Omnidirectional shuttling to avoid valley excitations in Si/SiGe quantum wells

Conveyor-mode shuttling is a key approach for implementing intermediate-range coupling between electron-spin qubits in quantum dots. Initial implementations are encouraging; however, long shuttling trajectories are guaranteed to encounter regions of low conduction-band valley energy splittings, due to the presence of random-alloy disorder in Si/SiGe quantum wells. Here, we theoretically explore two schemes for avoiding valley-state excitations at these valley-splitting minima, by allowing the electrons to detour around them. A multichannel shuttling scheme allows electrons to tunnel between parallel channels, while a two-dimensional (2D) shuttler provides full omnidirectional control. Using simulations, we estimate shuttling fidelities in these two schemes, obtaining a clear preference for the 2D shuttler. Based on such encouraging results, we propose a modular qubit architecture based on 2D shuttling, which enables all-to-all connectivity within qubit plaquettes and high-fidelity communication between different plaquettes.

💡 Research Summary

This paper addresses a critical obstacle for silicon‑based spin‑qubit quantum processors: the presence of random‑alloy disorder in Si/SiGe quantum wells creates spatially varying conduction‑band valley splittings (Eₙ), with average values around 100 µeV but large fluctuations (σ≈Ēᵥ/√π). Consequently, any long‑range conveyor‑mode shuttling trajectory inevitably encounters “valley‑splitting minima” where Eₙ drops below ~30 µeV, making Landau‑Zener transitions into excited valley states likely. Traditional 1‑D shuttlers can only shift the electron laterally by ≈20 nm, far insufficient to detour around these dangerous spots.

The authors propose two strategies that enable transverse motion large enough to avoid low‑Eₙ regions. The first, a multichannel shuttler, adds one or more parallel shuttling lanes separated by screening gates. Overlapping “clavier” gates provide the moving potential pocket, while independent control of the screening gates tunes the inter‑lane detuning (ε) and tunnel coupling (t_c). With a lane spacing of ≳100 nm, the transverse shift Δy meets the required ≈100 nm. However, because tunneling between lanes conserves the valley index, a random valley‑phase difference (δϕ) between the two lanes generates off‑diagonal inter‑valley couplings (t_eg, t_ge). The authors model the system with a four‑level Hamiltonian (ground and excited valley states in each lane) and treat the intra‑lane valley splittings Δ_L,R as complex Gaussian variables with zero mean and variance σ_Δ. Simulations use two protocols: a “paused” protocol where ε is linearly swept from –ε₀ to +ε₀ while t_c follows a sinusoidal envelope, and a “moving” protocol that additionally turns off t_c during transport to suppress errors from lever‑arm fluctuations. By scanning ε₀ and t₀, they find optimal points (e.g., ε₀≈750 µeV, t₀≈200 µeV) that yield transfer success probabilities P_suc ≈ 95 % in the presence of uncorrelated disorder. The dominant error source is the valley‑phase‑induced inter‑valley tunneling; when δϕ≈0 the error spikes dramatically. Overall, the multichannel approach improves transverse displacement but still suffers from valley‑phase‑related leakage.

The second, and more promising, approach is a fully two‑dimensional (2D) shuttler. Here the authors tile the surface with a lattice of “clavette” gates, each acting as a pixel that can be biased with a sinusoidal waveform. By appropriately phasing the signals, a moving potential pocket can be steered in any planar direction using only a modest number of control lines. Prior to shuttling, a 2D map of valley splittings is obtained (e.g., via the method of Ref.