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arXiv:quant-ph/0506198 · Physical Review B

Two-dimensional architectures for donor-based quantum computing

Lloyd C. L. Hollenberg, Andrew D. Greentree, Austin G. Fowler, Cameron J. Wellard

Published Jul 17, 2006• 257 citations
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Abstract

Through the introduction of a new electron spin transport mechanism, a 2D donor electron spin quantum computer architecture is proposed. This design addresses major technical issues in the original Kane design, including spatial oscillations in the exchange coupling strength and cross-talk in gate control. It is also expected that the introduction of nonlocality in qubit interaction will significantly improve the scaling fault-tolerant threshold over the nearest-neighbor linear array.

DOI
10.1103/physrevb.74.045311

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Through the introduction of a new electron spin transport mechanism, a 2D donor electron spin quantum computer architecture is proposed. This design addresses major technical issues in the original Kane design, including spatial oscillations in the exchange coupling strength and cross-talk in gate control. It is also expected that the introduction of nonlocality in qubit interaction will significantly improve the scaling fault-tolerant threshold over the nearest-neighbor linear array.
Solid state quantum computer architectures are often touted as inherently scalable on the basis of proven classical architecture miniaturisation - i.e. through sheer ease of component replication. However, this weak scaling argument misses the vast complexity of the implementation of fault-tolerant quantum protocols required to protect quantum information processing against errors. In a successful design of strongly scalable quantum computer architecture, highly non-trivial requirements such as qubit transport, logic gates for physically separated qubits, fast read-out and resources for classical processing and error correction must be incorporated. We review a new adiabatic scheme coherent (spin) transport by adiabatic passage (CTAP) for physical qubit transport particularly suited to atomic and solid-state systems. The tunnelling rates, transfer times and the effects of decoherence are calculated for CTAP using phosphorous donors in silicon. Using CTAP qubit transport we have proposed a bi-linear donor electron spin architecture with potential for scale-up to fault-tolerant operation. This architecture allows for the distribution of interaction, storage and readout regions and incorporates non-nearest-neighbour interactions between qubits. The transport rails which provide these non-local interactions, also provide alternative pathways to avoid non-functioning regions. The key questions under investigation are whether one can: perform fault-tolerant quantum computation on such an architecture, and determine quantitative estimates of the fault-tolerant threshold.
We propose a scheme for quantum information processing based on donor electron spins in semiconductors, with an architecture complementary to the original Kane proposal. We show that a na\"{\i}ve implementation of electron spin qubits provides only modest improvement over the Kane scheme, however through the introduction of global gate control we are able to take full advantage of the fast electron evolution timescales. We estimate that the latent clock speed is 100--1000 times that of the nuclear spin quantum computer with the ratio T2∕Tops{T}_{2}∕{T}_{\mathrm{ops}}T2​∕Tops​ approaching the 106{10}^{6}106 level.
Donor-based spin qubit offers a promising silicon quantum computing route for building large-scale qubit arrays, attributed to its long coherence time and advancements in nanoscale donor placement. However, the state-of-the-art device designs face scalability challenges, notably in achieving tunable two-qubit coupling and ensuring qubit addressability. Here, we propose a surface-code-compatible architecture, where each module has both tunable two-qubit gates and addressable single-qubit gates by introducing only a single extra donor in a pair of donors. We found that to compromise between the requirement of tunability and that of addressability, an asymmetric scheme is necessary. In this scheme, the introduced extra donor is strongly tunnel-coupled to one of the donor spin qubits for addressable single-qubit operation, while being more weakly coupled to the other to ensure the turning on and off of the two-qubit operation. The fidelity of single-qubit and two-qubit gates can exceed the fault-tolerant threshold in our design. Additionally, the asymmetric scheme effectively mitigates valley oscillations, allowing for engineering precision tolerances up to a few nanometers. Thus, our proposed scheme presents a promising prototype for large-scale, fault-tolerant, donor-based spin quantum processors.
We theoretically investigate cross-talk in hyperfine gate control of donor-qubit quantum computer architectures, in particular the Kane proposal. By solving the Poisson and Schrödinger equations numerically for the gated donor system, we calculate the change in hyperfine coupling and thus the error in spin-rotation for the donor nuclear-electron spin system, as the gate-donor distance is varied. We thus determine the effect of cross-talk-the inadvertent effect on non-target neighbouring qubits-which occurs due to closeness of the control gates (20-30 nm). The use of compensation protocols is investigated, whereby the extent of cross-talk is limited by the application of compensation bias to a series of gates. In the light of these factors, architectural implications are then considered.
In the Kane silicon-based electron-mediated nuclear spin quantum computer architecture, phosphorous is doped at precise positions in a silicon lattice, and the P donor nuclear spins act as qubits. Logical operations on the nuclear spins are performed using externally applied magnetic and electric fields. There are two important interactions: the hyperfine and exchange interactions, crucial for logical qubit operations. Single qubit operations are performed by applying radio frequency magnetic fields resonant with targeted nuclear spin transition frequencies, tuned by the gate-controlled hyperfine interaction. Two qubit operations are mediated through the exchange interaction between adjacent donor electrons. It is important to examine how these two interactions vary as functions of experimental parameters. Here we provide such an investigation. First, we examine the effects of varying several experimental parameters: gate voltage, inter donor separation, donor depth below the silicon oxide interface and back gate depth, to explore how these variables affect the donor electro density. Second, we calculate the hyperfine interaction and the exchange coupling as a function of these parameters. These calculations were performed using an anisotropic effective mass Hamiltonian. The electric field potential was obtained using Technology Computer Aided Design software, and the interfaces were modelled as a barrier using a step function. We aim to provide relevant information for the experimental design of these devices and highlight the significance of environmental factors other than gate potential that affect the donor electron.
Practical quantum computers require 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 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 leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.