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Bulletin of the American Physical Society

Resonant Microwave Mediated Interactions Between Distant Electron Spins

Felix Borjans, Xanthe Croot, Xiao Mi, Michael J. Gullans, J. R. Petta

Published Mar 4, 2020• 0 citations

Abstract

Abstract Nonlocal qubit interactions are a hallmark of advanced quantum information technologies1–5. The ability to transfer quantum states and generate entanglement over distances much larger than qubit length scales greatly increases connectivity and is an important step towards maximal parallelism and the implementation of two-qubit gates on arbitrary pairs of qubits6. Qubit-coupling schemes based on cavity quantum electrodynamics2, 7, 8 also offer the possibility of using high-quality-factor resonators as quantum memories3, 9. Extending qubit interactions beyond the nearest neighbour is particularly beneficial for spin-based quantum computing architectures, which are limited by short-range exchange interactions10. Despite the rapidly maturing device technology for silicon spin qubits11–16, experimental progress towards achieving long-range spin–spin coupling has so far been restricted to interactions between individual spins and microwave photons17–20. Here we demonstrate resonant microwave-mediated coupling between two electron spins that are physically separated by more than four millimetres. An enhanced vacuum Rabi splitting is observed when both spins are tuned into resonance with the cavity, indicating a coherent interaction between the two spins and a cavity photon. Our results imply that microwave-frequency photons may be used to generate long-range two-qubit gates between spatially separated spins.

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We report the coherent coupling of two electron spins at a distance via virtual microwave photons.Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spinphoton couplings up to around g s =2π ¼ 40 MHz.As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around 2J=2π ¼ 20 MHz.In addition, photon-number states are resolved from the shift 2χ s =2π ¼ -13 MHz that they induce on the spin frequency.These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins.Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.

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.

We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around

g_s/2\pi = 40 \text{MHz}

. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around

2J/2\pi = 20 \text{MHz}

. In addition, photon number states are resolved from the shift

2\chi_s/2\pi = -13 \text{MHz}

they induce on the spin frequency. These results could enable long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.

Electron spin qubits in microwave cavities provide a promising platform for scalable quantum computing hardware, leveraging long coherence times, charge-noise robustness and cavity mediated qubit-qubit interactions. While the strong spin-photon coupling regime is accessible via on-chip micromagnets, scaling conventional architectures by placing multiple qubits within a single shared resonator degrades transmission amplitudes, hence limiting large-scale efficiency. To overcome this limitation, we analyze a modular architecture where individual cavities containing a limited number of qubits are coupled via single-photon-exchange waveguides. Using input/output theory, we compute the transmission amplitudes for networks of two and three coupled cavities in various configurations. We map out the distinct physical regimes accessible by tuning key system parameters, offering a viable pathway for scalable cavity-based quantum spin qubit networks.

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.

Direct interactions between quantum particles naturally fall off with distance. However, future quantum computing architectures are likely to require interaction mechanisms between qubits across a range of length scales. In this work, we demonstrate a coherent interaction between two semiconductor spin qubits 250 μm apart using a superconducting resonator. This separation is several orders of magnitude larger than for the commonly used direct interaction mechanisms in this platform. We operate the system in a regime in which the resonator mediates a spin-spin coupling through virtual photons. We report the anti-phase oscillations of the populations of the two spins with controllable frequency. The observations are consistent with iSWAP oscillations of the spin qubits, and suggest that entangling operations are possible in 10 ns. These results hold promise for scalable networks of spin qubit modules on a chip.