Quantum-Enhanced Sampling of Schrödinger Bridges
Abstract
We consider the dynamic Schrödinger bridge problem on a finite state space and exploit its Markov structure to decompose the problem into an endpoint coupling and a collection of conditional Markov bridges. To sample from the conditional bridges, we develop a quantum Gibbs sampler based on quantum walks on the bridge path space. Under uniformly positive transition probabilities, we derive a spectral-gap bound and provide an explicit procedure for preparing the initial state. Compared with the update bounds of the corresponding classical Gibbs sampler, our quantum walk-query complexity improves the dependence on the time horizon T from quadratic to linear. For the endpoint coupling, we adapt a quantum box-constrained Newton method to compute the Schrödinger potentials, improving the matrix-scaling complexity, at fixed accuracy, from quadratic to N3/2 in the state-space size N. Finally, we show that exponential reweighting extends both the Schrödinger bridge formulation and the Gibbs spectral-gap estimate to models with additive running costs.
Related
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BibTeX
@misc{lollier2026quantumenhanced,
title = {{Quantum-Enhanced Sampling of Schrödinger Bridges}},
author = {Tom Lollier and Eyal Neuman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27103},
eprint = {2609.27103},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27103},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum-Enhanced Sampling of Schrödinger Bridges
AU - Tom Lollier
AU - Eyal Neuman
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27103
UR - https://arxiv.org/abs/2609.27103
AB - We consider the dynamic Schrödinger bridge problem on a finite state space and exploit its Markov structure to decompose the problem into an endpoint coupling and a collection of conditional Markov bridges. To sample from the conditional bridges, we develop a quantum Gibbs sampler based on quantum walks on the bridge path space. Under uniformly positive transition probabilities, we derive a spectral-gap bound and provide an explicit procedure for preparing the initial state. Compared with the update bounds of the corresponding classical Gibbs sampler, our quantum walk-query complexity improves the dependence on the time horizon T from quadratic to linear. For the endpoint coupling, we adapt a quantum box-constrained Newton method to compute the Schrödinger potentials, improving the matrix-scaling complexity, at fixed accuracy, from quadratic to N^3/2 in the state-space size N. Finally, we show that exponential reweighting extends both the Schrödinger bridge formulation and the Gibbs spectral-gap estimate to models with additive running costs.
ER -