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arXiv:1908.01869 · Physical Review X

High-Fidelity Measurement of Qubits Encoded in Multilevel Superconducting Circuits

Salvatore S. Elder, Christopher S. Wang, Philip Reinhold, Connor T. Hann, Kevin S. Chou, Brian Lester, Serge Rosenblum, Luigi Frunzio, Liang Jiang, Robert J. Schoelkopf

Published Jan 2, 2020• 82 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevx.10.011001

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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.
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.
Abstract High-fidelity and rapid readout of a qubit state is key to quantum computing and communication, and it is a prerequisite for quantum error correction. We present a readout scheme for superconducting qubits that combines two microwave techniques: applying a shelving technique to the qubit that effectively increases the energy-relaxation time, and a two-tone excitation of the readout resonator to distinguish among qubit populations in higher energy levels. Using a machine-learning algorithm to post-process the two-tone measurement results further improves the qubit-state assignment fidelity. We perform single-shot frequency-multiplexed qubit readout, with a 140 ns readout time, and demonstrate 99.5% assignment fidelity for two-state readout and 96.9% for three-state readout—without using a quantum-limited amplifier.
Quantum error correction of a grid-state qubit with state preparation and measurement errors below 10−310^{-3}10−3
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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.
The accurate measurement of quantum two-level objects (qubits) is crucial for developing quantum computers. Over the last decade, the measure of choice for benchmarking readout routines for superconducting qubits has been assignment fidelity; however, this method only focuses on the preparation of computational basis states and therefore does not provide a complete characterization of the readout. Here, we expand the focus to the use of detector tomography to fully characterize multiqubit readout of superconducting transmon qubits. The impact of different readout parameters on the rate of information extraction is studied using quantum-state reconstruction infidelity as a proxy. The results are then compared with assignment fidelities, showing good agreement for separable two-qubit states. We therefore propose the rate of infidelity convergence as a validation tool for assignment fidelity and a more comprehensive benchmark for single- and multiqubit readout optimization. To make the best use of experimental resources, we investigate the most efficient distribution of a limited shot budget between detector tomography and state reconstruction within the context of single- and two-qubit experiments. To address the growing interest in three-qubit gates and test the scalability of the validation tool, we perform three-qubit quantum-state tomography that goes beyond conventional readout-error-mitigation methods and find a factor-of-30 reduction in quantum infidelity. Our results demonstrate that qubit readout correlations are not induced by a significantly reduced state distinguishability. Consequently, correlation coefficients can serve as a valuable tool in qubit readout optimization.
Fast, high-fidelity, and low back-action readout plays a crucial role in the advancement of quantum error correction (QEC). Here, we demonstrate high-performance multiplexed readout of superconducting qubits using a tunable broadband Purcell filter, effectively resolving the fundamental trade-off between measurement speed and photon-noise-induced dephasing. By dynamically tuning the filter parameters, we suppress photon-noise-induced dephasing by a factor of 7 in idle status, while enabling rapid, high-fidelity readout in measurement status. We achieve 99.6\% single-shot readout fidelity with 100~ns readout pulse, limited primarily by relaxation errors during readout. Using a multilevel readout protocol, we further attain 99.9\% fidelity in 50~ns. Simultaneous readout of three qubits using 100~ns pulses achieves an average fidelity of 99.5\% with low crosstalk. Additionally, the readout exhibits high quantum-nondemolition (QND) performance: 99.4\% fidelity over repeated measurements and a low leakage rate below 0.1\%. Building on the tunable broadband filter, we further propose a scalable readout scheme for surface code QEC with enhanced multiplexing capability, offering a promising solution for fast and scalable QEC.