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arXiv:0908.0817 · Physical Review A

Fighting decoherence in a continuous two-qubit odd- or even-parity measurement with a closed-loop setup

Anne E. B. Nielsen

Published Jan 12, 2010• 6 citations
arXivHTMLPDF

Abstract

A parity measurement on two qubits, each consisting of a single atom in a cavity, can be realized by measuring the phase shift of a probe beam which interacts sequentially with the two qubits, but imperfections lead to decoherence within the subspaces of a given parity. We demonstrate that a different setup, where the probe light interacts repeatedly with the qubits, can reduce the rate of decoherence within the odd- or the even-parity subspace significantly. We consider both the case of a resonant and the case of a nonresonant light-atom interaction and find that the performance is comparable if the parameters are chosen appropriately.

DOI
10.1103/physreva.81.012307

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A parity measurement on two qubits, each consisting of a single atom in a cavity, can be realized by measuring the phase shift of a probe beam which interacts sequentially with the two qubits, but imperfections lead to decoherence within the subspaces of a given parity. We demonstrate that a different setup, where the probe light interacts repeatedly with the qubits, can reduce the rate of decoherence within the odd- or the even-parity subspace significantly. We consider both the case of a resonant and the case of a nonresonant light-atom interaction and find that the performance is comparable if the parameters are chosen appropriately.
We propose and analyze a physical implementation of two-qubit parity measurements as required for continuous error correction, assuming a setup in which the individual qubits are strongly coupled to separate optical cavities. A single optical probe beam scatters sequentially from the two cavities, and the continuous parity measurement is realized via fixed quadrature homodyne photodetection. We present models based on quantum stochastic differential equations (QSDEs) for both an ideal continuous parity measurement and our proposed cavity quantum electrodynamics (cavity QED) implementation; a recent adiabatic elimination theorem for QSDEs is used to assert strong convergence of the latter to the former in an appropriate limit of physical parameters. Performance of the cavity QED scheme is studied via numerical simulation with experimentally realistic parameters.
Repeated closed-loop control operations acting as piecewise-constant Liouville superoperators conditioned on the outcomes of regularly performed measurements may effectively be described by a fixed-point iteration for the density matrix. Even when all Liouville superoperators point to the completely mixed state, feedback of the measurement result may lead to a pure state, which can be interpreted as selective dampening of undesired states. Using a microscopic model, we exemplify this for a single qubit, which can be purified in an arbitrary single-qubit state by tuning the measurement direction and two qubits that may be purified towards a Bell state by applying a special continuous two-local measurement. The method does not require precise knowledge of decoherence channels and works for large reservoir temperatures provided measurement, processing, and control can be implemented in a continuous fashion.
We present a concept for performing direct parity measurements on three or more qubits in microwave structures with superconducting resonators coupled to Josephson-junction qubits. We write the quantum-eraser conditions that must be fulfilled for the parity measurements as requirements for the scattering phase shift of our microwave structure. We show that these conditions can be fulfilled with present-day devices. We present one particular scheme, implemented with two-dimensional cavity techniques, in which each qubit should be coupled equally to two different microwave cavities. The magnitudes of the couplings that are needed are in the range that has been achieved in current experiments. A quantum calculation indicates that the measurement is optimal if the scattering signal can be measured with near single-photon sensitivity. A comparison with an extension of a related proposal from cavity optics is presented. We present a second scheme, for which a scalable implementation of the four-qubit parities of the surface quantum error correction code can be envisioned. It uses three-dimensional cavity structures, using cavity symmetries to achieve the necessary multiple resonant modes within a single resonant structure.
Parity measurement is a central tool for many quantum information processing tasks. In this work, we propose a method to directly measure two- and four-qubit parity with low overhead in hardware and software while remaining robust to experimental imperfections. Our scheme relies on dispersive qubit-cavity coupling and photon counting that is sensitive only to intensity; both ingredients are widely realized in many different quantum computing modalities. For a leading technology in quantum computing, superconducting integrated circuits, we analyze the measurement contrast and the back action of the scheme and show that this measurement comes close enough to an ideal parity measurement to be applicable to quantum error correction.
We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that, for a probe electromagnetic field in a particular quantum state; namely, a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary backaction on the probe state. This leads to a parity measurement protocol where the main effect of the transmission losses is a decrease in the measurement strength. By repeating the nondestructive (weak) parity measurement, one achieves a high-fidelity entanglement in spite of a significant transmission loss.
The photon number parity is a binary observable playing an important role in the description of the non-classical features of light. In microwave experiments, this observable can be measured by using a single Rydberg atom evolving in a two dimension space and interacting dispersively with a field stored in one or two cavities. The procedure, based on atomic interferometry, maps the field parity (+ 1 or − 1) onto the states of the two-level atom. By performing repeated measurements of the field parity, it is possible to observe field quantum jumps, to reconstruct the complete Wigner function of an arbitrary field and to study how it evolves due to decoherence.