Electrical Interconnects for Silicon Spin Qubits

TL;DR

The work investigates long-range spin interconnects for silicon spin qubits by proposing a resistive topgate that forms a one-dimensional channel between quantum dots. It develops a momentum-incoherent transport model and analyzes spin decoherence via spin-orbit coupling, valley physics, and nuclear spins, finding the D\'yakonov–Perel' mechanism to dominate while motional narrowing mitigates other noise sources, yielding spin-decoherence lengths that are favorable for practical distances. The authors derive Kraus operators and a fidelity expression for transport, establishing $L_1$ (relaxation length) and $L_2$ (decoherence length) and showing that entanglement fidelity decays primarily with length through $L_2$, with $L_1$ playing a secondary role. They conclude that resistive interconnects could enable high-fidelity, long-range gates (tens to hundreds of micrometers) in silicon spin-qubit architectures, informing experimental tests and future device designs.

Abstract

Scalable spin qubit devices will likely require long-range qubit interconnects. We propose to create such an interconnect with a resistive topgate. The topgate is positively biased, to form a channel between the two dots; an end-to-end voltage difference across the nanowire results in an electric field that propels the electron from source dot to target dot. The electron is momentum-incoherent, but not necessarily spin-incoherent; we evaluate threats to spin coherence due to spin-orbit coupling, valley physics, and nuclear spin impurities. We find that spin-orbit coupling is the dominant threat, but momentum-space motional narrowing due to frequent scattering partially protects the electron, resulting in characteristic decoherence lengths ~15 mm for plausible parameters.

Figures (4)

• Figure 1: Top: proposed device. A Si/SiGe heterostructure confines an electron to the thin Si layer. A resistive topgate creates a one-dimensional channel in the Si layer and generates an electric field along the channel; an electron in the channel undergoes momentum-incoherent but spin-coherent transport down the channel. Bottom left: entanglement fidelity of transport across the channel as a function of channel length and spin-orbit interaction. Spin-orbit interaction couples the electron's spin degree of freedom to its momentum degree of freedom, which is incoherent due to scattering. Momentum-space motional narrowing, caused by frequent scattering, partially protects the spin degree of freedom. The bold line shows Dresselhaus spin-orbit coupling $\beta = 1\;\mathrm{peV\cdot cm}$, the value we expect for our devices (cf App. \ref{['app:soc:value']}.) Bottom right: a potential architecture using interconnects to connect plaquettes of five dots, four filled (filled circles) and one empty (empty circle).
• Figure 2: Sources of decoherence.(a) Spin-orbit coupling: as the electron scatters, the effective field due to spin-orbit coupling changes randomly. We find that this is the dominant source of decoherence. (b) Spatially-varying $g$-factor: the effective $g$-factor varies along the channel; scattering processes mean the electron spends an unpredictable amount of time in different effective $g$-factors. (c) Diabatic valley transitions: The valley splitting has a large random component, due to (e.g.) alloy disorder at the interface, so sometimes it is small. At points where it is small, the electron can diabatically transition to an excited state, which has a slightly different $g$ factor. (d) Spin-valley hotspots: When the valley splitting is on resonance with the Zeeman field, spin-valley coupling can flip both spin and valley; later spin-independent valley relaxation (e.g. due to phonons) brings the electron back to the valley ground state, now in a different spin state. (e) Nuclear spin impurities: As the electron passes near the rare spin-1/2 $\ce{^{29}Si}$, hyperfine interaction with the $\ce{^{29}Si}$ nuclear spin can change the electron spin.
• Figure 3: Decoherence lengths due to spin-orbit coupling across electron temperatures. The decoherence length is approximately mobility-independent. Because we take the Zeeman field to be along the interconnect, the effective Dresselhaus field is parallel to the quantization axis and decoherence dominates; were we to take the Zeeman field perpendicular to the interconnect, the effective Dresselhaus field would still dominate, but would then cause relaxation of approximately the same magnitude.
• Figure 4: Decoherence length resulting from spatial $g$-factor variation, across electron wavepacket lengths. Because the Larmor frequency variation is central-limiting, it is best understood as a standard deviation per unit length $\sigma_0$. The red dotted line shows $\sigma_0$ corresponding to a dot-to-dot $g$ factor variation $\Delta g / g = 10^{-3}$, consistent with SiMOS measurements jockSiliconSingletTriplet2022a; the black dashed line shows a heuristic estimate for SiGe devices, corresponding to $\Delta g / g = 10^{-4}$.