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arXiv:2009.07425 · Physical Review Research

Benchmarking quantum state transfer on quantum devices

Yi-Te Huang, Jhen-Dong Lin, Huan-Yu Ku, Yueh-Nan Chen

Published Apr 12, 2021• 11 citations
arXivHTMLPDF

Abstract

Quantum state transfer (QST) provides a method to send arbitrary quantum states from one system to another.Such a concept is crucial for transmitting quantum information into the quantum memory, quantum processor, and quantum network.The standard benchmark of QST is the average fidelity between the prepared and received states.In this work we provide a new benchmark which reveals the nonclassicality of QST based on spatiotemporal steering (STS).More specifically, we show that the local-hidden-state (LHS) model in STS can be viewed as the classical strategy of state transfer.Therefore, we can quantify the nonclassicality of the QST process by measuring the spatiotemporal steerability.We then apply the spatiotemporal steerability measurement technique to benchmark quantum devices including the IBM quantum experience and QuTech quantum inspire under QST tasks.The experimental results show that the spatiotemporal steerability decreases as the circuit depth increases, and the reduction agrees with the noise model, which refers to the accumulation of errors during the QST process.Moreover, we provide a quantity to estimate the signaling effect which could result from gate errors or intrinsic non-Markovian effect of the devices.

DOI
10.1103/physrevresearch.3.023038

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Quantum state transfer (QST) provides a method to send arbitrary quantum states from one system to another.Such a concept is crucial for transmitting quantum information into the quantum memory, quantum processor, and quantum network.The standard benchmark of QST is the average fidelity between the prepared and received states.In this work we provide a new benchmark which reveals the nonclassicality of QST based on spatiotemporal steering (STS).More specifically, we show that the local-hidden-state (LHS) model in STS can be viewed as the classical strategy of state transfer.Therefore, we can quantify the nonclassicality of the QST process by measuring the spatiotemporal steerability.We then apply the spatiotemporal steerability measurement technique to benchmark quantum devices including the IBM quantum experience and QuTech quantum inspire under QST tasks.The experimental results show that the spatiotemporal steerability decreases as the circuit depth increases, and the reduction agrees with the noise model, which refers to the accumulation of errors during the QST process.Moreover, we provide a quantity to estimate the signaling effect which could result from gate errors or intrinsic non-Markovian effect of the devices.
Spatio-temporal quantum steering provides a framework for benchmarking the nonclassicality of general quantum state transfer processes. A central diagnostic is the no-signaling-in-time (NSIT) condition, whose violation can indicate basis-dependent hardware errors. However, finite measurement statistics may also yield apparent violations, thereby obscuring the detection of basis-dependent hardware errors. To address this, we construct a statistical hypothesis test under the null hypothesis that NSIT violations arise solely from statistical fluctuations. Combining the statistical properties of NSIT violation under the null hypothesis with Chebyshev's inequality, we obtain a distribution-free upper bound on the ppp-value without parametric assumptions. We apply this method to two examples. For a single-qubit state-transfer experiment on a superconducting processor, we observe several instances that the NSIT violation is observed and the null hypothesis is simultaneously rejected by a small ppp-value, providing statistical evidence of basis-dependent hardware errors. For a seven-qubit Hayden-Preskill teleportation protocol on IonQ devices, the null hypothesis is also rejected even when the average fidelity exceeds the classical threshold, while the associated nonclassicality measure vanishes. Our results highlight the necessity of statistical hypothesis testing for detecting basis-dependent errors in near-term quantum devices.
Spatial and temporal correlations in quantum noise challenge the local Markovian models commonly used in quantum information processing. We develop a unified operational framework for quantifying temporal, spatial, and total spatiotemporal correlations in general quantum processes. Using process tensors, we define these quantities through optimal distinguishability from Markovian, spatially local, and fully uncorrelated processes. Optimization over admissible probing combs ensures monotonicity under every superprocess that preserves the corresponding free set, while Choi-state functionals and restricted probes provide accessible lower bounds. We establish hierarchy and interpolation relations among the correlation measures and derive dimension-dependent upper bounds on temporal correlations transmitted by quantum memories, with tighter bounds for classical memory, together with universal ceilings imposed by the system dimension. These bounds turn certified lower estimates into witnesses of minimum memory dimension, nonclassicality under a memory-dimension constraint, and inconsistencies in the assumed process model. We illustrate the results with effective superconducting-qubit models featuring ZZZZZZ and XYXYXY interactions, exhibiting saturation of classical-memory, quantum-memory, and system-dimension ceilings. These results pave the way toward practical approaches to characterizing and addressing spatiotemporally correlated errors in quantum devices.
We introduce the concept of spatio-temporal steering (STS), which reduces, in special cases, to Einstein-Podolsky-Rosen steering and the recently-introduced temporal steering. We describe two measures of this effect referred to as the STS weight and robustness. We suggest that these STS measures enable a new way to assess nonclassical correlations in an open quantum network, such as quantum transport through nano-structures or excitation transfer in a complex biological system. As one of our examples, we apply STS to check nonclassical correlations among sites in a photosynthetic pigment-protein complex in the Fenna-Matthews-Olson model.
Not all entangled states can exhibit quantum steering, and determining whether a given entangled state is steerable is a crucial problem in quantum information theory. The main challenge lies in verifying the existence of a local hidden-state (LHS) model capable of reproducing all post-measurement assemblages generated by arbitrary measurements. To address this, we propose a machine learning-based framework that employs batch sampling of measurements and gradient-based optimization to construct an optimal LHS model. We validate our method by analyzing the steerability of two-qubit Werner and two-qutrit isotropic states. For Werner states, our approach saturates the analytical visibility bounds under three Pauli measurements, arbitrary projective measurements (PVMs), and arbitrary positive operator-valued measurements (POVMs). For isotropic states, we achieve the known analytical bounds under arbitrary PVMs. We further investigate the steerability of this class of states under arbitrary POVMs, and our results suggest that POVMs can offer an advantage over PVMs in revealing the steerability of such states.
Quantum teleportation, the process by which Alice can transfer an unknown quantum state to Bob by using preshared entanglement and classical communication, is one of the cornerstones of quantum information. The standard benchmark for certifying quantum teleportation consists in surpassing the maximum average fidelity between the teleported and the target states that can be achieved classically. According to this figure of merit, not all entangled states are useful for teleportation. Here we propose a new benchmark that uses the full information available in a teleportation experiment and prove that all entangled states can implement a quantum channel which cannot be reproduced classically. We introduce the idea of nonclassical teleportation witness to certify if a teleportation experiment is genuinely quantum and discuss how to quantify this phenomenon. Our work provides new techniques for studying teleportation that can be immediately applied to certify the quality of quantum technologies.
Abstract A crucial task to obtain optimal and reliable quantum devices is to quantify their overall performance. The average fidelity of quantum gates is a particular figure of merit that can be estimated efficiently by randomized benchmarking (RB). However, the concept of gate-fidelity itself relies on the crucial assumption that noise behaves in a predictable, time-local, or so-called Markovian manner, whose breakdown can naturally become the leading source of errors as quantum devices scale in size and depth. We analytically show that error suppression techniques such as dynamical decoupling (DD) and Pauli-twirling can operationally Markovianize RB: (i) fast DD reduces non-Markovian RB to an exponential decay plus longer-time corrections, while on the other hand, (ii) Pauli-twirling generally does not affect the average, but (iii) it always suppresses the variance of such RB outputs. We demonstrate these effects numerically with a qubit noise model. Our results show that simple and efficient error suppression methods can simultaneously tame non-Markovian noise and allow for standard and reliable gate quality estimation, a fundamentally important task in the path toward fully functional quantum devices.