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Learning shallow quantum circuits with many-qubit gates
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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.
Forward citations
Cited by 2 Pith papers
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Information-Computation Gaps in Quantum Learning via Low-Degree Likelihood
A quantum extension of the low-degree method shows that state designs imply computational hardness for many single-copy quantum measurement strategies, yielding new information-computation gaps.
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An unconditional distribution learning advantage with shallow quantum circuits
Shallow quantum circuits (QNC0) are proven to outperform shallow classical circuits (NC0) as hypothesis classes for PAC distribution learning of a constructed distribution family, with an error advantage of 1/pi.
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