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arXiv:1204.6308 · Physical Review Letters

Characterization of Addressability by Simultaneous Randomized Benchmarking

Jay Gambetta, Antonio D. Corcoles, Seth Merkel, Blake Johnson, John A. Smolin, Jerry M. Chow, Colm A. Ryan, Chad T. Rigetti, Stefano Poletto, Thomas Ohki, M. B. Ketchen, Matthias Steffen

Published Dec 11, 2012• 290 citations
arXivHTMLPDF

Abstract

The control and handling of errors arising from cross talk and unwanted interactions in multiqubit systems is an important issue in quantum information processing architectures. We introduce a benchmarking protocol that provides information about the amount of addressability present in the system and implement it on coupled superconducting qubits. The protocol consists of randomized benchmarking experiments run both individually and simultaneously on pairs of qubits. A relevant figure of merit for the addressability is then related to the differences in the measured average gate fidelities in the two experiments. We present results from two similar samples with differing cross talk and unwanted qubit-qubit interactions. The results agree with predictions based on simple models of the classical cross talk and Stark shifts.

DOI
10.1103/physrevlett.109.240504

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The control and handling of errors arising from cross talk and unwanted interactions in multiqubit systems is an important issue in quantum information processing architectures. We introduce a benchmarking protocol that provides information about the amount of addressability present in the system and implement it on coupled superconducting qubits. The protocol consists of randomized benchmarking experiments run both individually and simultaneously on pairs of qubits. A relevant figure of merit for the addressability is then related to the differences in the measured average gate fidelities in the two experiments. We present results from two similar samples with differing cross talk and unwanted qubit-qubit interactions. The results agree with predictions based on simple models of the classical cross talk and Stark shifts.
Ternary quantum processors offer significant potential computational advantages over conventional qubit technologies, leveraging the encoding and processing of quantum information in qutrits (three-level systems). To evaluate and compare the performance of such emerging quantum hardware it is essential to have robust benchmarking methods suitable for a higher-dimensional Hilbert space. We demonstrate extensions of industry standard randomized benchmarking (RB) protocols, developed and used extensively for qubits, suitable for ternary quantum logic. Using a superconducting five-qutrit processor, we find an average single-qutrit process infidelity of 3.8×10^{-3}. Through interleaved RB, we characterize a few relevant gates, and employ simultaneous RB to fully characterize crosstalk errors. Finally, we apply cycle benchmarking to a two-qutrit CSUM gate and obtain a two-qutrit process fidelity of 0.85. Our results present and demonstrate RB-based tools to characterize the performance of a qutrit processor, and a general approach to diagnose control errors in future qudit hardware.
As quantum circuits increase in size, it is critical to establish scalable multiqubit fidelity metrics. Here we investigate, for the first time, three-qubit randomized benchmarking (RB) on a quantum device consisting of three fixed-frequency transmon qubits with pairwise microwave-activated interactions (cross-resonance). We measure a three-qubit error per Clifford of 0.106 for all-to-all gate connectivity and 0.207 for linear gate connectivity. Furthermore, by introducing mixed dimensionality simultaneous RB-simultaneous one- and two-qubit RB-we show that the three-qubit errors can be predicted from the one- and two-qubit errors. However, by introducing certain coherent errors to the gates, we can increase the three-qubit error to 0.302, an increase that is not predicted by a proportionate increase in the one- and two-qubit errors from simultaneous RB. This demonstrates the importance of multiqubit metrics, such as three-qubit RB, on evaluating overall device performance.
We implement a complete randomized benchmarking protocol on a system of two superconducting qubits. The protocol consists of randomizing over gates in the Clifford group, which experimentally are generated via an improved two-qubit cross-resonance gate implementation and single-qubit unitaries. From this we extract an optimal average error per Clifford operation of 0.09360.09360.0936. We also perform an interleaved experiment, alternating our optimal two-qubit gate with random two-qubit Clifford gates, to obtain a two-qubit gate error of 0.06530.06530.0653. We compare these values with a two-qubit gate error of $\ensuremath{\sim}0.12$ obtained from quantum process tomography, which is likely limited by state preparation and measurement errors.
Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.
Currently available quantum computing hardware based on superconducting transmon architectures realizes networks of hundreds of qubits with the possibility of controlled nearest-neighbor interactions. However, the inherent noise and decoherence effects of such quantum chips considerably alter basic gate operations and lead to imperfect outputs of the targeted quantum computations. In this work, we focus on the characterization of crosstalk effects, which manifest themselves in correlations between simultaneously executed quantum gates on neighboring qubits. After a short explanation of the physical origin of such correlations, we show how to efficiently and systematically characterize the magnitude of such crosstalk effects on an entire quantum chip using the randomized benchmarking protocol. We demonstrate the introduced protocol by running it on real quantum hardware provided by IBM and observe significant alterations in gate fidelities due to crosstalk. Lastly, based on the gained information, we propose more accurate means to simulate noisy quantum hardware by devising a crosstalk-aware noise model.
To improve the performance of multi-qubit algorithms on quantum devices it is critical to have methods for characterizing non-local quantum errors such as crosstalk. To address this issue, we propose and test an extension to the analysis of simultaneous randomized benchmarking data -- correlated randomized benchmarking. We fit the decay of correlated polarizations to a composition of fixed-weight depolarizing maps to characterize the locality and weight of crosstalk errors. From these errors we introduce a crosstalk metric which indicates the distance to the closest map with only local errors. We demonstrate this technique experimentally with a four-qubit superconducting device and utilize correlated RB to validate crosstalk reduction when we implement an echo sequence.