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Quantum computers in the NISQ era are prone to noise. A range of quantumerror mitigation techniques has been proposed to address this issue. Zero-noiseextrapolation (ZNE) stands out as a promising one. ZNE involves increasing thenoise levels in a circuit and then using extrapolation to infer the zero noisecase from the noisy results obtained. This paper presents a novel ZNE approachthat does not require circuit folding or noise scaling to mitigate depolarizingand/or decoherence noise.  To mitigate depolarizing noise, we propose leveraging the extreme/infinitenoisy case, which allows us to avoid circuit folding. Specifically, the circuitoutput with extreme noise becomes the maximally mixed state. We show that usingcircuit-reliability metrics, simple linear extrapolation can effectivelymitigate depolarizing noise. With decoherence noise, different states decayinto the all-zero state at a rate that depends on the number of excited statesand time. Therefore, we propose a state- and latency-aware exponentialextrapolation that does not involve folding or scaling. When dealing with aquantum system affected by both decoherence and depolarizing noise, we proposeto use our two mitigation techniques in sequence: first applying decoherenceerror mitigation, followed by depolarizing error mitigation.  A common limitation of ZNE schemes is that if the circuit of interest suffersfrom high noise, scaling-up noise levels could not provide useful data forextrapolation. We propose using circuit-cut techniques to break a large quantumcircuit into smaller sub-circuits to overcome this limitation. This way, thenoise levels of the sub-circuits are lower than the original circuit, and ZNEcan become more effective in mitigating their noises.

Folding-Free ZNE: A Comprehensive Quantum Zero-Noise Extrapolation Approach for Mitigating Depolarizing and Decoherence Noise