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arXiv:2406.06442 · Quantum Science and Technology

Resonator-mediated quantum gate between distant charge qubits

Florian Kayatz, Jonas Mielke, Guido Burkard

Published Sep 4, 2024• 3 citations
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Abstract

Abstract Strong charge-photon coupling allows the coherent coupling of a charge qubit, realized by a single charge carrier (either an electron or a hole) in a double quantum dot, to photons of a microwave resonator. Here, we theoretically demonstrate that, in the dispersive regime, the photons can mediate both an i SWAP gate as well as a i SWAP gate between two distant charge qubits. We provide a thorough discussion of the impact of the dominant noise sources, resonator damping and charge qubit dephasing on the average gate fidelity. Assuming a state-of-the art resonator decay rate and charge qubit dephasing rate, the predicted average gate fidelities are below 90%. However, a decrease of the charge qubit dephasing rate by one order of magnitude is conjectured to result in gate fidelities surpassing 95%.

DOI
10.1088/2058-9565/ad7756

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Abstract Strong charge-photon coupling allows the coherent coupling of a charge qubit, realized by a single charge carrier (either an electron or a hole) in a double quantum dot, to photons of a microwave resonator. Here, we theoretically demonstrate that, in the dispersive regime, the photons can mediate both an i SWAP gate as well as a i SWAP gate between two distant charge qubits. We provide a thorough discussion of the impact of the dominant noise sources, resonator damping and charge qubit dephasing on the average gate fidelity. Assuming a state-of-the art resonator decay rate and charge qubit dephasing rate, the predicted average gate fidelities are below 90%. However, a decrease of the charge qubit dephasing rate by one order of magnitude is conjectured to result in gate fidelities surpassing 95%.
Recent experiments with silicon qubits demonstrated strong coupling of a microwave resonator to the spin of a single electron in a double quantum dot, opening up the possibility of long-range spin-spin interactions. We present our theoretical calculation of effective interactions between distant quantum dot spins coupled by a resonator, and propose a protocol for fast, high-fidelity two-qubit gates consistent with experimentally demonstrated capabilities. Our simulations show that, in the presence of noise, spin-spin entangling gates significantly outperform cavity-mediated gates on charge qubits.
Nuclear spins show exceptionally long coherence times but the underlying good isolation from their environment is a challenge when it comes to controlling nuclear spin qubits. A particular difficulty, not only for nuclear spin qubits, is the realization of two-qubit gates between distant qubits. Recently, strong coupling between an electron spin and microwave resonator photons as well as a microwave resonator mediated coupling between two electron spins both in the resonant and the dispersive regime have been reported and, thus, a microwave resonator mediated electron spin two-qubit gate seems to be in reach. Inspired by these findings, we theoretically investigate the interaction of a microwave resonator with a hybrid quantum dot-donor (QDD) system consisting of a gate-defined Si QD and a laterally displaced 31P^{31}\mathrm{P}31P phosphorous donor atom implanted in the Si host material. We find that driving the QDD system allows to compensate the frequency mismatch between the donor nuclear spin splitting in the MHz regime and typical superconducting resonator frequencies in the GHz regime, and also enables an effective nuclear spin-photon coupling. While we expect this coupling to be weak, we predict that coupling the nuclear spins of two distant QDD systems dispersively to the microwave resonator allows the implementation of a resonator-mediated nuclear spin two-qubit iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ gate with a gate fidelity approaching 9090%90.
The recent realization of a coherent interface between a single electron in a silicon quantum dot and a single photon trapped in a superconducting cavity opens the way for implementing photon-mediated two-qubit entangling gates. In order to couple a spin to the cavity electric field, some type of spin-charge hybridization is needed, which impacts spin control and coherence. In this work we propose a cavity-mediated two-qubit gate and calculate cavity-mediated entangling gate fidelities in the dispersive regime, accounting for errors due to the spin-charge hybridization, as well as photon- and phonon-induced decays. By optimizing the degree of spin-charge hybridization, we show that two-qubit gates mediated by cavity photons are capable of reaching fidelities exceeding 9090%90 in present-day device architectures. High iswap gate fidelities are achievable even in the presence of charge noise at the level of $2\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{eV}$.
Implementing two-qubit gates via strong coupling between quantum-dot qubits and a superconducting microwave cavity requires achieving coupling rates that are much faster than decoherence rates. Typically, this involves tuning the qubit either to a sweet spot, where it is relatively insensitive to charge noise, or to a point where it is resonant with the microwave cavity. Unfortunately, such operating points seldom coincide. Here we theoretically investigate protocols, based on transverse or longitudinal sideband driving, for implementing two-qubit gates between quantum-dot hybrid qubits, mediated by a microwave cavity. The rich physics in these qubits gives rise to two types of sweet spots, which can occur at operating points with strong charge dipole moments. Such strong interactions provide new opportunities for off-resonant gating, thereby removing one of the main obstacles for long-distance two-qubit gates. We find that the transverse driving scheme yields faster gates, while longitudinal driving yields gates that are more resilient to photon decay. Our results suggest that the numerous tuning knobs of quantum-dot hybrid qubits make them good candidates for strong coupling. In particular, we show that off-resonant red-sideband-mediated two-qubit gates can exhibit fidelities greater than 9595%95 for realistic operating parameters, and we describe improvements that could potentially yield gate fidelities greater than 9999%99.
Abstract Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots. They constitute a promising approach to quantum information processing, complementary to superconducting qubits. Here, we demonstrate coherent coupling between a superconducting transmon qubit and a semiconductor double quantum dot (DQD) charge qubit mediated by virtual microwave photon excitations in a tunable high-impedance SQUID array resonator acting as a quantum bus. The transmon-charge qubit coherent coupling rate (~21 MHz) exceeds the linewidth of both the transmon (~0.8 MHz) and the DQD charge qubit (~2.7 MHz). By tuning the qubits into resonance for a controlled amount of time, we observe coherent oscillations between the constituents of this hybrid quantum system. These results enable a new class of experiments exploring the use of two-qubit interactions mediated by microwave photons to create entangled states between semiconductor and superconducting qubits.
The realization of a coherent interface between distant charge or spin qubits in semiconductor quantum dots is an open challenge for quantum information processing. Here, we demonstrate both resonant (real) and nonresonant (virtual) photon-mediated coherent interactions between double quantum-dot charge qubits separated by several tens of micrometers. We present clear spectroscopic evidence of the resonant collective enhancement of the coupling of two qubits and the resonator. With both qubits in resonance with each other but detuned from the resonator, we observe exchange coupling between the qubits mediated by virtual photons. In both instances, pronounced bright and dark states governed by the symmetry of the qubit-field interaction are found. Our observations are in excellent quantitative agreement with master-equation simulations. The extracted two-qubit coupling strengths significantly exceed the linewidths of the combined resonator-qubit system, which indicates that this approach is viable for creating photon-mediated two-qubit gates in quantum-dot-based systems.