Exponentially tighter bounds on limitations of quantum error mitigation
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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.
Originalsprog | Engelsk |
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Tidsskrift | Nature Physics |
ISSN | 1745-2473 |
DOI | |
Status | E-pub ahead of print - 2024 |
Bibliografisk note
Funding Information:
This work has been supported by the Federal Ministry of Education and Research (RealistiQ, QPIC-1, MUNIQC-Atoms and PhoQuant), the Federal Ministry for Economic Affairs and Climate Action (PlanQK and EniQmA), the German Research Foundation (CRC 183), the Einstein Foundation (Einstein Research Unit on Quantum Devices), the Quant-ERA (HQCC), the European Research Council (DebuQC), the Cluster of Excellence MATH+ and the Alexander von Humboldt Foundation. The research is also part of the Munich Quantum Valley (K-8), which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus. D.S.F. acknowledges financial support from the Villum Foundation through the QMATH Centre of Excellence (Grant No. 10059), the Quant-ERA ERA-NET Cofund in Quantum Technologies implemented within the European Union\u2019s Horizon 2020 Programme (QuantAlgo) through the Innovation Fund Denmark and from the European Research Council (Grant Agreement No. 81876). D.S.F. acknowledges that this work benefited from a government grant managed by the French National Agency for Research under the Plan France 2030 (Reference ANR-22-PETQ-0007).
Publisher Copyright:
© The Author(s) 2024.
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