Model-Based Optimization of Superconducting Qubit Readout

Andreas Bengtsson, Alex Opremcak, Mostafa Khezri, Daniel Sank, Alexandre Bourassa, Kevin J. Satzinger, Sabrina Hong, Catherine Erickson, Brian J. Lester, Kevin C. Miao, Alexander N. Korotkov, Julian Kelly, Zijun Chen, and Paul V. Klimov

Phys. Rev. Lett. 132, 100603 – Published 8 March 2024

Abstract

Measurement is an essential component of quantum algorithms, and for superconducting qubits it is often the most error prone. Here, we demonstrate model-based readout optimization achieving low measurement errors while avoiding detrimental side effects. For simultaneous and midcircuit measurements across 17 qubits, we observe 1.5% error per qubit with a 500 ns end-to-end duration and minimal excess reset error from residual resonator photons. We also suppress measurement-induced state transitions achieving a leakage rate limited by natural heating. This technique can scale to hundreds of qubits and be used to enhance the performance of error-correcting codes and near-term applications.

Received 8 August 2023
Accepted 2 February 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.100603

Physics Subject Headings (PhySH)

Quantum benchmarking Quantum error correction Quantum gates Quantum information with solid state qubits Quantum software

Superconducting qubits

Quantum Information, Science & Technology

Authors & Affiliations

Andreas Bengtsson ¹, Alex Opremcak¹, Mostafa Khezri¹, Daniel Sank ¹, Alexandre Bourassa ¹, Kevin J. Satzinger¹, Sabrina Hong ¹, Catherine Erickson¹, Brian J. Lester¹, Kevin C. Miao¹, Alexander N. Korotkov^1,2, Julian Kelly¹, Zijun Chen¹, and Paul V. Klimov¹

¹Google Quantum AI, Santa Barbara, 93111 California, USA
²Department of Electrical and Computer Engineering, University of California, Riverside, 92521 California, USA

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Vol. 132, Iss. 10 — 8 March 2024

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Images

Figure 1
(a) The optimization workflow. We build error models from fixed parameters like resonator frequency and linewidth, which we then run an optimizer on to find a set of variable parameters (e.g., pulse amplitude and length) that gives low errors. The output of the optimizer is a unique pulse shape for each qubit, as well as qubit frequency (not shown). (b) Examples of readout error mechanisms. The middle qubit, which is in $| 1 ⟩$ , is coupled to two other qubits. During readout of the middle qubit its excitation can relax to $| 0 ⟩$ ; swap into $| 1 ⟩$ of the right qubit; or combine with the excitation in the left qubit to $| 2 ⟩$ . Additionally, photons in the readout resonator can excite the qubit up to a high state. (c) Number of photons in the readout resonator as a function of time, both simulated (solid line) and measured (circles). The inset shows the simulated values on a logarithmic scale. Residual photons can cause reset and dephasing errors.
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Figure 2
Error models and their dependence on readout parameters. (a) Separation and relaxation errors, and residual photon number, versus the qubit frequency with amplitude and length kept fixed. Circles are measured data, and lines are simulated values. As the qubit frequency changes, we track the readout pulse frequency to be centered between the two dressed resonator states. The peak at 6 GHz is due to a two-level system defect. (b) and (c) show the same models, but versus pulse amplitude and length, respectively. The total readout time is kept constant, such that when the pulse length increases, the ringdown time decreases. The nonswept parameters are kept fixed at the values indicated by the dashed vertical lines in the respective panels.
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Figure 3
Benchmarking of the optimized readout performance. We compare three optimization strategies: in situ; ex situ with only predictive models; ex situ with predictive and heuristic models. (a) The distance-3 surface code with 9 data qubits (yellow) and 8 measure qubits (blue), used for the benchmarking. (b) Simultaneous measurement errors for two cases: all qubits, only measure qubits. We prepare a set of random states across the qubits and perform simultaneous measurements. The data show the combination of the two cases. (c) Reset error added by a preceding measurement, benchmarked on the measure qubits. The excess reset error is caused by residual photons in the readout resonator. (d) Average leakage probability in the measure qubits after preparing $| 1 ⟩$ and performing $N$ measurements. The dashed line shows the heating limit where the measurements are replaced by an equivalent amount of waiting time.
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