End-to-End Molecular Dynamics with a Langevin Thermostat on Quantum Circuits

• URL: http://arxiv.org/abs/2605.30143v1
• Date: Thu, 28 May 2026 16:05:54 GMT
• Title: End-to-End Molecular Dynamics with a Langevin Thermostat on Quantum Circuits
• Abstract summary: We construct a quantum-circuit framework for finite-temperature molecular dynamics in the canonical ensemble (NVT)<n>The classical nuclear phase-space distribution is encoded as a Koopman--von Neumann (KvN) wave function, and canonical state preparation is formulated as Langevin-type Fokker--Planck relaxation.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a quantum-circuit framework for finite-temperature molecular dynamics in the canonical ensemble (NVT) with a Langevin thermostat, connecting canonical state preparation to subsequent physical-property readouts. The classical nuclear phase-space distribution is encoded as a Koopman--von Neumann (KvN) wave function, and canonical state preparation is formulated as Langevin-type Fokker--Planck relaxation. The Hamiltonian Liouville flow, momentum friction, and momentum diffusion are decomposed into separate circuit blocks. The friction block is represented by a symmetrized momentum-space dilation, whereas the diffusion block is implemented as a cosine filter realized by probabilistic imaginary-time evolution (PITE). We analytically quantify the leading-order temperature bias caused by replacing the Gaussian diffusion kernel with this PITE-realized cosine filter. This analysis yields an internal-temperature correction that targets the desired physical equilibrium distribution. As a proof-of-concept demonstration connecting quantum chemistry to KvN nuclear dynamics, we study the H$_2$ molecule. Numerical simulations show relaxation from a nonequilibrium phase-space distribution to a canonical KvN state. From this canonical state, we demonstrate two complementary readouts: a dynamical quantum-phase-estimation readout of the vibrational density of states associated with the H--H stretch coordinate and a static canonical evaluation of the transition-state-theory (TST) rate constant. This work demonstrates, in a minimal molecular system, a circuit-level protocol that connects Langevin canonical state preparation to physical-property calculations, providing a concrete step toward quantum--classical hybrid molecular dynamics on quantum computers.

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