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Variational quantum Monte Carlo (VMC) combined with neural-network quantum states offers a novel angle of attack on the curse-of-dimensionality encountered in a particular class of partial differential equations (PDEs); namely, the real- and imaginary time-dependent Schrödinger equation. In this paper, we present a simple generalization of VMC applicable to arbitrary time-dependent PDEs, showcasing the technique in the multi-asset Black-Scholes PDE for pricing European options contingent on many correlated underlying assets.
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This content will become publicly available on December 10, 2025
Quadratic Quantum Variational Monte Carlo
This paper introduces the Quadratic Quantum Variational Monte Carlo (Q2 VMC) algorithm, an innovative algorithm in quantum chemistry that significantly enhances the efficiency and accuracy of solving the Schrödinger equation. Inspired by the discretization of imaginary-time Schrödinger evolution, Q2 VMC employs a novel quadratic update mechanism that integrates seamlessly with neural network-based ansatzes. Our extensive experiments showcase Q2 VMC's superior performance, achieving faster convergence and lower ground state energies in wavefunction optimization across various molecular systems, without additional computational cost. This study not only advances the field of computational quantum chemistry but also highlights the important role of discretized evolution in variational quantum algorithms, offering a scalable and robust framework for future quantum research.
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- Award ID(s):
- 2505865
- PAR ID:
- 10631809
- Publisher / Repository:
- Advances in Neural Information Processing Systems 37 (NeurIPS 2024)
- Date Published:
- ISBN:
- 9798331314385
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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