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arXiv:1902.05704 · Physical review. B./Physical review. B

Long-distance entangling gates between quantum dot spins mediated by a superconducting resonator

Ada Warren, Edwin Barnes, Sophia E. Economou

Published Oct 16, 2019• 33 citations
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Abstract

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.

DOI
10.1103/physrevb.100.161303

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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.
We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.
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 $2\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{eV}$.
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.
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.
Electron spin qubits in silicon quantum dots are an attractive candidate for large-scalable quantum computation. An essential step for quantum information processing based on spin qubits is to realize the spatially separated two-qubit gate and entanglement with high fidelity. Here, we consider two spin qubits coupled to a common superconducting resonator in circuit quantum electrodynamics. We investigate the long-range two-qubit iSWAP gate mediated by virtual microwave photons using a Gaussian smoothing pulse. We show that the entangling gate fidelity can reach [Formula: see text] under realistic experimental conditions and analyze the factors limiting gate fidelity. Moreover, we numerically demonstrate the generation of remote Bell entangled states of spin qubits with high fidelity. In addition, this spin–resonator architecture can be used to implement quantum algorithms using our scheme. These results pave the way for quantum information processing with spin qubits.
Significant experimental advances in single-electron silicon spin qubits have opened the possibility of realizing long-range entangling gates mediated by microwave photons. Recently proposed imaginary swap (iswap) gates, however, require tuning qubit energies into resonance and have limited fidelity due to charge noise. We present a photon-mediated cross-resonance gate that is consistent with realistic experimental capabilities and requires no resonant tuning. Furthermore, we propose gate sequences capable of suppressing errors due to quasistatic noise for both the cross-resonance and iswap gates.