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arXiv:cond-mat/0509557 · Physical Review Letters

Four-Qubit Device with Mixed Couplings

M. Grajcar, A. Izmalkov, S. H. W. van der Ploeg, S. Linzen, T. Pleceník, Th. Wagner, Uwe Hübner, Evgeni V. Il’ichev, H.‐G. Meyer, Anatoly Yu. Smirnov, Peter J. Love, Alec Maassen van den Brink, M. H. S. Amin, Sergey V. Uchaikin, Alexandre M. Zagoskin

Published Feb 2, 2006• 75 citations
arXivHTMLPDF

Abstract

We present the first experimental results on a device with more than two superconducting qubits. The circuit consists of four three-junction flux qubits, with simultaneous ferro- and antiferromagnetic coupling implemented using shared Josephson junctions. Its response, which is dominated by the ground state, is characterized using low-frequency impedance measurement with a superconducting tank circuit coupled to the qubits. The results are found to be in excellent agreement with the quantum-mechanical predictions.

DOI
10.1103/physrevlett.96.047006

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We implement the impedance measurement technique in order to characterize superconducting structures designed for applications in quantum computing. We report an experimental study of the circuit consisting of three small Josephson junctions incorporated in a low-inductance superconducting loop. Measurements of the circuit response to an applied weak ac bias as a function of the external magnetic flux φe yield complete information on the properties of the circuit. We found that the system displays two metastable states. From experimental data, we have determined the magnetic field dependent Josephson energy U(φe) of these states, the potential barrier ΔU between these states, as well as the difference of the critical currents of the junction in the loop.
We develop a theory for the quantum circuit consisting of a superconducting loop interrupted by four Josephson junctions and pierced by a magnetic flux (either static or time-dependent). In addition to the similarity with the typical three-junction flux qubit in the double-well regime, we demonstrate the difference of the four-junction circuit from its three-junction analogue, including its advantages over the latter. Moreover, the four-junction circuit in the single-well regime is also investigated. Our theory provides a tool to explore the physical properties of this four-junction superconducting circuit.
We develop a theory for the quantum circuit consisting of a superconducting loop interrupted by four Josephson junctions and pierced by a magnetic flux (either static or time-dependent). In addition to the similarity with the typical three-junction flux qubit, we demonstrate the difference of the four-junction circuit from its three-junction analogue, especially its distinct advantages over the latter. Moreover, the four-junction circuit in the phase regime is also investigated. Our theory provides a tool to explore the physical properties of this four-junction superconducting circuit.
We study a flux qubit consisting of a symmetrical pair of superconducting loops, with two Josephson junctions in each, joined by a common Josephson junction---a `twin' flux qubit. The qubit is capacitively coupled to a transmission line, which allows us to characterize the spectrum of the device by measuring the scattering of propagated electromagnetic waves. We perform a detailed analytical analysis of the double-loop system, revealing its properties, and compare experimental results with numerical simulations. At half-flux quantum bias of both loops, the qubit is protected against global and local magnetic field fluctuations with much less sensitivity to the global field in the second order. The system selection rules allow even-odd transitions and prohibit transitions between even-even or odd-odd levels due to the symmetry of the device.
We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a superconducting quantum interference device. Those two elements allow to engineer qubits Hamiltonians with XX, YY, and ZZ interactions, including ultrastrongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely, the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.