Relationship between costs for quantum error mitigation and non-Markovian measures

Hakoshima, Hideaki; Matsuzaki, Yuichiro; Endo, Suguru

doi:10.1103/physreva.103.012611

Cited by 23 publications

(23 citation statements)

References 43 publications

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“…Our results offer various new research directions. Non-Markovian dynamics have shown promise in decreasing sampling costs in error metigation [51]. Since non-Markovianity is known to be deeply related to the trace distance [52], our newly established relations between trace distance and quantum error mitigation hint at promising relations between the two fields.…”

Section: Discussionmentioning

confidence: 95%

Fundamental limits of quantum error mitigation

Takagi

Endo²,

Minagawa

et al. 2021

Preprint

Self Cite

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The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantage. This motivated the development of various quantum error-mitigation protocols, each representing a method to extract useful computational output by combining measurement data from multiple samplings of the available imperfect quantum device. What are the ultimate performance limits universally imposed on such protocols? Here, we derive a fundamental bound on the sampling overhead that applies to a general class of error-mitigation protocols, assuming only the laws of quantum mechanics. We use it to show that (1) the sampling overhead to mitigate local depolarizing noise for layered circuits -such as the ones used for variational quantum algorithms -must scale exponentially with circuit depth, and (2) the optimality of probabilistic error cancellation method among all strategies in mitigating a certain class of noise. We discuss how our unified framework and general bounds can be employed to benchmark and compare various present methods of error mitigation and identify situations where present error-mitigation methods have the greatest potential for improvement.

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Section: Discussionmentioning

confidence: 95%

Fundamental limits of quantum error mitigation

Takagi

Endo²,

Minagawa

et al. 2021

Preprint

Self Cite

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show abstract

“…However, they require the knowledge of the unitary operator that prepares the state of interest and assume that the noise affecting the state and its dual are similar. The increased depth of the circuit can be problematic for the latter assumption in the presence of non-Markovian errors [30].…”

Section: Error Mitigation Using Multiple Copiesmentioning

confidence: 99%

Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors

Seif¹,

Cian²,

Zhou³

et al. 2022

Preprint

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Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurements to circumvent the need for coherent access to multiple copies at an exponential cost. We study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We optimize measurement resources under realistic experimental constraints and apply our method to an experiment preparing Greenberger-Horne-Zeilinger (GHZ) state with trapped ions. In addition to improving stabilizer measurements, the analysis of the improved results reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.

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“…With the rapid progresses of quantum computing and quantum simulation technologies [23][24][25][26][27], the top down approach alone is no longer satisfying, since the noises on those quantum devices could be extremely difficult to know before hand. In the mean time, there is an increasing need for a quantitive description of the noises on near-term quantum devices, such as to characterize the overall fidelities of noisy quantum experiments, or for error correction and error mitiga-tion [28][29][30][31]. Therefore an efficient way to characterize the (non-Markovian) open quantum dynamics based only on the experimentally accessible quantities, instead of resorting to the top down approach, is highly desirable.…”

Section: Process Tensor Framework For Mqementioning

confidence: 99%

Quantifying Non-Markovianity in Open Quantum Dynamics

Guo

2022

SciPost Phys.

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Characterization of non-Markovian open quantum dynamics is both of theoretical and practical relevance. In a seminal work [Phys. Rev. Lett. 120, 040405 (2018)], a necessary and sufficient quantum Markov condition is proposed, with a clear operational interpretation and correspondence with the classical limit. Here we propose two non-Markovianity measures for general open quantum dynamics, which are fully reconciled with the Markovian limit and can be efficiently calculated based on the multi-time quantum measurements of the system. A heuristic algorithm for reconstructing the underlying open quantum dynamics is proposed, whose complexity is directly related to the proposed non-Markovianity measures. The non-Markovianity measures and the reconstruction algorithm are demonstrated with numerical examples, together with a careful reexamination of the non-Markovianity in quantum dephasing dynamics.

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Relationship between costs for quantum error mitigation and non-Markovian measures

Cited by 23 publications

References 43 publications

Fundamental limits of quantum error mitigation

Fundamental limits of quantum error mitigation

Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors

Quantifying Non-Markovianity in Open Quantum Dynamics

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