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This research demonstrates that uncorrected noise effectively truncates quantum circuits to logarithmic depth for observable estimation tasks, eliminating the risk of barren plateaus under non-unital conditions. The authors conclude that noisy intermediate-scale devices are unlikely to outperform shallow classical algorithms unless circuit designs explicitly leverage these noise characteristics.
Noise-induced shallow circuits and absence of barren plateaus
arXiv:2403.13927v3 Announce Type: replace Abstract: Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that in the task of estimating observable expectation values any noise truncates most quantum circuits to effectively logarithmic depth. We then prove that quantum circuits under any non-unital noise do not exhibit barren plateaus for cost functions composed of local observables. However, by using the effective shallowness, we also design an efficient classical algorithm to estimate observable expectation values within any constant additive accuracy, with high probability over the choice of the circuit, in any circuit architecture. Taken together, our results establish that, unless we carefully engineer quantum circuits to take advantage of the noise, noisy quantum circuits are unlikely to offer an advantage over shallow ones for algorithms that output observable expectation value estimates, such as many variational quantum machine learning proposals.
Abstract:Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that in the task of estimating observable expectation values any noise truncates most quantum circuits to effectively logarithmic depth. We then prove that quantum circuits under any non-unital noise do not exhibit barren plateaus for cost functions composed of local observables. However, by using the effective shallowness, we also design an efficient classical algorithm to estimate observable expectation values within any constant additive accuracy, with high probability over the choice of the circuit, in any circuit architecture. Taken together, our results establish that, unless we carefully engineer quantum circuits to take advantage of the noise, noisy quantum circuits are unlikely to offer an advantage over shallow ones for algorithms that output observable expectation value estimates, such as many variational quantum machine learning proposals.
Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph)
arXiv:2403.13927 [quant-ph]
(or arXiv:2403.13927v3 [quant-ph] for this version)
https://doi.org/10.1038/s41567-026-03245-z DOI(s) linking to related resources
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