Quantum algorithm enables simulation of strongly nonlinear stochastic differential equations
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[Submitted on 6 Jun 2026]
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Summary
This paper presents a quantum algorithm for solving a broad class of N-dimensional stochastic differential equations (SDEs) with dissipation and quadratic drift, extending beyond previous quantum algorithms that were limited to weak nonlinearity and sparse systems. The algorithm applies to strongly nonlinear systems with all-to-all interactions, and for norm-preserving drifts (satisfied by key fluid dynamics discretizations), it approximates expectation values of low-order correlation functions with rigorous error bounds at a cost polynomial in log(N) and linear in evolution time. The main technical advance is a subroutine for simulating an auxiliary system of N interacting quantum harmonic oscillators with cost polylogarithmic in N. The authors formulate turbulence models including Navier-Stokes and damped Euler equations within this framework, opening a route to quantum simulation of strongly nonlinear SDEs governing turbulence and nonlinear wave dynamics.
Key quotes
· 5 pulledWe present a quantum algorithm for a broad class of $N$-dimensional stochastic differential equations with dissipation and quadratic drift.
The algorithm applies to strongly nonlinear systems with all-to-all interactions, thereby extending the scope of previously known quantum algorithms that were limited to weak nonlinearity and sparse systems.
Our main technical advance is a subroutine for simulating an auxiliary system of $N$ interacting quantum harmonic oscillators with cost polylogarithmic in $N$.
For norm-preserving drifts, a condition satisfied by key fluid dynamics discretizations, our method approximates expectation values of low-order correlation functions with rigorous error bounds.
We formulate turbulence models, including Navier-Stokes and damped Euler equations, within this framework, opening a route to quantum simulation of strongly nonlinear SDEs governing turbulence and nonlinear wave dynamics.
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