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arXiv:2105.14360 · PRX Quantum

Calibration of Flux Crosstalk in Large-Scale Flux-Tunable Superconducting Quantum Circuits

Xi Dai, Daniel Tennant, Robbyn Trappen, Antonio Martinez, Denis Melanson, Muhammet Ali Yurtalan, Yongchao Tang, S. Novikov, Jeffrey A. Grover, Steven Disseler, James I. Basham, Rabindra Nath Das, David K. Kim, Alexander J. Melville, Bethany M. Niedzielski, Steven J. Weber, Jonilyn Yoder, Daniel A. Lidar, Adrian Lupaşcu

Published Oct 20, 2021• 39 citations
arXivHTMLPDF

Abstract

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%.

DOI
10.1103/prxquantum.2.040313

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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%.
Abstract Flux tunability is an important engineering resource for superconducting circuits. Large-scale quantum computers based on flux-tunable superconducting circuits face the problem of flux crosstalk, which needs to be accurately calibrated to realize high-fidelity quantum operations. Typical calibration methods either assume that circuit elements can be effectively decoupled and simple models can be applied, or require a large amount of data. Such methods become ineffective as the system size increases and circuit interactions become stronger. Here we propose a new method for calibrating flux crosstalk, which is independent of the underlying circuit model. Using the fundamental property that superconducting circuits respond periodically to external fluxes, crosstalk calibration of N flux channels can be treated as N independent optimization problems, with the objective functions being the periodicity of a measured signal depending on the compensation parameters. We demonstrate this method on a small-scale quantum annealing circuit based on superconducting flux qubits, achieving comparable accuracy with previous methods. We also show that the objective function usually has a nearly convex landscape, allowing efficient optimization.
Flux tunability is an important engineering resource for superconducting circuits. Large-scale quantum computers based on flux-tunable superconducting circuits face the problem of flux crosstalk, which needs to be accurately calibrated to realize high-fidelity quantum operations. Typical calibration methods either assume that circuit elements can be effectively decoupled and simple models can be applied, or require a large amount of data. Such methods become ineffective as the system size increases and circuit interactions become stronger. Here we propose a new method for calibrating flux crosstalk, which is independent of the underlying circuit model. Using the fundamental property that superconducting circuits respond periodically to external fluxes, crosstalk calibration of N flux channels can be treated as N independent optimization problems, with the objective functions being the periodicity of a measured signal depending on the compensation parameters. We demonstrate this method on a small-scale quantum annealing circuit based on superconducting flux qubits, achieving comparable accuracy with previous methods. We also show that the objective function usually has a nearly convex landscape, allowing efficient optimization.
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.
Crosstalk refers to unwanted qubit addressing. This is particularly detrimental when scaling up quantum information systems because unintended interactions limit their overall performance. For superconducting qubits, tunable couplings and frequency tunability achieved through externally applied magnetic fluxes enable high-fidelity entangling gates; however, they also introduce crosstalk through unintended flux coupling. In this work, we investigate the impact of time-dependent external magnetic fluxes in quantized circuits on superconducting qubit couplings. We find that non-trivial cross-voltage driving emerges between capacitively linked qubits when the magnetic flux threading the SQUID loop of a qubit varies in time, in a manner analogous to Faraday's law of induction. Crucially, we show that this effect enables fast single qubit control through the coupler element in standard tunable-coupler architectures, potentially eliminating the need for individual microwave XYXYXY control lines.
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.
Crosstalk refers to unwanted qubit addressing. This is particularly detrimental when scaling up quantum information systems because unintended interactions limit their overall performance. For superconducting qubits, tunable couplings and frequency tunability achieved through externally applied magnetic fluxes enable high-fidelity entangling gates; however, they also introduce crosstalk through unintended flux coupling. In this work, we investigate the impact of time-dependent external magnetic fluxes in quantized circuits on superconducting qubit couplings. We find that nontrivial cross-voltage driving emerges between capacitively linked qubits when the magnetic flux threading the superconducting loop of a qubit varies in time, in a manner analogous to Faraday’s law of induction. Crucially, we show that this effect enables fast single-qubit control through the coupler element in standard tunable-coupler architectures, potentially eliminating the need for individual microwave X Y control lines.