Exponentially tighter bounds on limitations of quantum error mitigation
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Exponentially tighter bounds on limitations of quantum error mitigation. / Quek, Yihui; Stilck França, Daniel; Khatri, Sumeet; Meyer, Johannes Jakob; Eisert, Jens.
I: Nature Physics, 2024.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Exponentially tighter bounds on limitations of quantum error mitigation
AU - Quek, Yihui
AU - Stilck França, Daniel
AU - Khatri, Sumeet
AU - Meyer, Johannes Jakob
AU - Eisert, Jens
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024
Y1 - 2024
N2 - Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault-tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively ‘undone’ for larger system sizes. Our framework rigorously captures large classes of error-mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to those of current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. Noise also impacts other near-term applications by constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.
AB - Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault-tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively ‘undone’ for larger system sizes. Our framework rigorously captures large classes of error-mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to those of current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. Noise also impacts other near-term applications by constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian.
U2 - 10.1038/s41567-024-02536-7
DO - 10.1038/s41567-024-02536-7
M3 - Journal article
AN - SCOPUS:85199557914
JO - Nature Physics
JF - Nature Physics
SN - 1745-2473
ER -
ID: 402828396