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Physical Review B

Engineered selection rules for tunable coupling in a superconducting quantum circuit

K. Harrabi, Fumiki Yoshihara, A. O. Niskanen, Yasunobu Nakamura, J. S. Tsai

Published Jan 20, 2009• 28 citations
Publisher

Abstract

Engineering selection rules of transitions is a useful strategy for coupling and decoupling qubits in superconducting quantum circuits. Following this approach, we implement a tunable coupling scheme between two flux qubits. The qubits are coupled parametrically under microwave driving via the nonlinear inductance of a third qubit. The measured on-state coupling as well as the off-state residual coupling depends on the coupler bias and agrees quantitatively with a calculation of transition matrix elements of a three-qubit Hamiltonian.

DOI
10.1103/physrevb.79.020507

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Engineering selection rules of transitions is a useful strategy for coupling and decoupling qubits in superconducting quantum circuits. Following this approach, we implement a tunable coupling scheme between two flux qubits. The qubits are coupled parametrically under microwave driving via the nonlinear inductance of a third qubit. The measured on-state coupling as well as the off-state residual coupling depends on the coupler bias and agrees quantitatively with a calculation of transition matrix elements of a three-qubit Hamiltonian.
We have studied a tunable coupling scheme of two superconducting flux qubits biased at the degeneracy point. The qubits are coupled parametrically under microwave driving, via nonlinear inductance of a third qubit biased slightly away from the degeneracy point. The observed on-state coupling as well as the off-state residual coupling depend non-monotonically on the coupler bias point and agree quantitatively with calculations based on a three-qubit Hamiltonian. This simple model is useful to optimize the parameters for a large on/off ratio.
To do large-scale quantum information processing, it is necessary to control the interactions between individual qubits while retaining quantum coherence. To this end, superconducting circuits allow for a high degree of flexibility. We report on the time-domain tunable coupling of optimally biased superconducting flux qubits. By modulating the nonlinear inductance of an additional coupling element, we parametrically induced a two-qubit transition that was otherwise forbidden. We observed an on/off coupling ratio of 19 and were able to demonstrate a simple quantum protocol.
The authors propose a qubit-qubit coupling scheme for superconducting flux quantum bits (qubits), where quantized Josephson junction resonator and microwave irradiation are utilized. The junction is used as a tunable inductance controlled by changing the bias current flowing through the junction, and thus the circuit works as a tunable resonator. This enables them to make any qubits interact with the resonator. Entanglement between two of many qubits whose level splittings satisfy some conditions is formed by microwave irradiation causing a two-photon Rabi oscillation. Since the size of the resonator can be as large as submillimeters and qubits interact with it via mutual inductance, their scheme makes it possible to construct a quantum gate involving remote qubits.
For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper, we derive the general interaction mediated by such a circuit under the Born-Oppenheimer approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations, and a quantum part, associated with the coupler's zero-point energy. Our result is nonperturbative in the qubit-coupler coupling strengths and in the coupler nonlinearity. This can lead to significant departures from previous, linear theories for the interqubit coupling, including nonstoquastic and many-body interactions. Our analysis provides explicit and efficiently computable series for any term in the interaction Hamiltonian and can be applied to any superconducting qubit type. We conclude with a numerical investigation of our theory using a case study of two coupled flux qubits, and in particular study the regime of validity of the Born-Oppenheimer approximation.
We have realized controllable coupling between two three-junction flux qubits by inserting an additional coupler loop between them, containing three Josephson junctions. Two of these are shared with the qubit loops, providing strong qubit-coupler interaction. The third junction gives the coupler a nontrivial current-flux relation; its derivative (i.e., the susceptibility) determines the coupling strength J, which thus is tunable in situ via the coupler's flux bias. In the qubit regime, J was varied from approximately 45 (antiferromagnetic) to approximately -55 mK (ferromagnetic); in particular, J vanishes for an intermediate coupler bias. Measurements on a second sample illuminate the relation between two-qubit tunable coupling and three-qubit behavior.
Nonpairwise multiqubit interactions present a useful resource for quantum information processors. Their implementation would facilitate more efficient quantum simulations of molecules and combinatorial optimization problems, and they could simplify error suppression and error correction schemes. Here, we present a superconducting circuit architecture in which a coupling module mediates two-local and three-local interactions between three flux qubits by design. The system Hamiltonian is estimated via multiqubit pulse sequences that implement Ramsey-type interferometry between all neighboring excitation manifolds in the system. The three-local interaction is coherently tunable over several MHz via the coupler flux biases and can be turned off, which is important for applications in quantum annealing, analog quantum simulation, and gate-model quantum computation.