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Fundamental Research

Optimal readout of superconducting qubits exploiting high-level states

Can Wang, Ming-Cheng Chen, Chao‐Yang Lu, Jian-Wei Pan

Published Jan 1, 2021• 11 citations
Publisher

Abstract

High-fidelity initialization, manipulation, and measurement of qubits are important in quantum computing. For the Google’s Sycamore processor, the gate fidelity of single- and two-qubit logic operations has improved to>99.6%, whereas single-shot measurement fidelity remains at the level of 97%, which severely limits the application of the superconducting approach to large-scale quantum computing. The current measurement scheme relies on the dispersive interaction between the qubit and the readout resonator, which was proposed back in 2004. However, the measurement fidelity is limited by the trade-off between the state separation and relaxation time of the two-level system. Recently, an exciting phenomenon was observed experimentally, wherein the separation-decay limit could be alleviated by exploiting the cascade decay nature of the higher levels; however, the mechanism and effectiveness of this phenomenon are still unclear. Herein, we present a theoretical tool to extract different types of errors in high-level states encoding dispersive measurement. For the realistic parameters of Google’s Sycamore processor, the use of state |2〉 is sufficient to suppress 92% of the decay readout error on average, where the total readout error is dominated by the background thermal excitation. We also show counter-intuitively that, the assistance of high-level states is effective in the measurement of logic 0, where there is no decay process.

DOI
10.1016/j.fmre.2020.12.008

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High-fidelity initialization, manipulation, and measurement of qubits are important in quantum computing. For the Google’s Sycamore processor, the gate fidelity of single- and two-qubit logic operations has improved to>99.6%, whereas single-shot measurement fidelity remains at the level of 97%, which severely limits the application of the superconducting approach to large-scale quantum computing. The current measurement scheme relies on the dispersive interaction between the qubit and the readout resonator, which was proposed back in 2004. However, the measurement fidelity is limited by the trade-off between the state separation and relaxation time of the two-level system. Recently, an exciting phenomenon was observed experimentally, wherein the separation-decay limit could be alleviated by exploiting the cascade decay nature of the higher levels; however, the mechanism and effectiveness of this phenomenon are still unclear. Herein, we present a theoretical tool to extract different types of errors in high-level states encoding dispersive measurement. For the realistic parameters of Google’s Sycamore processor, the use of state |2〉 is sufficient to suppress 92% of the decay readout error on average, where the total readout error is dominated by the background thermal excitation. We also show counter-intuitively that, the assistance of high-level states is effective in the measurement of logic 0, where there is no decay process.
Qubit measurements are central to quantum information processing.In the field of superconducting qubits, standard readout techniques are limited not only by the signal-to-noise ratio, but also by state relaxation during the measurement.In this work, we demonstrate that the limitation due to relaxation can be suppressed by using the many-level Hilbert space of superconducting circuits: In a multilevel encoding, the measurement is corrupted only when multiple errors occur.Employing this technique, we show that we can directly resolve transmon gate errors at the level of one part in 10 3 .Extending this idea, we apply the same principles to the measurement of a logical qubit encoded in a bosonic mode and detected with a transmon ancilla, implementing a proposal by Hann et al. [Phys. Rev. A 98, 022305 (2018)].Qubit state assignments are made based on a sequence of repeated readouts, further reducing the overall infidelity.This approach is quite general, and several encodings are studied; the codewords are more distinguishable when the distance between them is increased with respect to photon loss.The trade-off between multiple readouts and state relaxation is explored and shown to be consistent with the photon-loss model.We report a logical assignment infidelity of 5.8 × 10 -5 for a Fock-based encoding and 4.2 × 10 -3 for a quantum error correction code (the S ¼ 2, N ¼ 1 binomial code).Our results not only improve the fidelity of quantum information applications, but also enable more precise characterization of process or gate errors.
Single-shot fidelity is the standard benchmark for superconducting qubit readout, yet it does not directly minimize the wall-clock time needed to certify a quantum state. We treat the dispersive measurement record as a stochastic communication channel and compute the classical Chernoff information governing the multi-shot error exponent, using a trajectory model that incorporates T1 relaxation with full cavity memory. The integration time that maximizes single-shot fidelity and the time that minimizes total certification time do not coincide. For representative transmon parameters and hardware overheads, the throughput-optimal window is longer, cutting certification time by roughly 9-11%, with the gain saturating near 1.13x in the high-readout-power and high-overhead regime. Benchmarking the extracted classical information against the unit-efficiency Gaussian Chernoff limit defines an information-extraction efficiency: dispersive schemes capture ~45% at short integration times, dropping to eta_info(tau_rate) ~ 12% at tau_rate ~ 1.22 us as T1-induced trajectory smearing accumulates. These results connect readout calibration directly to the operational objective of minimizing certification time in high-throughput superconducting processors.
Measuring the state of qubits is one of the fundamental operations of a quantum computer. Currently, state-of-the-art high-fidelity single-shot readout of superconducting qubits relies on parametric amplifiers at the millikelvin stage. However, parametric amplifiers are challenging to scale beyond hundreds of qubits owing to practical size and power limitations. Nanobolometers have a multitude of properties that are advantageous for scalability and have recently shown sensitivity and speed promising for qubit readout, but such thermal detectors have not been demonstrated for this purpose. In this work, we utilize an ultrasensitive bolometer in place of a parametric amplifier to experimentally demonstrate single-shot qubit readout. With a readout duration of 13.9 μs13.9~μ\mathrm{s}13.9 μs, we achieve a single-shot fidelity of 0.618 which is mainly limited by the energy relaxation time of the qubit, T1=28 μsT_1 = 28~μ\mathrm{s}T1​=28 μs. Without the T1T_1T1​ errors, we find the fidelity to be 0.927. In the future, high-fidelity single-shot readout may be achieved by straightforward improvements to the chip design and experimental setup, and perhaps most interestingly by the change of the bolometer absorber material to reduce the readout time to the hundred-nanosecond level and beyond.
Measuring the state of a qubit is a key fundamental operation of a quantum computer. High-fidelity single-shot readout of superconducting qubits can be achieved using parametric amplifiers at millikelvin temperatures. However, scaling parametric amplifiers beyond hundreds of qubits is challenging due to practical size and power limitations. Nanobolometers can, in contrast, offer scalability, sensitivity and speed suitable for qubit readout. Here we show that a bolometer can provide single-shot qubit readout with a readout duration of 13.9 μs and a single-shot fidelity of 0.618. The fidelity is mainly limited by the energy relaxation time of the qubit (28 μs), and a fidelity of 0.927 is found after removing errors arising from this relaxation. In the future, higher-fidelity single-shot readout may be achieved through improvements in chip design and experimental setup, as well as a change in the bolometer absorber material to reduce the readout time to the level of hundreds of nanoseconds and below.
If general quantum information processing and communication using superconducting qubits is to be successful, it is crucial to realize fast, single-shot readout with fidelity approaching 100%. Starting from the physics of measurement, the authors explore current engineering limitations and find a way to halve the measurement time for single-shot dispersive readout, without sacrificing fidelity. This theoretical and experimental insight may bring superconducting quantum technology even closer to the demanding thresholds of quantum computing.
High-fidelity qubit measurements play a crucial role in quantum computation, communication, and metrology. In recent experiments, it has been shown that readout fidelity can be improved by performing repeated quantum nondemolition (QND) readouts of a qubit's state through an ancilla. For a qubit encoded in a two-level system, the fidelity of such schemes is limited by the fact that a single error can destroy the information in the qubit. On the other hand, if a bosonic system is used, this fundamental limit can be overcome by utilizing higher levels such that a single error still leaves states distinguishable. In this work, we present a robust readout scheme which leverages both repeated QND readouts and higher-level encodings to asymptotically suppress the effects of mode relaxation and individual measurement infidelity. We calculate the measurement fidelity in terms of general experimental parameters, provide an information-theoretic description of the scheme, and describe its application to several encodings, including cat and binomial codes.