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Universal scalable characterization and correction of pulse distortions in controlled quantum systems

Liang-Liang Guo, Peng Duan, Sheng Zhang, Xin-Xin Yang, Chi Zhang, Lei Du, Hai-Feng Zhang, Hao-Ran Tao, Tian-Le Wang, Zhi-Long Jia, Zhao-Yun Chen, and Guo-Ping Guo

Phys. Rev. Applied 21, 064060 – Published 26 June 2024

Abstract

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 $1 \times 10^{- 3}$ , 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.

Received 19 April 2023
Revised 13 May 2024
Accepted 21 May 2024

DOI:https://doi.org/10.1103/PhysRevApplied.21.064060

Physics Subject Headings (PhySH)

Optoelectronics Quantum control Quantum error correction Quantum gates Quantum information with solid state qubits Quantum simulation

Superconducting qubits

Microwave techniques

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Liang-Liang Guo^1,2, Peng Duan^1,2,*, Sheng Zhang^1,2, Xin-Xin Yang ^1,2, Chi Zhang^1,2, Lei Du^1,2, Hai-Feng Zhang ^1,2, Hao-Ran Tao^1,2, Tian-Le Wang^1,2, Zhi-Long Jia^1,2,3, Zhao-Yun Chen^4,†, and Guo-Ping Guo ^1,2,3,‡

¹Chinese Academy of Sciences (CAS) Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
²CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
³Origin Quantum Computing Company Limited, Hefei, Anhui 230088, China
⁴Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui 230088, China

^*Corresponding author: [email protected]
^†Corresponding author: [email protected]
^‡Corresponding author: [email protected]

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Vol. 21, Iss. 6 — June 2024

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Figure 1
Two methods to describe LTI systems. (a) The unit step response of different control lines: the legend is valid for all subplots. The green circle is the response sampled during the experiment and the orange line is the fitting result with Eq. (4). (b) The pole-zero plot, where $\times$ indicates poles and the circle indicates zeros.
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Figure 2
The unit step response of the AWG with or without correction. (a) The rising edge of the response. The rise time after correction increases slightly because of the use of the Gaussian FIR digital filter. (b),(c) The (b) short- and (c) long-time-scale response. We fit the uncorrected response and Eq. (4) with five real poles is adequate to fit the IIR behavior well. The response after correction is smoothed with a moving-average filter.
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Figure 3
The determination of the low-temperature line response using closed-loop optimization. (a) The pulse sequence used to optimize the system-function parameters. On the $X$ - $Y$ line, we play a sequence of Clifford gates with length $m$ , appended by recovery Clifford gates $C_{r}$ that make the ideal operation the identity. We define the sequence fidelity as the ground-state population ( $P_{0}$ ). (b) The change of the sequence fidelity at $m = 50$ versus the number of evaluations. The optimization converges to the target value, which is the fidelity of the RB sequence at $m = 50$ when no flux pulse is applied on the $Z$ line. (c) The unit step responses correspond to the parameters listed in Table 1. Variations between control lines with the same setup are indeed small. (d),(e) The sensitivity analysis of selected parameters for (d) $m = 1$ and (e) $m = 50$ . $δ$ is the deviation fraction of the parameters from their optimum.
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Figure 4
The residual response after distortion correction. (a) A schematic of the predistortion procedure. The desired pulse $V_{d} (t)$ is predistorted by digital filters before being sent to a digital-to-analog converter (DAC), then transmitted through control lines, and finally arrives at the qubit. (b),(c) The (b) short- and (c) long-time-scale residual responses after distortion correction. The unit step response is sampled using the cryoscope method [20] and the distortion is corrected to the range within $10^{- 3}$ . (d) A comparison of the calculation times between the two predistortion schemes. The digital filter comprises linear operations, whereas deconvolution involves Fourier-transform and inverse-Fourier-transform operations.
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Figure 5
The full wiring diagram of the experimental setup. The experimental wiring setup and quantum control system are developed jointly with OriginQ, Inc. The customized dc bias tee removes the capacitor and comprises a 6.7- $μ H$ conical inductor and a grounded 50- $Ω$ resistor at the dc port.
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Figure 6
The unit-step-response measurement of the flux control lines. (a) The pulse sequence used in this experiment. (b) We sweep the compensation amplitude $Δ Z$ to make the $π$ pulse recover its fidelity as we change the delay time. (c) The reconstructed unit step response and the system-function fit. We present the results for the bias tee with or without a grounded 50- $Ω$ resistor.
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Physical Review Applied

Universal scalable characterization and correction of pulse distortions in controlled quantum systems

Liang-Liang Guo, Peng Duan, Sheng Zhang, Xin-Xin Yang, Chi Zhang, Lei Du, Hai-Feng Zhang, Hao-Ran Tao, Tian-Le Wang, Zhi-Long Jia, Zhao-Yun Chen, and Guo-Ping Guo

Phys. Rev. Applied 21, 064060 – Published 26 June 2024

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