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arXiv:2406.04891

Dispersive Qubit Readout with Intrinsic Resonator Reset

Markus Jerger, Felix Motzoi, Gao, Y., Christian Dickel, Lukas F. Buchmann, Andreas Bengtsson, Giovanna Tancredi, Christopher Warren, Jonas Bylander, David Peter Divincenzo, R. Barends, Pavel A. Bushev

Published Jun 7, 2024• 0 citations
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Abstract

A key challenge in quantum computing is speeding up measurement and initialization. Here, we experimentally demonstrate a dispersive measurement method for superconducting qubits that simultaneously measures the qubit and returns the readout resonator to its initial state. The approach is based on universal analytical pulses and requires knowledge of the qubit and resonator parameters, but needs no direct optimization of the pulse shape, even when accounting for the nonlinearity of the system. Moreover, the method generalizes to measuring an arbitrary number of modes and states. For the qubit readout, we can drive the resonator to $\sim 10^2$ photons and back to $\sim 10^{-3}$ photons in less than $3 κ^{-1}$, while still achieving a $T_1$-limited assignment error below 1\%. We also present universal pulse shapes and experimental results for qutrit readout.

DOI
10.48550/arxiv.2406.04891

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A key challenge in quantum computing is speeding up measurement and initialization. Here, we experimentally demonstrate a dispersive measurement method for superconducting qubits that simultaneously measures the qubit and returns the readout resonator to its initial state. The approach is based on universal analytical pulses and requires knowledge of the qubit and resonator parameters, but needs no direct optimization of the pulse shape, even when accounting for the nonlinearity of the system. Moreover, the method generalizes to measuring an arbitrary number of modes and states. For the qubit readout, we can drive the resonator to ∼102\sim 10^2∼102 photons and back to ∼10−3\sim 10^{-3}∼10−3 photons in less than 3κ−13 κ^{-1}3κ−1, while still achieving a T1T_1T1​-limited assignment error below 1%. We also present universal pulse shapes and experimental results for qutrit readout.
A key challenge in quantum computing is speeding up measurement and initialization. Here, we experimentally demonstrate a dispersive measurement method for superconducting qubits that simultaneously measures the qubit and returns the readout resonator to its initial state. The approach is based on universal analytical pulses and requires knowledge of the qubit and resonator parameters, but needs no direct optimization of the pulse shape, even when accounting for the nonlinearity of the system. Moreover, the method generalizes to measuring an arbitrary number of modes and states. For the qubit readout, we can drive the resonator to ∼102\sim 10^2∼102 photons and back to ∼10−3\sim 10^{-3}∼10−3 photons in less than 3κ−13 κ^{-1}3κ−1, while still achieving a T1T_1T1​-limited assignment error below 1\%. We also present universal pulse shapes and experimental results for qutrit readout.
Measurement and readout speed impose limits for logical qubit and qudit performance in quantum computing. Here, we experimentally demonstrate a universal analytical method for designing bandwidth-efficient dispersive readout pulses that intrinsically reset the resonator and extend it to multiple quantum states. The approach is based on universal analytical pulses and requires knowledge of the qubit and resonator parameters, but needs no direct optimization of the pulse shape, even when accounting for the nonlinearity of the system. When correcting for the Kerr nonlinearity, we find even more precise solutions to the speed-versus-photon-number trade-off, achieving 10 2 photon readout with reset to 10 − 2 within 3 κ − 1 duration and amplifier efficiency- and T 1 -limited assignment error around 0.6%. Results on qubits and qutrits validate the approach.
We theoretically propose and experimentally implement a method of measuring a qubit by driving it close to the frequency of a dispersively coupled bosonic mode. The separation of the bosonic states corresponding to different qubit states begins essentially immediately at maximum rate, leading to a speedup in the measurement protocol. Also the bosonic mode can be simultaneously driven to optimize measurement speed and fidelity. We experimentally test this measurement protocol using a superconducting qubit coupled to a resonator mode. For a certain measurement time, we observe that the conventional dispersive readout yields close to 100% higher average measurement error than our protocol. Finally, we use an additional resonator drive to leave the resonator state to vacuum if the qubit is in the ground state during the measurement protocol. This suggests that the proposed measurement technique may become useful in unconditionally resetting the resonator to a vacuum state after the measurement pulse.
Fast, accurate, and low-leakage qubit measurement is a key requirement for quantum error correction. Here, we demonstrate measurement of a superconducting transmon qubit with a total duration of 97(1) ns, defined as the time from the start of the measurement pulse until the measurement-induced error on a subsequent πππ-pulse operation falls below 10−410^{-4}10−4. By combining a large state-averaged resonator decay rate of κeff/2πκ_\mathrm{eff}/2πκeff​/2π = 30.8 MHz with a dispersive shift close to the optimal SNR-per-photon condition, we achieve an assignment error of 0.17(1)% using a 58-ns measurement pulse, with residual readout photons depleting passively in tens of nanoseconds without an active depletion pulse. Using a repeated-measurement sequence together with a leakage-sensitive measurement, we benchmark the measurement-induced state transitions, finding a per-measurement leakage rate of 2.7(2)×10−52.7(2) \times 10^{-5}2.7(2)×10−5, only twice the background rate and two orders of magnitude below the measurement-induced relaxation rate, which dominates the assignment error. Floquet simulations indicate that the multiphoton resonances present at the operating point are weakly coupled and traversed diabatically, without causing leakage. These results demonstrate that a large resonator decay rate, combined with a dispersive shift close to the optimal SNR-per-photon condition, can enable fast, high-fidelity, low-leakage dispersive readout at small qubit-resonator detuning.
Designing quantum systems with the measurement speed and accuracy needed for quantum error correction using superconducting qubits requires iterative design and testing informed by accurate models and characterization tools. We introduce a single protocol, with few prerequisite calibrations, to measure the dispersive shift, resonator linewidth, and drive power used in the dispersive readout of superconducting qubits. We find that the resonator linewidth is poorly controlled, with a factor of 2 variation between the maximum and minimum measured values, and this variation is likely to require focused attention in future quantum error correction experiments. We also introduce a protocol for measuring the efficiency of the readout system using the same power levels as are used in typical qubit readout, and without the need to measure the qubit dephasing. We routinely run these protocols on chips with tens of qubits to a hundred qubits, driven by automation software with little human interaction. Using the extracted system parameters, we find that a model based on these parameters predicts the readout signal-to-noise ratio to within 10% over a device with 54 qubits.
Superconducting circuits constitue a promising platform for physically realizing a quantum computer. One of the most fundamental operations of a quantum computer is to measure the state of its quantum bits (qubits). The measurement process should be as fast as possible, in order to minimize errors in the computation caused by noise. Conventionally, the state of a qubit in a superconducting circuit is determined by coupling the qubit to a readout resonator and measuring how the state of the resonator changes when a readout pulse is applied to it. Recently, a method was proposed that makes it possible to read out the state of a qubit faster by applying pulses to both the resonator and the qubit simultaneously. In this thesis, we study whether this so-called multichannel technique could be used to unconditionally drive the readout resonator back to its initial state after the readout has been finished. Using numerical simulations, we find that compared to just waiting passively, the time it takes to initialize the resonator can be reduced by up to 86%. We also implement a part of the initialization protocol experimentally and find the results encouraging for the future implementation of the full protocol.