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Science

Quantum Coherent Tunable Coupling of Superconducting Qubits

A. O. Niskanen, K. Harrabi, Fumiki Yoshihara, Yasunobu Nakamura, Seth Lloyd, Jaw-Shen Tsai

Published May 3, 2007• 423 citations
Publisher

Abstract

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.

DOI
10.1126/science.1141324

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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.
Flux qubits (also known as persistent current qubits), one kind of superconducting tunnel junction circuits, are recently demonstrated as a promising candidate to realize quantum computations.In order to do large-scale quantum information processing, it is necessary to switch on and off the couplings between individual flux qubits in the time-domain while those qubits retain coherence.This report contains two parts: one is to describe my understanding of models, fabrications and measurements for one single flux qubit; the other is to compare two proposed schemes and the corresponding experimental realizations of coherent tunable couplings between flux qubits.
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.
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.
This thesis presents a detailed investigation of coherent tunable coupling between two coupled quantum circuits. Quantum circuits have the potential to be used as the fundamental building blocks in quantum processors. Any large scale quantum processor will be composed of a large number of these coupled circuits. The efficient implementation of quantum algorithms will be difficult without a reliable mechanism for controlling the interaction strength between coupled systems, while preserving the delicate quantum information stored in the coherent superpositions of quantum states. We show that a flux-biased rf-SQUID can be used to coherently mediate the interaction between two coupled quantum circuits, a phase qubit and LC resonator. This interaction results from an effective mutual inductance between the qubit and resonator as a result of their direct coupling to the rf-SQUID. The sign and magnitude of this effective mutual inductance can be tuned with applied flux to the rf-SQUID, thus controlling the coupled interactions over a large range. We observe the modulation in coupling strength using measurements in both the frequency and time domains. The measurements are shown to agree well with theoretical predictions. This thesis discusses all aspects of the experiments from a theoretical description of each component to the design, fabrication, experimental setup and measurements.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZZZZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off-resonantly. We show tunable coupling over one order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave crosstalk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)%99.43(1)\%99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.