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Realizing Rapid, High-Fidelity, Single-Shot Dispersive Readout of Superconducting Qubits
T. Walter, P. Kurpiers, S. Gasparinetti, P. Magnard, A. Potocnik, Y. Salathe, M. Pechal, M. Mondal, M. Oppliger, C. Eichler, A. Wallraff
TL;DR
Qubit relaxation during measurement limits how clearly its states can be distinguished. The paper optimizes dispersive readout using stronger interaction, resonator linewidth selection, a Purcell filter, and phase-sensitive amplification. It reports 98.25 ± 0.05% fidelity in 48 ns and 99.2% in 88 ns, and expects the design concepts to extend to multiplexed readout.
Problem
Qubit relaxation causes the excited-state response to approach the ground-state response, limiting their distinguishability during readout.
Source: §II · p. 2Method
The readout design combines stronger dispersive interaction and a suitable resonator linewidth with a Purcell filter and phase-sensitive parametric amplification.
Source: §I · p. 1Results
98.25 ± 0.05% readout fidelity was achieved in 48 ns with two-step pulses; at η = 0.75, fidelity reached 99.2% in 88 ns as amplifier bandwidth fell to 10 MHz.
Source: §II · p. 4Takeaways & Limitations
The authors expect their circuit-design concepts to be extensible to a multiplexed readout architecture.
Source: §IV · p. 5At the 99.2% fidelity setting, qubit lifetime T1 = 7.6 µs accounts for 76% of the excited-state error.
Source: §II · p. 4
Abstract
from arXiv · showhide
The speed of quantum gates and measurements is a decisive factor for the overall fidelity of quantum protocols when performed on physical qubits with finite coherence time. Reducing the time required to distinguish qubit states with high fidelity is therefore a critical goal in quantum information science. The state-of-the-art readout of superconducting qubits is based on the dispersive interaction with a readout resonator. Here, we bring this technique to its current limit and demonstrate how the careful design of system parameters leads to fast and high-fidelity measurements without affecting qubit coherence. We achieve this result by increasing the dispersive interaction strength, by choosing an optimal linewidth of the readout resonator, by employing a Purcell filter, and by utilizing phase-sensitive parametric amplification. In our experiment, we measure 98.25% readout fidelity in only 48 ns, when minimizing read-out time, and 99.2% in 88 ns, when maximizing the fidelity, limited predominantly by the qubit lifetime of 7.6 us. The presented scheme is also expected to be suitable for integration into a multiplexed readout architecture.
I. INTRODUCTION
Single-shot dispersive readout supports quantum protocols, but qubit decay during measurement limits state discrimination. This work speeds readout through stronger dispersive interaction and a suitable resonator linewidth, alongside a Purcell filter and phase-sensitive amplification.
I. INTRODUCTION
- Dispersive readout uses the qubit’s state-dependent frequency shift of a coupled resonator, and single-shot discrimination supports feedback tasks including error correction and teleportation.With quantum-limited amplification, state discrimination is predominantly limited by qubit decay during measurement.Source: §I · p. 1
- The experiment discriminates qubit states with fidelity above 98% in less than 50 ns.Source: §I · p. 1
- Stronger dispersive interaction and a suitable resonator linewidth shorten measurement, while a Purcell filter protects the qubit and a phase-sensitive amplifier detects microwave fields.Source: §I · p. 1
- A shaped two-step readout pulse populates the resonator faster than a simple square pulse.Source: §I · p. 1
II. DISCUSSION OF THE EXPERIMENT
The experiment combines a Purcell-filtered dispersive readout with optimized resonator parameters and phase-sensitive amplification. It demonstrates high assignment fidelity at short integration times, while longer measurements encounter qubit-transition errors.
II. DISCUSSION OF THE EXPERIMENT
- The device used a transmon-resonator dispersive coupling of χ/2π = −7.9 MHz, a Purcell-filtered effective linewidth κeff/2π = 37.5 MHz, and a qubit lifetime T1 = 7.6 µs.A phase-sensitive JPD amplifier operated with η = 0.66, 27 MHz bandwidth, and 26 dB gain.Source: §II · p. 1
- The experiment used preselection and gated or two-step pulses; 60,000 alternating ground- and excited-state preparations were fit with two Gaussians to set the decision threshold.The integrated quadrature is weighted in proportion to the mean difference between the state responses.Source: §II · p. 2
- State distinguishability peaked at τ = 64 ns; with longer integration, transitions increasingly limited fidelity, while overlap errors decreased with integration time.Transition errors increased with τ in proportion to 1 − e^(−τ/T1), with larger errors for prepared excited states.Source: §II · p. 3
- At τ = 56 ns, fidelity was 98.42 ± 0.07% with overlap error 0.39 ± .01%, matching Ref. in roughly one-third of its integration time.The experiment also reported 99.2% fidelity in less than a fourth of the integration time reported in Ref..Source: §II · pp. 3–4
- Overlap error decreased monotonically with measurement power, but total readout error reached a minimum at ndrive = 2.5 before rising from measurement-induced mixing.At 88 ns, the excited-state error was 0.96 ± 0.06%; the qubit lifetime accounted for 76% of it, and the remaining mixing estimate was an upper bound.Source: §II · p. 4
- 98.25 ± .05% fidelity was reached in 48 ns with a two-step pulse, while 99.2% required 88 ns with higher amplifier gain and 10 MHz bandwidth.The two-step result was 8 ns faster than gated measurements; the higher-gain configuration had longer integration time due to reduced bandwidth.Source: §II · p. 4
A. Dynamics of readout circuit
The readout information rate depends on the separation of the ground- and excited-state responses, and the integrated signal can be optimized by tuning the dispersive shift relative to the resonator linewidth. The best ratio depends on integration time.
A. Dynamics of readout circuit
- The phase-sensitive information rate S(t) is proportional to the difference between the ground- and excited-state responses in one quadrature.In the quasisteady-state limit, the full system can be reduced to readout-resonator dynamics when J ≪ κp.Source: A. Dynamics of readout circuit · p. 4
- In steady state, s(τ) is maximized at |χ/κeff| = 0.5, independent of the other fixed parameters.At short times, χτ ≲ 4.5, increasing κeff relative to χ can increase the initial signal while lowering its steady-state value.Source: A. Dynamics of readout circuit · p. 5
- For integration times below 50 ns, the integrated signal is larger at |χ/κeff| = 0.2 than at |χ/κeff| = 0.5.The experiment chose the 0.2 ratio to optimize short-time readout with a gated pulse.Source: A. Dynamics of readout circuit · p. 5
- For the optimal ratio |χ/κeff| = 0.5, the time to reach steady state is inversely proportional to χ, so larger χ accumulates signal faster.When χ and κeff become comparable to κp, the full dynamics, including the Purcell filter, converge more slowly to the steady-state ratio than the quasisteady-state solution predicts.Source: A. Dynamics of readout circuit · p. 5
B. Constraints
The achievable dispersive shift χ is bounded by Purcell protection, transmon coherence, and the validity of the dispersive approximation. The experiment balances these constraints through its choice of detuning and readout photon number.
B. Constraints
- Purcell filters allow |χ/κeff| ≈ 1/2 at larger χ without reaching a Purcell-limited qubit lifetime, but readout speed remains bounded by the maximum χ.Source: B. Constraints · p. 5
- In a transmon, increasing anharmonicity can favor larger χ but also reduces coherence through charge dispersion; the estimated dephasing upper bound was 150 µs near 6.3 GHz.The sample did not reach that estimated upper bound because of other dephasing mechanisms and fabrication limitations.Source: B. Constraints · p. 5
- The dispersive approximation requires ncrit ≫ 1, while avoiding unwanted qubit transitions requires ndrive ≪ ncrit; the experiment used ncrit ≈ 13 and ndrive ≈ ncrit/5.This choice gave λ ∼ 1.8% and a measurement-induced error < 0.23% at τ = 56 ns.Source: B. Constraints · p. 5
- To keep detuning ∆/2π ≈ 1.6 GHz while using the chosen ncrit, the design used g/2π ≈ 210 MHz and positive detuning to exploit χ's asymmetry with ∆.This allowed χ/2π > −7.5 MHz within the stated constraints.Source: B. Constraints · p. 5
IV. CONCLUSIONS
The authors demonstrate faster, higher-fidelity readout through circuit-parameter optimization and identify transmon-related constraints on χ. They expect the design concepts to extend to multiplexed readout, while measurement-induced mixing remains a topic for further investigation.
IV. CONCLUSIONS
- Optimizing circuit parameters increased the speed and fidelity of qubit readout, and the design concepts are expected to extend to multiplexed readout.The authors identify constraints on χ from the transmon and its dispersive interaction.Source: §IV · p. 5
- The role of measurement-induced mixing as a readout limitation remains an aspect for further investigation.The authors regard improvements in qubit T1 and amplifier performance as better-understood routes to further readout improvement.Source: §IV · p. 5
Appendix A: Setup details and sample characterization
This appendix describes the measurement chain and sample characterization, including resonator and qubit spectroscopy and readout-power calibration. A band-pass Purcell filter improves qubit lifetime beyond the limit imposed by readout-resonator bandwidth.
Appendix A: Setup details and sample characterization
- The output signal passes through the Purcell filter, isolation and coupling components, the JPD and further amplification before down-conversion and digitization by the FPGA.The ADC samples at 1 GHz; FPGA integration uses 8 ns bins.Source: Appendix A · p. 6
- The measured qubit lifetime is 30–100 times longer than predicted without the Purcell filter, though it is often shorter than the filter-imposed limit.The authors attribute the shortfall to fabrication limitations.Source: Appendix A · pp. 6–7
- Resonator transmission spectra for ground and excited states are fit with an input-output model to extract circuit parameters, while standard qubit spectroscopy determines frequency and anharmonicity.The fit assumes equal small internal loss rates for the filter and readout resonator.Source: Appendix A · p. 7
- Photon number is calibrated from the qubit ac-Stark shift versus drive power; output power tracks input power only at low readout powers because of self-Kerr nonlinearity.Figure 6 shows the frequency and power calibrations, with the optimal drive power marked.Source: Appendix A · p. 7, Figure 6 · p. 7
Appendix B: Preselection and histogram analysis
Preselection rejects events identified as excited before readout, reducing systematic errors from thermal or residual excitation. The appendix also describes the histogram fit and the limits of its transition model.
Appendix B: Preselection and histogram analysis
- Preselection thresholds the integrated value from the last 50 ns of the premeasurement pulse at the fitted Gaussian’s 99% cumulative distribution, rejecting likely thermally excited states.The procedure is intended to prevent systematic errors from thermal or residual excitation.Source: Appendix B · p. 7
- The rejected-event fraction increases with resonator drive, consistent with measurement-induced mixing; at vanishing drive, 0.3±0.1% excess rejection is attributed to residual thermal population.The authors identify reduced thermal photon flux at the qubit frequency as an additional benefit of the Purcell filter.Source: Appendix B · p. 7
- The single-shot histogram model uses normal distributions for filtered-quadrature counts and amplitudes for prepared-to-detected state combinations.The model does not account for transitions during measurement, though the authors consider it a reasonable approximation for the short times studied.Source: Appendix B · pp. 7–8
- Figure 7 characterizes amplifier gain versus frequency and signal power, and compares amplified-quadrature noise spectra with the amplifier on and off.The caption reports a peak gain of approximately 19.7 dB and a 3 dB bandwidth of 27 MHz.Source: Figure 7 · p. 8
Appendix C: Calibration of measurement efficiency
The appendix calibrates output-line measurement efficiency using phase-sensitive parametric amplification and noise measurements. Its estimated amplifier efficiency depends on gain, with higher gain trading off bandwidth.
Appendix C: Calibration of measurement efficiency
- Output-line efficiency is calibrated from added-noise measurements and expressed as the product of amplifier noise performance and loss before the amplifier.The amplifier’s noise performance is assessed in phase-sensitive operation, which amplifies and detects one signal quadrature.Source: Appendix C · p. 8
- The JPD’s pump power and flux bias set its gain, while an interferometrically adjusted cancellation tone suppresses pump leakage; peak gain is 19.7 dB at 4.754 GHz.The 1 dB compression point is about 10 dB above the qubit-readout power.Source: Appendix C · p. 8
- To measure phase-sensitive efficiency, two equal-power tones symmetrically detuned from the pump are phase-aligned along the amplified quadrature, and their noise spectrum is measured.The signal tones are detuned by 488 kHz on either side of the pump; the ADC records 8.192 µs at 1 ns resolution.Source: Appendix C · pp. 8–9
- At 4G0 = 26 dB, the estimated amplifier noise performance is ηφamp = 0.92; raising gain to 4G0 = 35 dB yields ηφamp = 0.99 at the cost of bandwidth.The estimate assumes parametric-amplifier noise is dominated by amplified vacuum noise and accounts for following HEMT noise divided by amplifier gain.Source: Appendix C · p. 9
Appendix D: Overlap error model
The overlap-error model represents the two qubit states as equal-variance Gaussian distributions and incorporates the response of the measurement-filter chain. It uses numerically solved signal dynamics without a quasi-steady-state assumption.
Appendix D: Overlap error model
- The readout is modeled as a random variable drawn from equal-variance Gaussian state distributions with opposite means, and without transitions the optimal threshold is their intersection.The variance is σ2(t) = 1/(4η).Source: Appendix D · p. 9
- The filter response combines the parametric amplifier, 8 ns FPGA boxcar integration and mode-matched digital weighting; the theory curves use full-system numerical solutions without a quasi-steady-state assumption.The model uses the response function of relevant filter elements for the measurement signal.Source: Appendix D · p. 9