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AIP conference proceedings

Quantum Nondemolition Measurement of a Superconducting Flux Qubit

Kohji Takashima, Munehiro Nishida, Shigemasa Matsuo, Noriyuki Hatakenaka

Published Jan 1, 2006• 1 citation
Publisher

Abstract

Quantum nondemolition (QND) measurements allow us to measure an observable of a quantum system without introducing a back‐action on this observable due to the measurement itself. Here we propose a method for the QND measurement of a superconducting flux qubit by extending the spin QND measurement. Under an adequate condition, qubit and interaction Hamiltonian satisfy QND conditions and then QND measurement of a superconducting flux qubit is possible.

DOI
10.1063/1.2355016

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Quantum nondemolition (QND) measurements allow us to measure an observable of a quantum system without introducing a back‐action on this observable due to the measurement itself. Here we propose a method for the QND measurement of a superconducting flux qubit by extending the spin QND measurement. Under an adequate condition, qubit and interaction Hamiltonian satisfy QND conditions and then QND measurement of a superconducting flux qubit is possible.
We show that an LCLCLC parametric transducer can be effectively used to monitor an adiabatic evolution of the superconducting flux qubit. We propose a scheme to measure the qubit's state, which is a quantum nondemolition measurement. The scheme can be easily extended to a three-qubit system and allows the reading out of the qubits' states while the system remains in the ground state. An implementation of the adiabatic quantum algorithm MAXCUT for three superconducting flux qubits is discussed.
In a qubit system, the measurement operator does not necessarily commute with the qubit Hamiltonian, so that the readout process demolishes (mixes) the qubit energy eigenstates. The readout time is therefore limited by such a mixing time and its fidelity will be reduced. A quantum nondemolition readout scheme is proposed in which the charge of a flux qubit is measured. The measurement operator is shown to commute with the qubit Hamiltonian in the reduced two-level Hilbert space, even though the Hamiltonian contains noncommuting charge and flux terms.
We present a measurement protocol for a flux qubit coupled to a dc-superconducting quantum interference device (SQUID), representative of any two-state system with a controllable coupling to a harmonic-oscillator quadrature, which consists of two steps. First, the qubit state is imprinted onto the SQUID via a very short and strong interaction. We show that at the end of this step the qubit dephases completely, although the perturbation of the measured qubit observable during this step is weak. In the second step, information about the qubit is extracted by measuring the SQUID. This step can have arbitrarily long duration, since it no longer induces qubit errors.
We study the quantitative characterization of the performance of qubit measurements in this paper. In particular, the back-action evading nature of quantum nondemolition (QND) readout of qubits is fully quantified by quantum trace distance. Only computational basis states are necessary to be taken into consideration. Most importantly, we propose an experimentally efficient method to evaluate the QND fidelity based on the classical trace distance, which uses an experimental scheme with two consecutive measurements. The three key quantifiers of a measurement, i.e., QND fidelity, readout fidelity, and projectivity, can be derived directly from the same experimental scheme. Besides, we present the relationships among these three factors. Theoretical simulation results for the dispersive readout of superconducting qubits show the validity of the proposed QND fidelity. Efficient quantification of measurement performance is of practical significance for the diagnosis, performance improvement, and design of measurement apparatuses.