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arXiv:quant-ph/0512144 · Physical Review A

Heisenberg-limited measurements with superconducting circuits

Alexandre Guillaume, Jonathan P. Dowling

Published Apr 27, 2006• 2 citations
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Abstract

We describe an assembly of $N$ superconducting qubits contained in a single-mode cavity. In the dispersive regime, the correlation between the cavity field and each qubit results in an effective interaction between qubits that can be used to dynamically generate maximally entangled states. With only collective manipulations, we show how to create maximally entangled quantum states and how to use these states to reach the Heisenberg limit in the determination of the qubit bias control parameter (gate charge for charge qubits, external magnetic flux for rf-superconducting quantum interference devices).

DOI
10.1103/physreva.73.040304

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We describe an assembly of NNN superconducting qubits contained in a single-mode cavity. In the dispersive regime, the correlation between the cavity field and each qubit results in an effective interaction between qubits that can be used to dynamically generate maximally entangled states. With only collective manipulations, we show how to create maximally entangled quantum states and how to use these states to reach the Heisenberg limit in the determination of the qubit bias control parameter (gate charge for charge qubits, external magnetic flux for rf-superconducting quantum interference devices).
We describe an assembly of N Cooper-pair boxes (CPB) contained in a single mode cavity. In the dispersive regime, the correlation between the cavity field and each Cooper-pair box results in an effective interaction between CPBs that can be used to dynamically generate maximally entangled states. With only collective manipulations, we show how to create maximally entangled quantum states and how to use these states to reach the Heisenberg limit in the determination of a spectroscopy frequency. This scheme can be applied to other types of superconducting qubits.
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We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.
This paper proposes a method of generating multipartite entanglement through using d.c. superconducting quantum interference devices (SQUID) inside a standing wave cavity. In this scheme, the d.c. SQUID works in the charge region. It is shown that, a large number of important multipartite entangled states can be generated by a controllable interaction between a cavity field and qubits. It is even possible to produce entangled states involving different cavity modes based on the measurement of charge qubits states. After such superpositions states are created, the interaction can be switched off by the classical magnetic field through the SQUID, and there is no information transfer between the cavity field and the charge qubits.
We demonstrate the controllable generation of multi-photon Fock states in circuit quantum electrodynamics (circuit QED). The external bias flux regulated by a counter can effectively adjust the bias time on each superconducting flux qubit so that each flux qubit can pass in turn through the circuit cavity and thereby avoid the effect of decoherence. We further investigate the quantum correlation dynamics of coupling superconducting qubits in a Fock state. The results reveal that the lower the photon number of the light field in the number state, the stronger the interaction between qubits is, then the more beneficial to maintaining entanglement between qubits it will be.