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arXiv · 2411.03245

Quantum Error Mitigation via Linear-Depth Verifier Circuits

Angus Mingare·Anastasia Moroz·Marcell D Kovacs·Andrew G Green
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Abstract

Implementing many important sub-circuits on near-term quantum devices remains a challenge due to the high levels of noise and the prohibitive depth on standard nearest-neighbour topologies. Overcoming these barriers will likely require quantum error mitigation (QEM) strategies. This work introduces the notion of efficient, high-fidelity verifier circuit architectures that we propose for use in such a QEM scheme. We provide a method for constructing verifier circuits for any quantum circuit that is accurately represented by a low-dimensional matrix product operator (MPO). We demonstrate our method by constructing explicit verifier circuits for multi-controlled single unitary gates as well as the quantum Fourier transform (QFT). By transpiling the circuits to a 2D array of qubits, we estimate the crossover point where the verifier circuit is shallower than the circuit itself, and hence useful for QEM. We propose a method of in situ QEM using the verifier circuit architecture. We conclude that our approach may be useful for calibrating quantum sub-circuits to counter coherent noise but cannot correct for the incoherent noise present in current devices.

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Angus Mingare, Anastasia Moroz, Marcell D Kovacs, Andrew G Green. 2024-11-05. Quantum Error Mitigation via Linear-Depth Verifier Circuits. https://arxiv.org/abs/2411.03245

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