Efficient quantum circuits improve flow model simulation with neural networks
An Efficient Quantum Circuit for Flow Model Execution Using Quantum Neural Networks
Machine Learning
Summary
Flow models help transform one set of data into another by following certain paths. This paper shows how to use quantum computers to run these models more efficiently by simulating quantum states that behave like the flow paths. To do this, the authors combine existing quantum memory techniques with a trained quantum neural network to reduce the complexity of the circuit needed. Their experiments show this new method keeps accuracy while using fewer computational resources.
What this means in practice
- •For quantum software engineers: Design quantum circuits that efficiently simulate probability distributions following flow models with fewer resources.
- •For financial modeling teams: Implement faster quantum algorithms for simulating stochastic processes and their dynamics using improved flow-based quantum circuits.
Authors
Rui Che, Ludvig af Klinteberg
Abstract
Flow models generate trajectories from an initial distribution to a target distribution by solving an ordinary differential equation defined by a velocity field. Flow matching learns this velocity field by modeling the transport dynamics between the two distributions. Wavefunction flow establishes a formal connection between flow models and quantum dynamics by introducing a continuity Hamiltonian, which drives the Schrödinger evolution of quantum states. In this paper, we investigate accurate and efficient quantum simulation of the wavefunction flow, thereby realizing the efficient implementation of flow models on quantum computers. We first leverage a quantum read-only memory (QROM)-based phase kickback framework for the wavefunction flow simulation, generating probability densities that closely match those produced by the corresponding conventional flow model. To address the high circuit-resource cost, we further incorporate a trained quantum neural network (QNN) into the phase kickback framework, replacing QROM for data encoding. Numerical experiments demonstrate that our proposed method implements flow models on quantum computers more efficiently, since it maintains the accuracy of wavefunction flow simulation compared with the QROM-based framework, and significantly reduces the circuit resources.