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.
We demonstrate how gradient ascent pulse engineering optimal control methods can be implemented on donor-electron-spin qubits in Si semiconductors with an architecture complementary to the original Kane's proposal. We focus on the high-fidelity-controlled-NOT (CNOT) gate and explicitly find its digitized control sequences by optimizing its fidelity over the external controls of the hyperfine
A and exchange
J interactions. This high-fidelity-CNOT gate has an error of about ${10}^{\ensuremath{-}6}$, below the error threshold required for fault-tolerant quantum computation, and its operation time of 100 ns is about three times faster than 297 ns of the proposed global control scheme. It also relaxes significantly the stringent distance constraint of two neighboring donor atoms of 10--20 nm as reported in the original Kane's proposal to about 30 nm in which surface
A and
J gates may be built with current fabrication technology. The effects of the control voltage fluctuations, the dipole-dipole interaction, and the electron-spin decoherence on the CNOT gate fidelity are also discussed.
Achieving low-error, exchange-interaction operations in quantum dots for quantum computing imposes simultaneous requirements on the exchange energy's dependence on applied voltages. A double quantum dot qubit, approximated with a quadratic potential, is solved using a full configuration interaction method. This method is more accurate than Heitler-London and Hund-Mulliken approaches and captures new and significant qualitative behavior. We show that multiple regimes can be found in which the exchange energy's dependence on the bias voltage between the dots is compatible with current quantum error correction codes and state-of-the-art electronics. Identifying such regimes may prove valuable for the construction and operation of quantum gates that are robust to charge fluctuations, particularly in the case of dynamically corrected gates.