Noise-induced shallow circuits and absence of barren plateaus

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.

16+46 pages, 8 figures

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Cited by in corpus (6)

• Barren Plateaus in Variational Quantum Computing
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets
• Emergence of noise-induced barren plateaus in arbitrary layered noise models
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Learning complexity gradually in quantum machine learning models