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arXiv:2303.03347 · Physical Review Applied

Learning-Based Calibration of Flux Crosstalk in Transmon Qubit Arrays

Cora N. Barrett, Amir H. Karamlou, Sarah E. Muschinske, Ilan T. Rosen, Jochen Braumüller, Rabindra Nath Das, David K. Kim, Bethany M. Niedzielski, Meghan Schuldt, Kyle Serniak, Mollie E. Schwartz, Jonilyn Yoder, Terry P. Orlando, Simon Gustavsson, Jeffrey A. Grover, William D. Oliver

Published Aug 28, 2023• 21 citations
arXivHTMLPDF

Abstract

Superconducting quantum processors comprising flux-tunable data and coupler qubits are a promising platform for quantum computation. However, magnetic flux crosstalk between the flux-control lines and the constituent qubits impedes precision control of qubit frequencies, presenting a challenge to scaling this platform. In order to implement high-fidelity digital and analog quantum operations, one must characterize the flux crosstalk and compensate for it. In this work, we introduce a learning-based calibration protocol and demonstrate its experimental performance by calibrating an array of 16 flux-tunable transmon qubits. To demonstrate the extensibility of our protocol, we simulate the crosstalk matrix learning procedure for larger arrays of transmon qubits. We observe an empirically linear scaling in calibration time with system size while maintaining a median qubit frequency error below 300 kHz.

DOI
10.1103/physrevapplied.20.024070

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Superconducting quantum processors comprising flux-tunable data and coupler qubits are a promising platform for quantum computation. However, magnetic flux crosstalk between the flux-control lines and the constituent qubits impedes precision control of qubit frequencies, presenting a challenge to scaling this platform. In order to implement high-fidelity digital and analog quantum operations, one must characterize the flux crosstalk and compensate for it. In this work, we introduce a learning-based calibration protocol and demonstrate its experimental performance by calibrating an array of 16 flux-tunable transmon qubits. To demonstrate the extensibility of our protocol, we simulate the crosstalk matrix learning procedure for larger arrays of transmon qubits. We observe an empirically linear scaling in calibration time with system size while maintaining a median qubit frequency error below 300 kHz.
Magnetic flux tunability is an essential feature in most approaches to quantum computing based on superconducting qubits.Independent control of the fluxes in multiple loops is hampered by crosstalk.Calibrating flux crosstalk becomes a challenging task when the circuit elements interact strongly.We present a novel approach to flux crosstalk calibration, which is circuit model independent and relies on an iterative process to gradually improve calibration accuracy.This method allows us to reduce errors due to the inductive coupling between loops.The calibration procedure is automated and implemented on devices consisting of tunable flux qubits and couplers with up to 27 control loops.We devise a method to characterize the calibration error, which is used to show that the errors of the measured crosstalk coefficients are all below 0.17%.
Superconducting qubits have achieved exceptional gate fidelities, exceeding the error-correction threshold in recent years. One key ingredient of such improvement is the introduction of tunable couplers to control the qubit-to-qubit coupling through frequency tuning. Moving toward fault-tolerant quantum computation, increasing the number of physical qubits is another step toward effective error correction codes. Under a multiqubit architecture, flux control (Z) lines are crucial in tuning the frequency of the qubits and couplers. However, dense flux lines result in magnetic flux crosstalk, wherein magnetic flux applied to one element inadvertently affects neighboring qubits or couplers. This crosstalk obscures the idle frequency of the qubit when flux bias is applied, which degrades gate performance and calibration accuracy. In this study, we characterize flux crosstalk and suppress it in a multiqubit-coupler chip with multi-Z lines without adding additional readout for couplers. By quantifying the mutual flux-induced frequency shifts of qubits and couplers, we construct a cancellation matrix that enables precise compensation of non-local flux, demonstrating a substantial reduction in Z-line crosstalk from 56.5‰ to 0.13‰, which is close to statistical error. Flux compensation corrects the CZ SWAP measurement, leading to a symmetric map with respect to flux bias. Compared with a crosstalk-free calculated CZ SWAP map, the measured map indicates that our approach provides a near-zero crosstalk for the coupler-transmon system. These results highlight the effectiveness of our approach in enhancing flux crosstalk-free control and supporting its potential for scaling superconducting quantum processors.
In recent years, several architectures have been proposed for implementing two-qubit operations on fluxonium superconducting qubits. A particularly promising approach, which was demonstrated experimentally by Refs. [1,2], employs a transmon superconducting qubit as a tunable coupler between the fluxonium qubits. These experiments have shown that the transmon coupler enables fast, high-fidelity two-qubit operations while suppressing unwanted ZZ crosstalk between the fluxonium qubits. In this work, we numerically study the scalability of this architecture. We find that, when trivially scaling this architecture, crosstalk from spectator qubits limits the gate fidelity to below 90%. We show that these spectator errors can be reduced to below 10−410^{-4}10−4 by reducing the coupling strength and by dynamically tuning transmons that are not used for a two-qubit operation to an off position. We further investigate the resilience of the operation to direct capacitive coupling between the transmon couplers and to microwave crosstalk.
A challenge in building large-scale superconducting quantum processors is the precise control and manipulation of the qubit state. However, the crosstalk between the microwave control lines impedes the parallel execution of high-fidelity digital and analog quantum operations. Here, we propose and demonstrate a universal compensation protocol for calibrating the microwave signal crosstalk. We also introduce amplified error sequences to optimize accuracy. Furthermore, we show a definitive improvement in parallel gate operations with crosstalk cancellation, demonstrating the technique's effectiveness. This work paves the way for superconducting hardware that features the automated calibration of microwave crosstalk, leading to enhanced fidelities in multiqubit circuits.
To scale up the number of qubits in a quantum processor, it is important that each qubit, or pair of qubits, can be controlled individually. Flux crosstalk between frequency-tunable superconducting qubits means that assumptions about addressability may no longer be valid. In this study, the authors detail several methods for measuring flux crosstalk between transmon qubits. These crosstalk metrics can then be used to predict $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}s$ performance of two-qubit gates, and thus employed as engineering milestones on the path to truly scalable quantum computers.
Flux-tunable superconducting qubits offer the potential for quantum information processing and simulation. However, flux crosstalk complicates achieving precise qubit frequency control, as characterizing and compensating for it becomes more challenging when scaling up circuits. In this study, we propose a design featuring a dual flux line for flux-tunable superconducting qubits, consisting of a pair of parallel current lines directing the current back to the enclosure. We conduct experimental comparisons of the DC flux crosstalk between the dual flux line design and the traditional one-way approach within a single chip. We observe a significant reduction in the DC flux crosstalk when utilizing the dual flux line, as supported by electromagnetic field simulations. Our design introduces an approach to scaling up flux-tunable superconducting circuits while maintaining a modest on-chip footprint.