Learning shallow quantum circuits with many-qubit gates

• URL: http://arxiv.org/abs/2410.16693v1
• Date: Tue, 22 Oct 2024 04:48:36 GMT
• Title: Learning shallow quantum circuits with many-qubit gates
• Authors: Francisca Vasconcelos, Hsin-Yuan Huang,
• Abstract summary: We present the first computationally-efficient algorithm for average-case learning of quantum circuits with many-qubit gates. We show that the learned unitary can be efficiently synthesized in poly-logarithmic depth.
• Score: 1.879968161594709
• License:
• 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 -- 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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