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arXiv:1207.2944 · Physical Review Letters

Feedback Control of a Solid-State Qubit Using High-Fidelity Projective Measurement

Diego Ristè, Cornelis Christiaan Bultink, Konrad W. Lehnert, L. DiCarlo

Published Dec 10, 2012• 192 citations
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Abstract

We demonstrate feedback control of a superconducting transmon qubit using discrete, projective measurement and conditional coherent driving. Feedback realizes a fast and deterministic qubit reset to a target state with 2.4% error averaged over input superposition states, and allows concatenating experiments more than 10 times faster than by passive initialization. This closed-loop qubit control is necessary for measurement-based protocols such as quantum error correction and teleportation.

DOI
10.1103/physrevlett.109.240502

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We demonstrate feedback control of a superconducting transmon qubit using discrete, projective measurement and conditional coherent driving. Feedback realizes a fast and deterministic qubit reset to a target state with 2.4% error averaged over input superposition states, and allows concatenating experiments more than 10 times faster than by passive initialization. This closed-loop qubit control is necessary for measurement-based protocols such as quantum error correction and teleportation.
This chapter covers the development of feedback control of superconducting qubits using projective measurement and a discrete set of conditional actions, here referred to as digital feedback. We begin with an overview of the applications of digital feedback in quantum computing. We then introduce an implementation of high-fidelity projective measurement of superconducting qubits. This development lays the ground for closed-loop control based on the binary measurement result. A first application of digital feedback control is fast and deterministic qubit reset, allowing the repeated initialization of a qubit more than an order of magnitude faster than its relaxation rate. A second application employs feedback in a multi-qubit setting to convert the generation of entanglement by parity measurement from probabilistic to deterministic, targeting an entangled state with the desired parity every time.
Superconducting circuits have recently risen to the forefront of the solid-state prototypes for quantum computing. Reaching the stage of robust quantum computing requires closing the loop between measurement and control of quantum bits (qubits). This thesis presents the realization of feedback control of superconducting qubits based on projective measurement, with initial applications. The first application is a reset operation which initializes a qubit in the ground state fast and on demand. In a second experiment, we transform a cavity into a two-qubit parity meter, which is capable of generating entanglement starting from an unentangled superposition state. We then employ feedback to turn the generation of entanglement from probabilistic to deterministic, thus combining two key ingredients - parity measurement and feedback - of quantum error correction. As a third application, we transform a superconducting qubit into a charge-parity detector to investigate the limits of quasiparticle tunneling to qubit coherence. We find room for at least a tenfold increase in qubit coherence times before quasiparticles become the bottleneck. Finally, we present our latest results towards implementing the bit-flip error correction code in a five-qubit processor and discuss the role of feedback control in the future development of superconducting quantum circuits.
Measurement-based feedback control is central in quantum computing and precise quantum control. Here we realize a fast and flexible field-programmable-gate-array-based feedback control in an Xmon- superconducting-qubit system. The latency of room-temperature electronics is custom-optimized to be as short as 140 ns. Projective measurement of a signal qubit produces a feedback tag to implement a conditional pulse gate on the qubit. In a feedforward process, the measurement-based feedback tag is brought to a different target qubit for conditional control. In a two-qubit experiment, the feedback and feedforward controls are simultaneously implemented in consecutive steps. A quantum number is then generated by the signal qubit, and a random walk of the target qubit is correspondingly triggered and realized on the Bloch sphere. Our experiment provides a conceptually simple and intuitive benchmark for feedback control in a multiqubit system. The feedback system can be further scaled up for more-complex feedback-control experiments.
Abstract Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coherence time by 26% and reducing the single-qubit error rate from (8.5 ± 2.1) × 10−4 to (5.9 ± 0.7) × 10−4. Importantly, the resulting high-fidelity operation remains effective even away from the qubit flux-noise insensitive point, significantly increasing the frequency bandwidth over which the qubit can be operated with high fidelity. This approach is helpful in large qubit grids, where frequency crowding and parasitic interactions between the qubits limit their performance.
We developed a versatile integrated control and readout instrument for experiments with superconducting quantum bits (qubits), based on a field-programmable gate array (FPGA) platform. Using this platform, we perform measurement-based, closed-loop feedback operations with 428 ns platform latency. The feedback capability is instrumental in realizing active reset initialization of the qubit into the ground state in a time much shorter than its energy relaxation time T1. We show experimental results demonstrating reset of a fluxonium qubit with 99.4 % fidelity, using a readout-and-drive pulse sequence approximately 1. 5 µs long. Compared to passive ground state initialization through thermalization, with the time constant given by T1 = 80 µs, the use of the FPGA-based platform allows us to improve both the fidelity and the time of the qubit initialization by an order of magnitude.
Persistent control of a transmon qubit is performed by a feedback protocol based on continuous heterodyne measurement of its fluorescence. By driving the qubit and cavity with microwave signals whose amplitudes depend linearly on the instantaneous values of the quadratures of the measured fluorescence field, we show that it is possible to stabilize permanently the qubit in any targeted state. Using a Josephson mixer as a phase-preserving amplifier, it was possible to reach a total measurement efficiency η=35%, leading to a maximum of 59% of excitation and 44% of coherence for the stabilized states. The experiment demonstrates multiple-input multiple-output analog Markovian feedback in the quantum regime.