Electron Exchange Coupling for Single Donor Solid-State Qubits

Abstract

Inter-valley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighbouring phosphorus donor electron states in silicon \cite{Koiller02,Koiller02A}. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wavefunctions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller et. al. [Phys. Rev. Lett. 88,027903(2002),Phys. Rev. B. 66,115201(2002)], significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighbouring donors that have been implanted into the silicon substrate using an 15keV ion beam in the so-called 'top down' fabrication scheme for a Kane solid-state quantum computer. In addition we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wavefunctions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighbouring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller.

10 Pages, 8 Figures. To appear in Physical Review B

References in corpus (8)

• Electron Spin Resonance Transistors for Quantum Computing in Silicon-Germanium Heterostructures
• Exchange in silicon-based quantum computer architecture
• Towards the fabrication of phosphorus qubits for a silicon quantum computer
• Strain effects on silicon donor exchange: Quantum computer architecture considerations
• Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces
• Fast Non-Adiabatic Two Qubit Gates for the Kane Quantum Computer
• Error Rate of the Kane Quantum Computer CNOT Gate in the Presence of Dephasing
• A Non-Adiabatic Controlled Not Gate for the Kane Solid State Quantum Computer

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• Global control and fast solid-state donor electron spin quantum computing
• Spin quantum computation in silicon nanostructures
• Donor Electron Wave Functions for Phosphorus in Silicon: Beyond Effective Mass Theory
• Single-shot readout and relaxation of singlet/triplet states in exchange-coupled ${}^{31}$P electron spins in silicon
• Robust CNOT gates from almost any interaction
• Charge qubits in semiconductor quantum computer architectures: Tunnel coupling and decoherence
• Engineering inter-qubit exchange coupling between donor bound electrons in silicon
• Shallow donor wavefunctions and donor-pair exchange in silicon: Ab initio theory and floating-phase Heitler-London approach
• Robust two-qubit gates for donors in silicon controlled by hyperfine interactions
• Electric field driven donor-based charge qubits in semiconductors
• Single-spin readout for buried dopant semiconductor qubits
• Phosphorus donors in highly strained silicon
• High-fidelity adiabatic inversion of a ${}^{31}\mathrm{P}$ electron spin qubit in natural silicon
• Valley interference and spin exchange at the atomic scale in silicon
• A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength
• Electrical readout of a spin qubit without double occupancy
• Full configuration interaction simulations of exchange-coupled donors in silicon using multi-valley effective mass theory
• Transport of Spin Qubits with Donor Chains under Realistic Experimental Conditions
• Optimal control of the silicon-based donor electron spin quantum computing
• Molecular orbital calculations of two-electron states for P donor solid-state spin qubits
• Towards Large-Scale Quantum Computation
• Two-spin relaxation of P-dimers in Silicon
• Controlled phase gate for solid-state charge qubits
• Voltage Control of Exchange Coupling in Phosphorus Doped Silicon
• Simulation of Si:P spin-based quantum computer architecture
• Large-scale atomistic density functional theory calculations of phosphorus-doped silicon quantum bits
• Effects of J-gate potential and interfaces on donor exchange coupling in the Kane quantum computer architecture
• The impact of nuclear spin dynamics on electron transport through donors
• Extracting inter-dot tunnel couplings between few donor quantum dots in silicon
• Exchange between deep donors in semiconductors: a quantum defect approach
• Dynamics of a driven spin coupled to an antiferromagnetic spin bath
• Optimisation of electrically-driven multi-donor quantum dot qubits
• Singlet-triplet minus mixing and relaxation lifetimes in a double donor dot