Noise-induced shallow circuits and absence of barren plateaus
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 any noise `truncates' most quantum circuits to effectively logarithmic depth, in the task of estimating observable expec...
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Main Authors | , , , , , , |
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Format | Journal Article |
Language | English |
Published |
20.03.2024
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Subjects | |
Online Access | Get full text |
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Summary: | 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 any noise `truncates' most quantum circuits to effectively
logarithmic depth, in the task of estimating observable expectation values. We
then prove that quantum circuits under any non-unital noise exhibit lack of
barren plateaus for cost functions composed of local observables. But, by
leveraging 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. The runtime of the algorithm is independent of circuit
depth, and for any inverse-polynomial target accuracy, it operates in
polynomial time in the number of qubits for one-dimensional architectures and
quasi-polynomial time for higher-dimensional ones. Taken together, our results
showcase that, unless we carefully engineer the circuits to take advantage of
the noise, it is unlikely that noisy quantum circuits are preferable over
shallow quantum circuits for algorithms that output observable expectation
value estimates, like many variational quantum machine learning proposals.
Moreover, we anticipate that our work could provide valuable insights into the
fundamental open question about the complexity of sampling from (possibly
non-unital) noisy random circuits. |
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DOI: | 10.48550/arxiv.2403.13927 |