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.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 ForumJul 16, 20251 citation

Achievements in Quantum Monte Carlo

MANFRED L. RISTIG

Recent Progress in Many-Body TheoriesJan 1, 19901 citation

The Use of the Monte Carlo Hamiltonian

H. Kröger, Xiaoyu Luo, Kevin J. M. Moriarty

In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In order to show its working in the case of the scalar $Φ^{4}_{1+1}$ model, we have computed thermodynamic functions like free energy, average energy, entropy and specific heat. We find good agreement between the results from the Monte Carlo Hamiltonian and standard Lagrangian lattice computations. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature. We address properties of the MC Hamiltonian, like a finite temperature window, and scaling properties. Also we discuss possible future applications - like quantum chaos in many-body systems, the non-perturbative computation of wave functions of elementary particles, as well as scattering amplitudes in high energy physics.In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In order to show its working in the case of the scalar $Φ^{4}_{1+1}$ model, we have computed thermodynamic functions like free energy, average energy, entropy and specific heat. We find good agreement between the results from the Monte Carlo Hamiltonian and standard Lagrangian lattice computations. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature. We address properties of the MC Hamiltonian, like a finite temperature window, and scaling properties. Also we discuss possible future applications - like quantum chaos in many-body systems, the non-perturbative computation of wave functions of elementary particles, as well as scattering amplitudes in high energy physics.

arXiv:hep-lat/0301012Jan 13, 20031 citation

INVESTIGATIONS IN QUANTUM MONTE CARLO

Matthew Clifford Wilson

Feb 2, 20070 citations

Application of quantum Monte Carlo integration to Markovian backward stochastic differential equations

Masato Fujita, Koichi Miyamoto, Jun Sekine

In this paper, we introduce a novel Quantum Least-Squares Monte Carlo (QLSM) algorithm for solving backward stochastic differential equations (BSDEs). The QLSM algorithm leverages quantum computing to enhance the efficiency of traditional least-squares Monte Carlo methods. We present the detailed procedure of the QLSM method and an evaluation of its accuracy and computational cost. This approach has significant potential for applications in mathematical finance, particularly in pricing complex financial derivatives and risk management.In this paper, we introduce a novel Quantum Least-Squares Monte Carlo (QLSM) algorithm for solving backward stochastic differential equations (BSDEs). The QLSM algorithm leverages quantum computing to enhance the efficiency of traditional least-squares Monte Carlo methods. We present the detailed procedure of the QLSM method and an evaluation of its accuracy and computational cost. This approach has significant potential for applications in mathematical finance, particularly in pricing complex financial derivatives and risk management.

JSIAM LettersJan 1, 20240 citations

Φ^{4}_{1+1}

model, we have computed thermodynamic functions like free energy, average energy, entropy and specific heat. We find good agreement between the results from the Monte Carlo Hamiltonian and standard Lagrangian lattice computations. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature. We address properties of the MC Hamiltonian, like a finite temperature window, and scaling properties. Also we discuss possible future applications - like quantum chaos in many-body systems, the non-perturbative computation of wave functions of elementary particles, as well as scattering amplitudes in high energy physics.