simulation on a classical machine is very time consuming since it requires Monte Carlo simulation with a large number of error-injection trials to model the effect of random noises. Orthogonal to existing QC simulation optimizations, we aim to accelerate the simulation by eliminating the redundant computation among those Monte Carlo simulation trials. We observe that the intermediate states of many trials can often be the same. Once these states are computed in one trial, they can be temporarily stored and reused in other trials. However, storing such states will consume significant memory space. To leverage the shared intermediate states without introducing too much storage overhead, we propose to statically generate and analyze the Monte Carlo simulation simulation trials before the actual simulation. Those trials are reordered to maximize the overlapped computation between two consecutive trials. The states that cannot be reused in follow-up simulation are dropped, so that we only need to store a few states. Experiment results show that the proposed optimization scheme can save on average 80% computation with only a small number of state vectors stored. In addition, the proposed simulation scheme demonstrates great scalability as more computation can be saved with more simulation trials or on future QC devices with reduced error rates.

ACM/IEEE Design Automation Conference (DAC)•Jul 1, 2020•11 citations

Simulation of Quantum Computation

Tzvetan S. Metodi, Arvin I. Faruque, Frederic T. Chong

Synthesis lectures on computer architecture•Jan 1, 2011•1 citation

Hamiltonian Monte Carlo enhanced by exact diagonalization

Anonymous, Martina Gisti, David J. Luitz +2 more

Strongly correlated fermionic systems are of great interest in condensed matter physics and numerical methods are indispensable tools for their study. However, existing approaches such as exact diagonalization (ED) and stochastic quantum Monte Carlo methods each suffer from fundamental limitations: ED is hindered by exponential scaling in system size, while Monte Carlo methods are plagued by sign problems and long autocorrelation times. These limitations restrict the accessible parameter space and developing algorithms that efficiently alleviate them remains a central challenge in computational physics. In this work, we propose a algorithm that combines ED and Hamiltonian Monte Carlo (HMC) to simulate two-dimensional (2D) arrays of coupled quantum wires, modeled as interacting fermionic Hubbard chains. We demonstrate how our hybrid implementation of HMC, which we dub H 2 MC , outperforms either method alone across several key simulation facets. When compared to pure ED, H 2 MC has a much more favorable computational scaling, which allows us to push simulations to much larger 2D arrays. H 2 MC also greatly alleviates the sign problem and reduces autocorrelation times when compared to pure HMC formulations utilizing either real or imaginary auxiliary fields. Our formalism demonstrates how complementary strengths of seemingly disparate methods can be leveraged to enable feasible simulations in an extended parameter space.

arXiv:2603.17788•Physical review. B./Physical review. B•Aug 13, 2026•0 citations

Simulation of Quantum Computation

Tzvetan S. Metodi, Frederic T. Chong

Synthesis lectures on computer architecture•Jan 1, 2006•0 citations
Efficient and robust uncertainty quantification (UQ) is essential in aerospace systems, as emphasized by both NASA’s CFD Vision 2030 and Certification by Analysis (CbA) 2040 initiatives. However, the extensive computational resources required by traditional UQ methods, especially when coupled with high-fidelity computational fluid dynamics (CFD) simulations, pose significant barriers. Quantum computing (QC) has been identified by the CFD Vision 2030 study as a promising technology to address these challenges, but has not yet been extensively explored in the context of UQ. In this study, a Quantum Computing-based Monte Carlo (QCMC) algorithm is implemented using a Qiskit simulator. This method utilizes Quantum Amplitude Estimation (QAE), specifically tailored for near-term Noisy Intermediate-Scale Quantum (NISQ) computers. The QCMC method demonstrates comparable accuracy to classical Monte Carlo (MC) methods on a two-dimensional heat diffusion problem while reducing the required number of samples (oracle calls) by ∼8X. By substantially lowering the computational overhead of UQ, this quantum computing-based algorithm could be a promising tool required to enable robust uncertainty-informed aerospace design.
Noisy Quantum Computing (QC) simulation on a classical machine is very time consuming since it requires Monte Carlo simulation with a large number of error-injection trials to model the effect of random noises. Orthogonal to existing QC simulation optimizations, we aim to accelerate the simulation by eliminating the redundant computation among those Monte Carlo simulation trials. We observe that the intermediate states of many trials can often be the same. Once these states are computed in one trial, they can be temporarily stored and reused in other trials. However, storing such states will consume significant memory space. To leverage the shared intermediate states without introducing too much storage overhead, we propose to statically generate and analyze the Monte Carlo simulation simulation trials before the actual simulation. Those trials are reordered to maximize the overlapped computation between two consecutive trials. The states that cannot be reused in follow-up simulation are dropped, so that we only need to store a few states. Experiment results show that the proposed optimization scheme can save on average 80% computation with only a small number of state vectors stored. In addition, the proposed simulation scheme demonstrates great scalability as more computation can be saved with more simulation trials or on future QC devices with reduced error rates.
Strongly correlated fermionic systems are of great interest in condensed matter physics and numerical methods are indispensable tools for their study. However, existing approaches such as exact diagonalization (ED) and stochastic quantum Monte Carlo methods each suffer from fundamental limitations: ED is hindered by exponential scaling in system size, while Monte Carlo methods are plagued by sign problems and long autocorrelation times. These limitations restrict the accessible parameter space and developing algorithms that efficiently alleviate them remains a central challenge in computational physics. In this work, we propose a algorithm that combines ED and Hamiltonian Monte Carlo (HMC) to simulate two-dimensional (2D) arrays of coupled quantum wires, modeled as interacting fermionic Hubbard chains. We demonstrate how our hybrid implementation of HMC, which we dub H 2 MC , outperforms either method alone across several key simulation facets. When compared to pure ED, H 2 MC has a much more favorable computational scaling, which allows us to push simulations to much larger 2D arrays. H 2 MC also greatly alleviates the sign problem and reduces autocorrelation times when compared to pure HMC formulations utilizing either real or imaginary auxiliary fields. Our formalism demonstrates how complementary strengths of seemingly disparate methods can be leveraged to enable feasible simulations in an extended parameter space.