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Bulletin of the American Physical Society

Demonstrating real-time feedback that enhances the performance of measurement sequence with cat states in a cavity

Nissim Ofek, Andrei Petrenko, Y. Liu, Brian Vlastakis, Liang Sun, Zaki Leghtas, Reinier Heeres, Katrina Sliwa, Mazyar Mirrahimi, Li-Nan Jiang, Michel Devoret, R. J. Schoelkopf

Published Mar 6, 2015• 2 citations

Abstract

back offers not just the convenience of streamlined data acquisition, but is an essential element in any quantum computational architecture that requires branching based on measurement outcomes. State-preparation, mitigating the effects of qubit decoherence, and recording the trajectories of quantum systems are just a few of the many potential applications of real-time feedback. Photon number parity measurements of cat states in superconducting resonators are a particularly useful platform for demonstrating the clear advantages of having sophisticated feedback schemes to enhance the performance a proposed error-correction protocol [Leghtas et.al. PRL 2013]. In a cQED architecture, where a transmon qubit is coupled to two superconducting cavities, we present a field-programmable gate array (FPGA) device capable of making decisions and calculations with latency times far shorter than the lifetimes of any of the system’s constituents. This level of performance opens the door to realizing many complex, previously unfeasible, experiments in superconducting qubit systems.

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We present and experimentally implement a real-time protocol for calibrating the frequency of a resonantly driven qubit, achieving exponential scaling in calibration precision with the number of measurements, up to the limit imposed by decoherence. The real-time processing capabilities of a classical controller dynamically generate adaptive probing sequences for qubit-frequency estimation. Each probing evolution time and drive frequency are calculated to divide the prior probability distribution into two branches, following a locally optimal strategy that mimics a conventional binary search. The scheme does not require repeated measurements at the same setting, as it accounts for state preparation and measurement errors. Its use of a parametrized probability distribution favors numerical accuracy and computational speed. We show the efficacy of the algorithm by stabilizing a flux-tunable transmon qubit, leading to improved coherence and gate fidelity. As benchmarked by gate-set tomography, the field-programmable gate array (FPGA) powered control electronics partially mitigates non-Markovian noise, which is detrimental to quantum error correction. The mitigation is achieved by dynamically updating and feeding forward the qubit frequency. Our protocol highlights the importance of feedback in improving the calibration and stability of qubits subject to drift and can be readily applied to other qubit platforms.

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