Efficiently sample equivalent random quantum circuits

Develop an efficient algorithm for sampling uniformly from the set of fixed-shape ancilla-free quantum circuits that implement the same channel as a prescribed circuit, thereby replacing the ideal equivalent-circuit distributions used in the worst-to-average-case analysis with efficiently samplable objects.

Background

The proposed reduction defines, for a circuit C and a prescribed length L, the distribution of all L-gate circuits of the same width that implement exactly the same channel as C. Such a distribution would conceal the original circuit’s description while preserving its functionality.

The authors explicitly use these distributions only as ideal objects because they do not know how to sample them efficiently. An efficient sampler would be a central ingredient in turning the conditional reduction into a practical obfuscation procedure.

References

Sampling from this distribution would give a description whose distribution depends only on the channel and the prescribed shape, which is precisely what we want from an obfuscator. However, we do not know how to sample it efficiently.

— Verifiable Quantum Advantage and Computation via Quantum Circuit Obfuscation  (2609.40289 - Gheorghiu et al., 30 Sep 2026) in Section “A worst-to-average-case reduction for ancilla-free qiO”