Quantum error mitigation via matrix product operators [article]

Yuchen Guo, Shuo Yang
<span title="2022-05-18">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors of measurement results via repeated experiments and postprocessing of data. Typical techniques for error mitigation, e.g., the quasi-probability decomposition method, ignore correlated errors between different gates. Here, we introduce a QEM method based on the
more &raquo; ... atrix product operator (MPO) representation of a quantum circuit that can characterize the noise channel with polynomial complexity. Our technique is demonstrated on a depth=4 fully parallel quantum circuit of up to N_q=10 qubits undergoing long-range spatially correlated noises. The circuit error is mitigated by several orders of magnitude with only a small bond dimension for the noise channel. The MPO representation increases the accuracy of modeling noises without consuming more experimental resources, which improves the QEM performance and broadens its scope of application. Our method is hopeful to be applied to circuits in higher dimensions with deeper depth and more qubits.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2201.00752v3">arXiv:2201.00752v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ingljzhmrvalbbupekexp3todm">fatcat:ingljzhmrvalbbupekexp3todm</a> </span>
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