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IEEE Conference on Decision and Control (CDC)

Quantum feedback control of coherent oscillations in a solid-state qubit

Rusko Ruskov, Q. Zhang, Alexander N. Korotkov

Published Apr 23, 2004• 0 citations
Publisher

Abstract

The performance of a quantum feedback loop designed to maintain a desired phase of quantum coherent oscillations in a single solid-state qubit is analyzed using the quantum Bayesian formalism. The degree of oscillations synchronization with classical reference signal is calculated as a function of feedback strength, taking also into account finite detector bandwidth, dephasing due to environment, and qubit energy asymmetry.

DOI
10.1109/cdc.2003.1271806

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The performance of a quantum feedback loop designed to maintain a desired phase of quantum coherent oscillations in a single solid-state qubit is analyzed using the quantum Bayesian formalism. The degree of oscillations synchronization with classical reference signal is calculated as a function of feedback strength, taking also into account finite detector bandwidth, dephasing due to environment, and qubit energy asymmetry.
We have studied theoretically the basic operation of a quantum feedback loop designed to maintain a desired phase of quantum coherent oscillations in a single solid-state qubit. The degree of oscillations synchronization with external harmonic signal is calculated as a function of feedback strength, taking into account available bandwidth and coupling to environment. The feedback can efficiently suppress the dephasing of oscillations if the qubit coupling to the detector is stronger than the coupling to the environment.
We discuss the operation of the one-qubit quantum feedback loop, which may be used for initialization of a qubit in a solid-state quantum computer. The continuous monitoring of a quantum state, which makes the feedback possible, is done by means of a weak continuous measurement and processing of the obtained information via quantum Bayesian equations. The properly designed quantum feedback loop can keep the desired phase of a single-qubit quantum coherent oscillations for infinitely long time, even in presence of a dephasing environment. Various nonidealities reduce the fidelity of the feedback synchronization. We report our study of the effects of finite available bandwidth and time delay on the one-qubit quantum feedback performance, and also discuss the effect of environment-induced dephasing.
We analyze the newly proposed quantum feedback loop for a solid-state qubit, based on monitoring the quadrature components of the current from a weakly coupled detector, which continuously measures the qubit. Similar to the earlier proposal of the "Bayesian" feedback, the feedback loop is used to maintain the coherent (Rabi)oscillations in a qubit for an arbitrarily long time; however, this is done in a significantly simpler way, which requires much smaller bandwidth of the control circuitry. The price for simplicity is a less-than-ideal operation: the fidelity is limited to about 95%. The feedback loop operation can be experimentally verified by appearance of a positive in-phase component of the detector current relative to an external oscillating signal used for synchronization. The quadrature-based quantum feedback seems to be within the reach of the present-day technology.
We propose an experiment on quantum feedback control of a solid-state qubit, which is within the reach of the present-day technology. Similar to an earlier proposal [R. Ruskov and A. N. Korotkov, Phys. Rev. B 66, 041401(R) (2002)], the feedback loop is used to maintain coherent oscillations in a qubit for an arbitrarily long time; however, this is done in a significantly simpler way, which eases the bandwidth problem. The main idea is to use the quadrature components of the noisy detector current to monitor approximately the phase of qubit oscillations. The price for simplicity is a less-than-ideal operation: the fidelity is limited to about 95%. The feedback loop operation can be experimentally verified by the appearance of a positive in-phase component of the detector current relative to an external oscillating signal used for synchronization.