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Silicon quantum processor with robust long-distance qubit couplings
Guilherme Tosi, Fahd A. Mohiyaddin, Vivien Schmitt, Stefanie Tenberg, Rajib Rahman, Gerhard Klimeck, Andrea Morello
TL;DR
Scalable silicon quantum processors need coherent qubits with reliable long-range coupling despite fabrication variability and noise. This paper proposes electrically controlled donor spin qubits with gate-tunable donor-interface coupling and dipole-mediated interactions. The model supports below-threshold operation without active noise cancellation, while image-charge effects impose uncertainty on practical coupling estimates.
Problem
Scalable donor-spin processors require reliable two-qubit coupling despite donor-placement uncertainty and electric noise.
Method
The design uses a two-level donor-interface orbital model, lateral gates for in situ Vt tuning, and electric dipole interactions modified by image-charge screening.
Results
∼2 orders of magnitude tuning of Vt is achieved in simulations, while the modeled dominant noise sources yield the paper’s reported low-error operation estimates.
Takeaways & Limitations
The proposed architecture can relax donor-placement requirements while retaining electrically tunable coupling and operation without dynamical noise cancellation.
Takeaways & Limitations
Image-charge fields in a real device are difficult to estimate precisely, so slightly larger inter-donor separations may be required.
Abstract
from arXiv · showhide
Practical quantum computers require the construction of a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a physical platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and allows hundreds of nanometers inter-qubit distances, therefore facilitating fabrication using current technology. All qubit operations are performed via electrical means on the electron-nuclear spin states of a phosphorus donor. Single-qubit gates use low power electric drive at microwave frequencies, while fast two-qubit gates exploit electric dipole-dipole interactions. Microwave resonators allow for millimeter-distance entanglement and interfacing with photonic links. Sweet spots protect the qubits from charge noise up to second order, implying that all operations can be performed with error rates below quantum error correction thresholds, even without any active noise cancellation technique.
S1. Validity of the two-level approximation for the electron orbital wavefunction
The donor-interface electron orbital can be modeled accurately as a two-level charge qubit over the proposal’s relevant electric-field range. Tight-binding calculations support this approximation because the interface valley splitting exceeds the donor-interface tunnel coupling.
- Model validity: The two-level charge-qubit model accurately approximates the donor-interface orbital states over the relevant parameter range.The model agrees well with atomistic tight-binding calculations for the donor-interface system.
- Relevant orbital states: The relevant low-energy states are the donor state |d⟩ and lower interface valley state |i⟩, while the upper valley state |v⟩ lies higher in energy.The donor and interface states are coupled through the donor-interface tunnel coupling.
- Validity range: The two-level model remains valid below the electric field at which the donor state anticrosses with the upper valley interface state.The approximation is valid for Ez below the upper-valley anticrossing field, provided Vs exceeds Vt.
- Validity condition: 71.7 GHz valley splitting exceeds the 9.3 GHz tunnel coupling, supporting the two-level approximation.The condition Vs much larger than Vt separates the upper interface valley state from the modeled two-level subspace.
S2. Tunnel coupling tunability between donor and interface
Ion implantation creates large uncertainty in donor depth and tunnel coupling, so the design adds lateral gates to tune the donor-interface tunnel coupling in situ. Simulations indicate that this approach can compensate the implantation-induced uncertainty while remaining compatible with nanofabrication.
- Motivation: A donor-depth uncertainty of approximately ±10 nm can produce more than 2 orders of magnitude uncertainty in Vt.Tunnel coupling decreases exponentially with donor depth, making in situ tuning necessary.
- Tuning mechanism: Additional left and right gates modify the potential landscape and laterally displace the interface wavefunction to tune Vt.The gate voltages change the distance between the donor and interface wavefunctions.
- Practical consequence: The gate scheme circumvents donor-depth and tunnel-coupling uncertainty without requiring precise donor placement.It relocates the sensitivity associated with valley oscillations from exchange interactions to a tunable tunnel coupling.
S3. Charge and gate noise
The analysis treats quasi-static and high-frequency electric noise affecting electrically driven flip-flop qubits. It identifies quasi-static electric-field noise and charge-phonon relaxation as the most deleterious modeled sources, while estimating smaller errors from high-frequency and lateral noise.
- Lateral noise: Horizontal charge noise produces at most 10^-4 gate-time-jitter errors and approximately 10^4 Hz extra dephasing through dispersive shifts.The predominantly vertical donor-interface dipole makes the qubits largely insensitive to horizontal charge noise.
- Gate noise: Low-temperature metallic-gate noise is estimated to be negligible, whereas room-temperature Johnson-Nyquist noise gives errors below 10^-5.The estimates use a 10^6 Hz quasi-static bandwidth and 100 mK device temperature for the low-temperature case.
- Quasi-static noise: 100 V/m quasi-static noise over a 10^6 Hz bandwidth corresponds to the assumed 1/ν charge-noise spectrum.This field level produces 1–3 µeV detuning noise for a 10–30 nm donor-interface separation.
- High-frequency noise: High-frequency noise estimates give error rates below 10^-4 for charge noise and below 10^-5 to 10^-6 for the stated Johnson-Nyquist cases.The latter values correspond to room-temperature and 100 mK effective noise temperatures, respectively.
- Dominant noise sources: Quasi-static Ez noise and charge-phonon relaxation are identified as the most deleterious modeled error sources for flip-flop qubits.The analysis is presented as a worst-case scenario without dynamical noise cancellation.
S4. Screening effect of metals and dielectrics
Image charges from the metal and oxide environment modify the donor-interface dipoles and therefore the dipole-dipole coupling. The real-device estimate is uncertain, but the assumed mixed interface generally enhances coupling while requiring somewhat larger donor separations.
- Image-charge screening: Metal interfaces enhance the vertical dipole field by a factor of 2 and the dipole coupling gdd by a factor of 4.Oxide interfaces instead reduce the field by half and gdd to a quarter of its bare value.
- Real-device estimate: For the assumed mixed metal-oxide structure, a 50% dipole enhancement yields a 125% improvement in gdd.This estimate uses Q = −0.5 for the image-charge contribution.
- Device boundary: The real-device image-charge field is difficult to estimate precisely because metal gates sit above an approximately 8 nm SiO2 layer.The resulting design implication is to target slightly larger inter-donor separations than in the main-text estimates.
- Lateral dipoles: For the assumed real structure, lateral dipole components are reduced to half their original value.Metal interfaces completely screen the lateral component, while SiO2 interfaces enhance it by 50%.
- Interaction model: The dipole-dipole interaction model incorporates both image-charge screening and angular dependence.The model treats the dipole components separately when modifying the interaction term.