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Physica Scripta

Purcell effect in a circuit-QED architecture implementation of a universal two-qubit gate

Elisabetta Paladino, Antonio D’Arrigo, G. Falci

Published Nov 1, 2012• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/2012/t151/014048

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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.
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We identify optimal operating conditions of an entangling two-qubit gate realized by a capacitive coupling of two transmons in a circuit-QED architecture. Sensitivity of the optimized gate to 1/f flux and critical current noise is suppressed to leading order. The procedure only requires a preliminary estimate of the 1/f noise amplitudes. No additional control or bias line beyond those used for the manipulation of individual qubits are needed. The proposed optimization is effective also in the presence of relaxation processes and of spontaneous emission through the resonator (Purcell effect).
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 identify the optimal operating conditions of an entangling two-qubit gate realized by capacitive coupling of two superconducting charge qubits in a transmission line resonator (the so-called 'transmons'). We demonstrate that the sensitivity of the optimized gate to 1/ f flux and critical current noise is suppressed to leading order. The procedure only requires a preliminary estimate of the 1/ f noise amplitudes. No additional control or bias line beyond those used for the manipulation of individual qubits is needed. The proposed optimization is effective also in the presence of relaxation processes and of spontaneous emission through the resonator (Purcell effect).
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum electrodynamics (cQED) architecture. There, the low energy states of a nonlinear electronic oscillator are isolated and addressed as a qubit. These qubits are capacitively coupled to the modes of a microwave-frequency transmission line resonator which serves as a quantum communication bus. Microwave electrical pulses are applied to the resonator to manipulate or measure the qubit state. State control is calibrated using diagnostic sequences that expose systematic errors. Hybridization of the resonator with the qubit gives it a nonlinear response when driven strongly, useful for amplifying the measurement signal to enhance accuracy. Qubits coupled to the same bus may coherently interact with one another via the exchange of virtual photons. A two-qubit conditional phase gate mediated by this interaction can deterministically entangle its targets, and is used to generate two-qubit Bell states and three-qubit GHZ states. These three-qubit states are of particular interest because they redundantly encode quantum information. They are the basis of the quantum repetition code prototypical of more sophisticated schemes required for quantum computation. Using a three-qubit Toffoli gate, this code is demonstrated to autonomously correct either bit- or phase-flip errors. Despite observing the expected behavior, the overall fidelity is low because of decoherence. A superior implementation of cQED replaces the transmission-line resonator with a three-dimensional box mode, increasing lifetimes by an order of magnitude. In-situ qubit frequency control is enabled with control lines, which are used to fully characterize and control the system Hamiltonian.
We consider a typical circuit QED setup where an artificial atom encodes a qubit and is dispersively coupled to a measurement resonator that in turn is coupled to a transmission line. We show theoretically that by placing another artificial atom in this transmission line to act as a filter, the Purcell decay of the qubit into the transmission line is suppressed. When strong control fields are applied in the transmission line, the filter is saturated and effectively switched off. Such a Purcell filtering capability permits both the control and measurement of the qubit using the single transmission line, while maintaining the long coherence time of the qubit in the absence of the control pulses. We show that high fidelity Pauli ${\ensuremath{\sigma}}_{x}$ gates on the qubit can be realized using simple pulse shapes. For devices that already use one transmission line both for control and measurement of the qubit, our paper provides a way to completely filter out the qubit frequency without removing the possibility of controlling the system. Further, combining the proposed filter with frequency multiplexing potentially enables both control and measurement of several qubits using a single Purcell-filtered transmission line. This will enhance the scalability of superconducting quantum processors by decreasing the number of the required transmission lines.