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arXiv:cond-mat/0412286 · Physical Review B

Quantum nondemolition charge measurement of a Josephson qubit

M. H. S. Amin

Published Apr 19, 2005• 4 citations
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Abstract

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.

DOI
10.1103/physrevb.71.140505

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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.
Quantum technologies, including those based on superconducting quantum circuits, require high-fidelity high-speed detection of the quantum state of a qubit. Standard quantum nondemolition readout of a superconducting qubit is based on its dispersive coupling to a resonator, but this method suffers from the Purcell effects: Purcell decay, critical photon number, and qubit-dependent Kerr nonlinearity. The authors propose a method in which both speed and fidelity of flux-qubit readout can avoid all three Purcell limitations.
The ability to perform high-fidelity quantum nondemolition qubit readout is pivotal for the realization of large and powerful quantum computers. Such readout of superconducting qubits is generally enabled by amplifying the weak dispersive measurement signals using phase-preserving quantum-limited Josephson amplifiers with sufficient gain to dilute the contribution of the added noise by the output chain. Here, we further enhance the qubit readout fidelity by (1) simultaneously measuring the two-mode squeezed states of the amplified readout signals at the signal and idler frequencies of the nondegenerate amplifier and (2) coherently combining them at the classical processing stage following a relative rotation that maximizes the signal to noise ratio of the qubit-encoded readout quadrature. Such readout scheme exhibits enhancement in the readout fidelity for all practical values of amplifier gain and noise added by the output chain and is fully compatible with frequency multiplexed setups used in large quantum processors.
We analyze the relaxation of a superconducting flux qubit during measurement. The qubit state is measured with a nonlinear oscillator driven across the threshold of bifurcation, acting as a switching dispersive detector. This readout scheme is of quantum nondemolition type. Two successive readouts are used to analyze the evolution of the qubit and the detector during the measurement. We introduce a simple transition rate model for characterizing the qubit relaxation and the detector switching process. Corrected for qubit relaxation the readout fidelity is at least 95%. Qubit relaxation strongly depends on the driving strength and the state of the oscillator.