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Optimal tuning of an entangling gate in a circuit-QED architecture

Antonio D’Arrigo, Elisabetta Paladino

Published Oct 3, 2011• 0 citations
OpenAlex

Abstract

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).

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A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.

arXiv:2107.11550•Applied Physics Letters•Nov 8, 2021•35 citations
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).
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).
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.
We analyze a high-fidelity two-qubit gate using fast flux pulses on superconducting fluxonium qubits. The gate is realized by temporarily detuning the magnetic flux through the fluxonium loop away from the half flux quantum sweet spot. We simulate dynamics of two capacitively coupled fluxoniums during the flux pulses and optimize the pulse parameters to obtain a highly accurate iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​-like entangling gate. We also evaluate the effect of the flux noise and qubit relaxation on the gate fidelity. Our results demonstrate that the gate error remains below ${10}^{\ensuremath{-}4}$ for a currently achievable magnitude of the flux noise and qubit relaxation time.
In recent years, the tunable coupling scheme has become the mainstream scheme for designing superconducting quan tum circuits. By working in the dispersive regime, the ZZ coupling and high-energy level leakage can be effectively suppressed and realize a high fidelity quantum gate. We propose a tunable fluxonium-transmon-transmon (FTT) cou pling scheme. In our system, the coupler is a frequency tunable transmon qubit. Both qubits and coupler are capacitively coupled. The asymmetric structure composed of fluxonium and transmon will optimize the frequency space and form a high fidelity two-qubit quantum gate. By decoupling, the effective coupling strength can be easily adjusted to close to the net coupling between qubits. We numerical simulation the master equation to reduce the quantum noise to zero. We study the performance of this scheme by simulating the general single-qubit Xπ/2 gate and two-qubit (iSWAP) gate. In the bias point of the qubits, we achieve a single qubit gate with 99.99% fidelity and a two-qubit gate with 99.95% fidelity. By adjusting the nonlinear Kerr coefficient of fluxonium to an appropriate value, we can achieve a multi-body entanglement state. We consider the correlation between the two qubits and the coupler, and the magnetic flux passing through one qubit has an effect on the other qubit and the coupler. Finally, we analyze the quantum correlation of the two-body entanglement state.
Scaling up superconducting quantum processors with optimized performance requires a sufficient flexibility in the choice of operating points for single and two qubit gates to maximize their fidelity and cope with imperfections. Flux control is an efficient technique to manipulate the parameters of tunable qubits, in particular to activate entangling gates. At flux sensitive points of operation, the ubiquitous presence of 1/f flux noise however gives rise to dephasing by inducing fluctuations of the qubit frequency. We show how two-tone modulation of the flux bias, a bichromatic modulation, gives rise to a continuum of dynamical sweet spots where dephasing due to slow flux noise is suppressed to first order for a wide range of time-averaged qubit frequencies. The qubits can be operated at these dynamical sweet spots to realize protected entangling gates and to avoid collisions with two-level-system defects.
A superconducting fluxonium circuit is an RF-superconducting quantum interference device-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and couplers are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices with the additional advantage of lower qubit frequency facilitating high-precision gating.