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arXiv:2309.09628 · Chinese Physics B

Correcting on-chip distortion of control pulses with silicon spin qubits

Ming Ni, Rong-Long Ma, Zhenzhen Kong, Ning 凝 Chu 楚, Wei-Zhu Liao, Sheng-Kai Zhu, Chu Wang, Gang 刚 Luo 罗, Di Liu, Gang 刚 Cao 曹, Guilei Wang, Hai-Ou Li, Guo‐Ping Guo

Published Nov 1, 2024• 2 citations
arXivHTMLPDF

Abstract

Abstract In semiconductor quantum dot systems, pulse distortion is a significant source of coherent errors, which impedes qubit characterization and control. Here, we demonstrate two calibration methods using a two-qubit system as the detector to correct distortion and calibrate the transfer function of the control line. Both methods are straightforward to implement, robust against noise, and applicable to a wide range of qubit types. The two methods differ in correction accuracy and complexity. The first, coarse predistortion (CPD) method, partially mitigates distortion. The second, all predistortion (APD) method, measures the transfer function and significantly enhances exchange oscillation uniformity. Both methods use exchange oscillation homogeneity as the metric and are suitable for any qubit driven by a diabatic pulse. We believe these methods will enhance qubit characterization accuracy and operation quality in future applications.

DOI
10.1088/1674-1056/ad8db1

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Abstract In semiconductor quantum dot systems, pulse distortion is a significant source of coherent errors, which impedes qubit characterization and control. Here, we demonstrate two calibration methods using a two-qubit system as the detector to correct distortion and calibrate the transfer function of the control line. Both methods are straightforward to implement, robust against noise, and applicable to a wide range of qubit types. The two methods differ in correction accuracy and complexity. The first, coarse predistortion (CPD) method, partially mitigates distortion. The second, all predistortion (APD) method, measures the transfer function and significantly enhances exchange oscillation uniformity. Both methods use exchange oscillation homogeneity as the metric and are suitable for any qubit driven by a diabatic pulse. We believe these methods will enhance qubit characterization accuracy and operation quality in future applications.
Gate-defined semiconductor quantum dots utilize fast electrical control to manipulate spin and charge states of individual electrons. Electrical pulse distortions can limit control fidelities but are difficult to measure at the device level. Here, we use detuning-axis pulsed spectroscopy to characterize baseband pulse distortions in a silicon double quantum-dot. We extract the gate-voltage impulse response and apply a digital pre-distortion filter to eliminate pulse distortions on timescales longer than 1~ns. With the pre-distortion, we reduce the frequency chirp of coherent exchange oscillations in a singlet-triplet qubit. Our results suggest a scalable and tuning-efficient method for characterizing pulse distortions in quantum-dot spin qubits.
For superconducting quantum processors, stable high-fidelity two-qubit operations depend on precise flux control of the tunable coupler. However, the pulse distortion poses a significant challenge to the control precision. Current calibration methods, which often rely on microwave crosstalk or additional readout resonators for coupler excitation and readout, tend to be cumbersome and inefficient, especially when couplers only have flux control. Here, we introduce and experimentally validate a pulse calibration scheme that exploits the strong coupling between qubits and couplers, eliminating the need for extra coupler readout and excitation. Our method directly measures the short-time and long-time step responses of the coupler flux pulse transient, enabling us to apply predistortion to subsequent signals using fast Fourier transformation and deconvolution. This approach not only simplifies the calibration process, but also significantly improves the precision and stability of the flux control. We demonstrate the efficacy of our method through the implementation of diabatic controlled-ZZZ (cz) and iiiswap gates with fidelities of $99.61\mathrm{%}\ifmmode\pm\else\textpm\fi{}0.04\mathrm{%}$ and $99.82\mathrm{%}\ifmmode\pm\else\textpm\fi{}0.02\mathrm{%}$, respectively, as well as a series of diabatic controlled-phase gates with high fidelities characterized by cross-entropy benchmarking. The consistency and robustness of our technique are further validated by the reduction in pulse distortion and phase error observed across multilayer cz gates. These results underscore the potential of our calibration and predistortion method to enhance the performance of two-qubit gates in superconducting quantum processors.
Flux-tunable superconducting qubits rely on fast flux control pulses to implement two-qubit entangling quantum gates, a key building block for quantum algorithms. However, distortion effects introduced by non-ideal control electronics, parasitic components, and the cryogenic quantum chip response can all degrade the gate fidelity. We present a digital predistortion (DPD) framework for characterizing and then compensating for these distortions using a combination of infinite impulse response (IIR) and finite impulse response (FIR) filters. Experiments on a flux-tunable quantum processing unit (QPU) demonstrate a successful correction of step-response distortions on the flux-control line, with a compensated control signal showing only sub-percent deviations from the ideal target linear behavior. The demonstrated method enables automated rapid calibration of flux control channels for superconducting QPUs.
The implementation of high-fidelity quantum gates for spin qubits requires accurate control of exchange interactions between electrons confined in quantum dots, but pulse distortions can limit this control accuracy. Although linear-dynamical distortions can be compensated for by appropriately convolving the control signal, determining the necessary convolution requires detailed knowledge of the distortion's transfer function, and therefore the calibration of numerous parameters. Alternatively, control pulses can be designed to have a net-zero time integral canceling out linear-dynamical pulse distortions. We generalize net-zero pulse designs to quasi-zero pulses allowing net-positive but reduced time integrals. Using these pulse designs, we systematically develop complete gate sets for exchange-only qubits, and study the resulting tradeoffs between pulse duration, fidelity, and the required number of tunable parameters, both in simulation and experiment. We benchmark the optimized gate pulses on Intel's Tunnel Falls six-dot device and show they achieve fidelities similar to those obtained with a full filtering approach, with identical pulse durations and fewer tuning parameters. This reduction in complexity opens the door to fast and easily automated calibration schemes compatible with large-scale commercial quantum devices.
Abstract Semiconductor spin qubits demonstrated single-qubit gates with fidelities up to 99.9 % benchmarked in the single-qubit subspace. However, tomographic characterizations reveal non-negligible crosstalk errors in a larger space. Additionally, it was long thought that the two-qubit gate performance is limited by charge noise, which couples to the qubits via the exchange interaction. Here, we show that coherent error sources such as a limited bandwidth of the control signals, diabaticity errors, microwave crosstalk, and non-linear transfer functions can equally limit the fidelity. We report a simple theoretical framework for pulse optimization that relates erroneous dynamics to spectral concentration problems and allows for the reuse of existing signal shaping methods on a larger set of gate operations. We apply this framework to common gate operations for spin qubits and show that simple pulse shaping techniques can significantly improve the performance of these gate operations in the presence of such coherent error sources. The methods presented in the paper were used to demonstrate two-qubit gate fidelities with F > 99.5 % in Xue et al (2022 Nature 601 343). We also find that single and two-qubit gates can be optimized using the same pulse shape. We use analytic derivations and numerical simulations to arrive at predicted gate fidelities greater than 99.9% with duration less than, 4 / ( Δ E z ) where Δ E z is the difference in qubit frequencies.
In quantum computation, control signals are adversely affected by distortion due to nonidealities in control chains. In order to implement high-fidelity digital and analog quantum operations, one must characterize the distortion and compensate for it. Here, we propose and experimentally verify an extensible method to model the behavior of control lines with the system function and correct it with digital filters. We correct the distortion of the superconducting-qubit flux control lines within a precision of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which ensures gate fidelity free of the limit of pulse distortion. For the purpose of more accurate and scalable parameter extraction of the low-temperature line response, we employ an optimization-based protocol and the convergence is fast by setting the result of adjacent control lines with the same setup as the initial values. The techniques presented here improve distortion calibration efficiency and enable distortion-free operations, which paves the way for high-precision control of quantum computation and quantum simulation.