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Science

Solid-State Qubits with Current-Controlled Coupling

T. Hime, P. A. Reichardt, B. L. T. Plourde, Timothy L. Robertson, C.-E. Wu, Alexey Vladimirovich Ustinov, John L. Clarke

Published Nov 30, 2006• 228 citations
Publisher

Abstract

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.

DOI
10.1126/science.1134388

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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 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.
In flux qubits, qubit states are commonly read out by a dc superconducting quantum interference device (SQUID), which is inductively coupled to the qubit and works as a persistent current detector. However, neither the bottom nor the top regions of the critical current modulation curve of the SQUID can be used for the readout. In this paper, we show that a flux-trap loop inserted to the readout SQUID provides the ability to adjust the working point, which helps to avoid this constraint. This improvement is useful for some complicated flux qubit experiments.
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.
Flux states of an RF SQUID are promising candidates for the implementation of quantum bits (qubits) for quantum computing. Accurate measurements of the flux states, especially in the time domain, require a controllable coupling between a qubit and a readout circuit (e.g., a dc SQUID magnetometer). Since the readout circuit can also be a source of decoherence, such a controllable coupling also allows one to control (minimize) the back action of the magnetometer. For this purpose we suggest a balanced, tunable transformer. This has a gradiometer configuration such that each arm is broken by a small loop containing two Josephson junctions. As a result the inductance of each arm can be adjusted by an applied bias flux. In the symmetrical case there is no coupling between the qubit and the magnetometer while a desired coupling can be achieved by changing the asymmetry of the arms. Similar transformers may be be useful for achieving controllable, lossless coupling that is required between qubits. Theoretical analysis of the noise back action of the transformer as well as preliminary experimental results are presented.
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.
Superconducting quantum interference devices (SQUIDs) have been realized with a built-in π∕2 phase shift of the superconducting wave function. Its design is inspired by the phase-shifter concept, first proposed by Ioffe et al. [Nature 398, 679 (1999)] as the key element in a solid-state qubit configuration. It exploits the dx2−y2 order parameter symmetry in the high-Tc cuprates in multilayer structures based on YBa2Cu3O7-Nb ramp-type Josephson contacts. By reversing the sign of the persistent circulating current in the phase-shifting element, the π∕2 SQUID can be controllably switched between two energetically degenerate ground states, with complementary magnetic flux dependencies.