Estimation of correlations and non-separability in quantum channels via unitarity benchmarking

Girling, Matthew; Cirstoiu, Cristina; Jennings, David

doi:10.48550/arxiv.2104.04352

Cited by 2 publications

(2 citation statements)

References 68 publications

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“…This is important because whenever coherent noise can be diagnosed and characterised, e.g. with via unitarity measures [8,24,68,69] or otherwise, in principle it could be addressed and calibrated if we have access to the E qubits. Precisely then, we may tell if the noise is unitary over the whole SE if we get a general non-exponential behaviour described by Eq.…”

Section: Numerical Example: Noise Memory Time-scales Markovianised Av...mentioning

confidence: 99%

Randomized benchmarking for non-Markovian noise

Figueroa-Romero,

Modi,

Stace

et al. 2021

Preprint

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Estimating the features of noise is the first step in a chain of protocols that will someday lead to fault tolerant quantum computers. The randomised benchmarking (RB) protocol is designed with this exact mindset, estimating the average strength of noise in a quantum processor with relative ease in practice. However, RB, along with most other benchmarking and characterisation methods, is limited in scope because it assumes that the noise is temporally uncorrelated (Markovian), which is increasingly evident not to be the case. Here, we combine the RB protocol with a recent framework describing non-Markovian quantum phenomena to derive a general analytical expression of the average sequence fidelity (ASF) for non-Markovian RB with the Clifford group. We show that one can identify non-Markovian features of the noise directly from the ASF through its deviations from the Markovian case, proposing a set of methods to collectively estimate these deviations, non-Markovian memory time-scales, and diagnose (in)coherence of non-Markovian noise in an RB experiment. Finally, we demonstrate the efficacy of our proposal by means of several proof-of-principle examples. Our methods are directly implementable and pave the pathway to better understanding correlated noise in quantum processors.

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Section: Numerical Example: Noise Memory Time-scales Markovianised Av...mentioning

confidence: 99%

Randomized benchmarking for non-Markovian noise

Figueroa-Romero,

Modi,

Stace

et al. 2021

Preprint

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“…It would be also very interesting to connect quantum average-case distances with commonly used figures of merit used to assess quality of quantum devices. Those include measures such as average fidelity [41] (which is perhaps the most widely used quality measure), or unitarity of quantum channels [29,73,74]. Furthermore, one can ask whether similar results can be obtained for different functions of output probability distributions such us classical fidelity or f -divergences [75,76].…”

Section: Open Problemsmentioning

confidence: 99%

Exploring Quantum Average-Case Distances: proofs, properties, and examples

Maciejewski¹,

Puchała²,

Oszmaniec³

2021

Preprint

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In this work, we perform an in-depth study of recently introduced average-case quantum distances . The average-case distances approximate, up to relative error, the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in which quantum objects of interest (states, measurements, or channels) are intertwined with random quantum circuits. Contrary to conventional distances, such as trace distance or diamond norm, they quantify average-case statistical distinguishability via random quantum circuits.We prove that once a family of random circuits forms an δ-approximate 4-design, with δ = o(d −8 ), then the average-case distances can be approximated by simple explicit functions that can be expressed via simple degree two polynomials in objects of interest. For systems of moderate dimension, they can be easily explicitly computed -no optimization is needed as opposed to diamond norm distance between channels or operational distance between measurements. We prove that those functions, which we call quantum average-case distances, have a plethora of desirable properties, such as subadditivity w.r.t. tensor products, joint convexity, and (restricted) data-processing inequalities. Notably, all of the distances utilize the Hilbert-Schmidt (HS) norm in some way. This gives the HS norm an operational interpretation that it did not possess before. We also provide upper bounds on the maximal ratio between worst-case and average-case distances, and for each of them we provide an example that saturates the bound. Specifically, we show that for each dimension d this ratio is at most d 1 2 , d, d 3 2 for states, measurements, and channels, respectively. To support the practical usefulness of our findings, we study multiple examples in which average-case quantum distances can be calculated analytically. Furthermore, we perform an extensive numerical study of systems up to 10 qubits where circuits have a form of variational ansätze with randomly chosen parameters. Despite the fact that such circuits are not known to form unitary designs, our results suggest that average-case distances are more suitable than the conventional distances for studying the performance of NISQ devices in such settings.

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Estimation of correlations and non-separability in quantum channels via unitarity benchmarking

Cited by 2 publications

References 68 publications

Randomized benchmarking for non-Markovian noise

Randomized benchmarking for non-Markovian noise

Exploring Quantum Average-Case Distances: proofs, properties, and examples

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