Molecular orbital calculations of two-electron states for P donor solid-state spin qubits

Abstract

We theoretically study the Hilbert space structure of two neighbouring P donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position and inter donor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, whilst the magnitude of the double occupancy probability can affect the error rate.

15 pages (2-column)

References in corpus (23)

• Electron Spin Resonance Transistors for Quantum Computing in Silicon-Germanium Heterostructures
• Hilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule
• Charge-based quantum computing using single donors in semiconductors
• Exchange in silicon-based quantum computer architecture
• An all silicon quantum computer
• Design and proof of concept for silicon-based quantum dot quantum bits
• Practical design and simulation of silicon-based quantum dot qubits
• Double-Occupancy Errors, Adiabaticity, and Entanglement of Spin-Qubits in Quantum Dots
• Hydrogenic Spin Quantum Computing in Silicon: A Digital Approach
• Silicon quantum computation based on magnetic dipolar coupling
• Global control and fast solid-state donor electron spin quantum computing
• Strain effects on silicon donor exchange: Quantum computer architecture considerations
• Electron Exchange Coupling for Single Donor Solid-State Qubits
• Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces
• Gate errors in solid state quantum computer architectures
• Gate-induced ionization of single dopant atoms
• Fast Non-Adiabatic Two Qubit Gates for the Kane Quantum Computer
• Nuclear magnetic resonance spectrum of 31P donors in silicon quantum computer
• Disentangling the exchange coupling of entangled donors in the Si quantum computer architecture
• Voltage Control of Exchange Coupling in Phosphorus Doped Silicon
• Gates for the Kane Quantum Computer in the Presence of Dephasing
• Simulation of Si:P spin-based quantum computer architecture
• Effects of J-gate potential and interfaces on donor exchange coupling in the Kane quantum computer architecture

Cited by in corpus (10)

• Silicon Quantum Electronics
• Robust CNOT gates from almost any interaction
• Engineering inter-qubit exchange coupling between donor bound electrons in silicon
• An Exchange-Coupled Donor Molecule in Silicon
• Strain and Electric Field Control of Hyperfine Interactions for Donor Spin Qubits in Silicon
• Full configuration interaction simulations of exchange-coupled donors in silicon using multi-valley effective mass theory
• Optimal control of the silicon-based donor electron spin quantum computing
• Linear and planar molecules formed by coupled P donors in silicon
• Exchange between deep donors in semiconductors: a quantum defect approach
• Dynamics of a driven spin coupled to an antiferromagnetic spin bath