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arXiv · 2410.16693

Learning shallow quantum circuits with many-qubit gates

Francisca Vasconcelos·Hsin-Yuan Huang
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Abstract

We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown QAC$^0$ circuits -- constant-depth circuits with arbitrary single-qubit gates and polynomially many $CZ$ gates of unbounded width -- with at most logarithmic ancilla, up to inverse-polynomially small error. Furthermore, we show that the learned unitary can be efficiently synthesized in poly-logarithmic depth. This work expands the family of efficiently learnable quantum circuits, notably since in finite-dimensional circuit geometries, QAC$^0$ circuits require polynomial depth to implement.

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Francisca Vasconcelos, Hsin-Yuan Huang. 2024-10-22. Learning shallow quantum circuits with many-qubit gates. https://arxiv.org/abs/2410.16693

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