Efficient sampling of noisy shallow circuits via monitored unraveling

• URL: http://arxiv.org/abs/2306.16455v2
• Date: Wed, 15 Nov 2023 16:07:02 GMT
• Title: Efficient sampling of noisy shallow circuits via monitored unraveling
• Authors: Zihan Cheng and Matteo Ippoliti
• Abstract summary: We introduce a classical algorithm for sampling the output of noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently-proposed "space-evolving block decimation" (SEBD) and extends it to the case of noisy circuits.
• Score: 0.03922370499388702
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a classical algorithm for sampling the output of shallow, noisy random circuits on two-dimensional qubit arrays. The algorithm builds on the recently-proposed "space-evolving block decimation" (SEBD) and extends it to the case of noisy circuits. SEBD is based on a mapping of 2D unitary circuits to 1D {\it monitored} ones, which feature measurements alongside unitary gates; it exploits the presence of a measurement-induced entanglement phase transition to achieve efficient (approximate) sampling below a finite critical depth $T_c$. Our noisy-SEBD algorithm unravels the action of noise into measurements, further lowering entanglement and enabling efficient classical sampling up to larger circuit depths. We analyze a class of physically-relevant noise models (unital qubit channels) within a two-replica statistical mechanics treatment, finding weak measurements to be the optimal (i.e. most disentangling) unraveling. We then locate the noisy-SEBD complexity transition as a function of circuit depth and noise strength in realistic circuit models. As an illustrative example, we show that circuits on heavy-hexagon qubit arrays with noise rates of $\approx 2\%$ per CNOT, based on IBM Quantum processors, can be efficiently sampled up to a depth of 5 iSWAP (or 10 CNOT) gate layers. Our results help sharpen the requirements for practical hardness of simulation of noisy hardware.

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