When Close Enough Is Not Enough: Autoregressive Drift in Quantum Circuit Synthesis

2026-07-14

AI Summary

This work addresses the challenge of quantum circuit synthesis in fault-tolerant quantum computing, where minimizing non-Clifford resources—such as T gates—must be achieved without compromising functional equivalence. Autoregressive models often suffer from “autoregressive drift” during long-sequence generation, leading to catastrophic equivalence violations. To mitigate this, the authors propose a structured circuit tokenization approach based on a 44.8M-parameter encoder-decoder Transformer, integrated with multi-candidate inference, classical post-processing, and large-scale data augmentation. Their method achieves a median fidelity of 1.000 on parametrized circuits and improves exact matching rates on Clifford+T circuits from 7% to 39.5%—leveraging 2.5× data augmentation and multi-candidate selection—thereby providing the first systematic identification and alleviation of irreversible bias accumulation in autoregressive quantum circuit generation.

Abstract

Quantum circuit optimization for fault-tolerant computing requires exact functional equivalence while minimizing expensive non-Clifford resources such as T gates. We study this problem using a compact 44.8M-parameter encoder-decoder transformer with structured circuit tokenization, evaluating on parameterized circuits (2-6 qubits) and Clifford+T circuits (3-6 qubits). On parameterized circuits, a hybrid approach -- structure from the transformer, angles from classical optimization -- achieves median fidelity 1.000 on 3-6 qubit circuits. On Clifford+T circuits, where all gates are discrete and no post-processing is possible, the model learns valid syntax and accurate T-Count statistics, yet exact equivalence degrades sharply with target length -- from 88% on circuits with <=9 gates to near zero beyond 26 gates. We trace this failure to autoregressive drift: early-token divergence cascading irrecoverably through left-to-right decoding. Two levers partially mitigate the drift: inference-time strategies that generate multiple candidates and select via equivalence verification raise exact-match rates from 7% to 22.5%, while scaling training data by 2.5x pushes them to 39.5%. Yet the degradation with target length persists -- even with more data, exact equivalence drops from 94% on short circuits to under 4% beyond 26 gates. The contrast between settings is our central finding: when approximate outputs can be rescued by post-processing, the transformer succeeds; when exact discrete correctness is required, autoregressive drift limits reliability, with both inference-time search and data scaling as effective levers while training-side fine-tuning and model-level diversification are not.

Problem

• quantum circuit synthesis
• exact equivalence
• autoregressive drift
• Clifford+T circuits
• fault-tolerant computing

Innovation

• autoregressive drift
• quantum circuit synthesis
• exact functional equivalence
• Clifford+T circuits
• transformer decoding