Bridge of 's: Quantum Circuit Optimization with Schr"odinger Bridges
quant-ph, cs.LG
Submitted: 2026-09-22
Updated: 2026-09-22
Comments: 25 pages, 11 figures, 12 tables
License: http://creativecommons.org/licenses/by/4.0/
The gist: Quantum circuit optimization replaces a circuit with an equivalent one of fewer gates and lower depth, reducing execution cost and error rate.
Terminology
Abstract
Quantum circuit optimization replaces a circuit with an equivalent one of fewer gates and lower depth, reducing execution cost and error rate. We ask whether a generative model can learn this transformation directly from examples, rather than selecting from a fixed rewrite library or rigid algebraic routines. We present Bridge of Ψ 's (BOPS), a generative model based on Schrödinger bridges, using a custom denoiser architecture, that learns a transformation from a source circuit into an equivalent optimized circuit. We train it on data constructed to be hard for existing optimizers, by applying rewrite rules backwards so that each input has a known lower-cost target. On held-out 8 qubits times 64 depth Clifford+ T circuits, BOPS reduces gate count by 2.46 times and depth by 2.45 times in geometric mean, outperforming all nine baseline optimizers. This constitutes the first generative model bridging quantum circuits and frontier machine learning methods, opening up the quantum compilation stack to learned optimization along multiple axes.
Sources
- Linear-Time T-Gate Optimization via Random Abstraction
- Quantum circuit optimization with deep reinforcement learning
- Synthesis of discrete-continuous quantum circuits with multimodal diffusion models
- Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation
- When Close Enough Is Not Enough: Autoregressive Drift in Quantum Circuit Synthesis
- Fast Classical Simulation of Quantum Circuits via Parametric Rewriting in the ZX-Calculus
- U-DiTs: Downsample Tokens in U-Shaped Diffusion Transformers
- Optimising quantum circuits is generally hard
- Equivariant Reinforcement Learning for Clifford Quantum Circuit Synthesis
- Inference-time Scaling of Diffusion Models through Classical Search
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