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arXiv:quant-ph/0406049 · Physical Review B

Entangling flux qubits with a bipolar dynamic inductance

B. L. T. Plourde, Jiancan Zhang, K. Birgitta Whaley, Frank K. Wilhelm, Timothy L. Robertson, T. Hime, S. Linzen, P. A. Reichardt, C.-E. Wu, John L. Clarke

Published Oct 5, 2004• 100 citations
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Abstract

We propose a scheme to implement controllable coupling between two flux qubits using the screening current response of a dc superconducting quantum interference device (SQUID). The coupling strength is adjusted by the current bias applied to the SQUID and can be varied continuously from positive to negative values, allowing cancellation of the direct mutual inductance between the qubits. We show that this variable coupling scheme permits efficient realization of universal quantum logic. The same SQUID can be used to determine the flux states of the qubits.

DOI
10.1103/physrevb.70.140501

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We propose a scheme to implement controllable coupling between two flux qubits using the screening current response of a dc superconducting quantum interference device (SQUID). The coupling strength is adjusted by the current bias applied to the SQUID and can be varied continuously from positive to negative values, allowing cancellation of the direct mutual inductance between the qubits. We show that this variable coupling scheme permits efficient realization of universal quantum logic. The same SQUID can be used to determine the flux states of the qubits.
The ability to switch the coupling between quantum bits (qubits) on and off is essential for implementing many quantum-computing algorithms. We demonstrated such control with two flux qubits coupled together through their mutual inductances and through the dc superconducting quantum interference device (SQUID) that reads out their magnetic flux states. A bias current applied to the SQUID in the zero-voltage state induced a change in the dynamic inductance, reducing the coupling energy controllably to zero and reversing its sign.
We present an approach to realize universal two-bit quantum gates using two SQUID flux qubits. In this approach the basic unit consists of two inductively coupled SQUIDs with realistic device parameters. Quantum logical gates are implemented by applying resonant microwave pulse to the qubits. This procedure is demonstrated by realizing a controlled-NOT (CNOT) gate and the maximally entangled states of the coupled qubits through highly accurate numerical solution of the time-dependent Schrodinger equation of the system. This coupling scheme is simple and can be readily extended to many-qubit circuits required for scalable quantum information processing.
We propose a theoretical scheme to generate flux-qubit clusters using XY\mathit{XY}XY interactions. In our scheme, two neighboring qubits are coupled via a dc superconducting quantum interference device (SQUID). All flux qubits are always biased at their optimal points. The XY\mathit{XY}XY interaction can be controlled by the bias current applied to the SQUID for the two coupled qubits with the same resonance frequencies or by the frequency of a microwave pulse applied to the SQUID for the two coupled qubits with unequal resonance frequencies. The generation of a ddd-dimensional cluster state needs only 2d2d2d steps. Existing technology allows us to rapidly modulate the bias current and easily control the frequency of the pulse, and thus our scheme is experimentally feasible.
We propose a scheme for entangled state measurement at flux qubits (quantum bits) depending on the sensitivity measurement of a dc SQUID (superconducting quantum interference device). The dc SQUID is used as a flux qubit readout device. The switching current distribution of the dc SQUID is sufficiently narrow to distinguish between two ground states of three Josephson junction qubits with a large mutual inductance between a qubit and the dc SQUID. However, discrimination between two ground states becomes difficult with the smaller mutual inductance that is preferable for qubit coherence. We employed averaging to increase the effective sensitivity. However the averaging smears out the entanglement over two qubits. We found that a Bell-pair measurement can be performed with flux qubits to prove the existence of an entangled state over two qubits. The pre-ensembled measurement scheme, in which our flux qubit readouts work, is preferable to entangled state measurement.
We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled dc superconducting quantum interference device (dc-SQUID). We determine the response function of the dc-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the back-action are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible.
A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.