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Bulletin of the American Physical Society

Fast dispersive, Purcell-filtered measurement and reset using smooth and simple analytic pulse shapes

Lukas F. Buchmann, Felix Motzoi, Christian Dickel

Published Mar 5, 2019• 0 citations
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We demonstrate a dispersive measurement pulse shaping technique that allows for arbitrarily fast quantum non-demolition, single-quadrature measurements of non-linear systems and unconditionally leaves the measurement resonator empty. For single-qubit measurements, current measurements are limited to the 99% fidelity range due to relaxation during the process. However, trying to go to shorter times to circumvent this with square or composite digital pulses leads to leftover cavity population after measurement of the same order of error. These effects can be suppressed using simple smooth pulse shapes from a similar family of pulses as DRAG shaping, used in the context of leakage removal in superconducting qubits; here, it can be derived exactly for arbitrarily many measured modes. Beyond single qubits, the measurement pulses are fully general to dispersive measurement systems. This includes multi-qubit and multi-state (leakage) measurements where the measurement can be done in a single shot and with a single homodyne phase. Another major challenge for fast measurement is depopulating Purcell filter cavities, which we show can readily be achieved using derivative shaping. Finally, we show how to apply the technique to cascaded cavity systems, e.g~for fast remote entanglement generation.
Rapid reset and readout of qubit states are essential for quantum error correction, yet accelerating these operations through stronger coupling to a dissipative environment inevitably increases qubit decay via the Purcell effect. Here we present a broadband Purcell filter that decouples the reset and readout paths, enabling both operations to be independently optimized without compromising qubit coherence. The filter employs two engineered notches - an intrinsic notch and a bandstop notch - to provide broadband Purcell protection, together with an additional reset stub that creates a reset mode below the protected band. To enable fast reset while suppressing filter-mediated interactions between qubits, we couple each qubit to a dedicated reset resonator. We experimentally demonstrate Purcell-limited relaxation times exceeding 1 ms across a 1.2 GHz bandwidth, simultaneously with 500 ns readout without a Josephson parametric amplifier and 100 ns reset with 99.6% efficiency. The reset resonator is designed with a deliberate kappa-chi mismatch, which suppresses photon-shot-noise-induced dephasing by a factor of 70 compared to the readout resonator. Our work provides a scalable hardware solution that resolves the traditional trade-off between fast qubit operations and qubit protection, advancing the prospects for fault-tolerant quantum computing.
Fast and accurate qubit measurement remains a critical challenge on the path to fault-tolerant quantum computing. In superconducting quantum circuits, fast qubit measurement has been achieved using a dispersively coupled resonator with a large externally limited linewidth. This necessitates the use of a Purcell filter that protects the qubit from relaxation through the readout channel. Here, we show that a readout resonator and filter resonator, coupled to each other both capacitively and inductively via a multiconductor transmission line, can produce a compact notch-filter circuit that effectively eliminates the Purcell decay channel through destructive interference. By utilizing linewidths as large as 42 MHz, we perform simultaneous readout of four qubits using a 56-ns integration window and benchmark an average assignment fidelity of 99.77%, with the highest qubit assignment fidelity exceeding 99.9%. Including the simulated readout ring-down time, the total readout duration was between 115 and 215 ns for the four qubits, which we anticipate can be reduced to around 100 ns with active ring-down pulse shaping. These results demonstrate a significant advancement in speed and fidelity for multiplexed superconducting-qubit readout.