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arXiv:1009.4470 · Physical Review Letters

Superconducting Qubit with Purcell Protection and Tunable Coupling

Jay Gambetta, Andrew Houck, Alexandre Blais

Published Jan 20, 2011• 128 citations
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Abstract

We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable qubit-resonator coupling strength g. This coupling can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0, the qubit is in a decoherence-free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore, we show that in this decoherence-free subspace, the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.

DOI
10.1103/physrevlett.106.030502

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We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable qubit-resonator coupling strength g. This coupling can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0, the qubit is in a decoherence-free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore, we show that in this decoherence-free subspace, the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.
We study spontaneous emission processes of two capacitively coupled superconducting qubits embedded in transmission-line resonators in a circuit-quantum electrodynamics architecture. We find that under proper conditions of the entanglement generating operation, a Purcell protection from spontaneous emission occurs. We discuss the dependence of this effect on the coupling energy between the two qubits and comment on the possibility of finding a trade-off between optimization of the gate with respect to low-frequency noise and relaxation effects.
The measurement of a superconducting qubit is implemented by coupling it to a resonator. The common choice is transverse coupling, which, in the dispersive approximation, introduces an interaction term that enables the measurement. This cross-Kerr term provides a qubit-state dependent dispersive shift in the resonator frequency with the device parameters chosen carefully to get sufficient signal while minimizing Purcell decay of the qubit. We introduce a two-mode circuit, nicknamed quantromon, with two orthogonal modes implementing a qubit and a resonator. Unlike before, where the coupling term emerges as a perturbative expansion, the quantromon has intrinsic cross-Kerr coupling by design. Our experiments implemented in a hybrid 2D–3D circuit QED architecture demonstrate some unique features of the quantromon like weak dependence of the dispersive shift on the qubit-resonator detuning and intrinsic Purcell protection. In a tunable qubit-frequency device, we show that the dispersive shift (2χ/2π) changes by only 0.8 MHz, while the qubit-resonator detuning (Δ/2π) is varied between 0.398 and 3.288 GHz. We also demonstrate Purcell protection in a second device where we tune the orthogonality between the two modes. Finally, we demonstrate a single-shot readout fidelity of 98.3%, which is comparable to the state-of-the-art measurements without the use of a parametric amplifier and suggests a potential simplification of the measurement circuitry for scaling up quantum processors.
Physical implementations of qubits can be extremely sensitive to environmental coupling, which can result in decoherence. While efforts are made for protection, coupling to the environment is necessary to measure and manipulate the state of the qubit. As such, the goal of having long qubit energy relaxation times is in competition with that of achieving high-fidelity qubit control and measurement. Here, we propose a method that integrates filtering techniques for preserving superconducting qubit lifetimes together with the dispersive coupling of the qubit to a microwave resonator for control and measurement. The result is a compact circuit that protects qubits from spontaneous loss to the environment, while also retaining the ability to perform fast, high-fidelity readout. Importantly, we show the device operates in a regime that is attainable with current experimental parameters and provide a specific example for superconducting qubits in circuit quantum electrodynamics.
Spontaneous emission through a coupled cavity can be a significant decay channel for qubits in circuit quantum electrodynamics. We present a circuit design that effectively eliminates spontaneous emission due to the Purcell effect while maintaining strong coupling to a low-Q cavity. Excellent agreement over a wide range in frequency is found between measured qubit relaxation times and the predictions of a circuit model. Using fast (nanosecond time-scale) flux biasing of the qubit, we demonstrate in situ control of qubit lifetime over a factor of 50. We realize qubit reset with 99.9% fidelity in 120 ns.
We introduce a new type of superconducting charge qubit that has a V-shaped energy spectrum and uses quantum interference to provide independently tunable qubit energy and coherent coupling to a superconducting cavity. Dynamic access to the strong coupling regime is demonstrated by tuning the coupling strength from less than 200 kHz to greater than 40 MHz. This tunable coupling can be used to protect the qubit from cavity-induced relaxation and avoid unwanted qubit-qubit interactions in a multiqubit system.
To control and measure the state of a quantum system, it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement backaction, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multimode element—an artificial molecule—with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential nonlinear modes, one of which is flux insensitive and used as the protected qubit mode. The second mode is flux tunable and serves via a cross-Kerr-type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit, which we refer to as P-mon, with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed. Published by the American Physical Society 2024