Abstract:
Proposed Silicon-based quantum computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing infrastructure of the powerful Si technology. Quantitative understanding of and precise physical control over donor (e.g. Phosphorus) exchange are crucial elements in the physics underlying the proposed Si-based quantum computer hardware. An important potential problem in this context is that inter-valley interference originating from the degeneracy in the Si conduction band edge causes fast oscillations in donor exchange coupling, which imposes significant constraints on the Si quantum computer architecture. In this paper we consider the effect of external strain on Si donor exchange in the context of quantum computer hardware. We study donor electron exchange in uniaxially strained Si, since strain partially lifts the valley degeneracy in the bulk. In particular, we focus on the effects of donor displacements among lattice sites on the exchange coupling, investigating whether inter-valley interference poses less of a problem to exchange coupling of donors in strained Si. We show, using the Kohn-Luttinger envelope function approach, that fast oscillations in exchange coupling indeed disappear for donor pairs that satisfy certain conditions for their relative positions, while in other situations the donor exchange coupling remains oscillatory, with periods close to interatomic spacing. We also comment on the possible role of controlled external strain in the design and fabrication of Si quantum computer architecture.

Abstract:
In bulk silicon, intervalley electronic interference has been shown to lead to strong oscillations in the exchange coupling between impurity electronic wavefunctions, posing a serious manufacturability problem for proposed quantum computers. Here we show that this problem does not arise in proposed architectures using Si/SiGe quantum dots because of the large in-plane strain in Si quantum wells together with the strong confinement potential typical of heterostructures.

Abstract:
We develop a theory for micro-Raman scattering by single and coupled two-donor states in silicon. We find the Raman spectra to have significant dependence on the donor exchange splitting and the relative spatial positions of the two donor sites. In particular, we establish a strong correlation between the temperature dependence of the Raman peak intensity and the interdonor exchange coupling. Micro-Raman scattering can therefore potentially become a powerful tool to measure interqubit coupling in the development of a Si quantum computer architecture.

Abstract:
We calculate the electron exchange coupling for a phosphorus donor pair in silicon perturbed by a J-gate potential and the boundary effects of the silicon host geometry. In addition to the electron-electron exchange interaction we also calculate the contact hyperfine interaction between the donor nucleus and electron as a function of the varying experimental conditions. Donor separation, depth of the P nuclei below the silicon oxide layer and J-gate voltage become decisive factors in determining the strength of both the exchange coupling and the hyperfine interaction - both crucial components for qubit operations in the Kane quantum computer. These calculations were performed using an anisotropic effective-mass Hamiltonian approach. The behaviour of the donor exchange coupling as a function of the device parameters varied provides relevant information for the experimental design of these devices.

Abstract:
Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideally suited candidates for qubits in such proposals, where shallow donor exchange gates are frequently invoked to perform two-qubit operations. An important potential problem in this context is that intervalley interference originating from the degeneracy in the Si conduction-band edge causes fast oscillations in donor exchange coupling, which imposes significant constraints on the Si quantum-computer architecture. We discuss the theoretical origin of such oscillations. Considering two substitutional donors in Si, we present a systematic statistical study of the correlation between relative position distributions and the resulting exchange distributions.

Abstract:
We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear-electron hyperfine and electron-electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Control-Not gate. The exchange interaction is constant and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.

Abstract:
We present a theoretical analysis of a microwave spectroscopy experiment on a charge qubit defined by a P$_2^+$ donor pair in silicon, for which we calculate Hamiltonian parameters using the effective-mass theory of shallow donors. We solve the master equation of the driven system in a dissipative environment to predict experimental outcomes. We describe how to calculate physical parameters of the system from such experimental results, including the dephasing time, $T_2$, and the ratio of the resonant Rabi frequency to the relaxation rate. Finally we calculate probability distributions for experimentally relevant system parameters for a particular fabrication regime.

Abstract:
First solid state quantum computer was built using transmons (cooper pair boxes). The operation of the computer is limited because of using a number of the rigit cooper boxes working with fixed frequency at temperatures of superconducting material. Here, we propose a novel architecture of quantum computer based on a flexible wire circuit of many coupled quantum nodes containing controlled atomic (molecular) ensembles. We demonstrate wide opportunities of the proposed computer. Firstly, we reveal a perfect storage of external photon qubits to multi-mode quantum memory node and demonstrate a reversible exchange of the qubits between any arbitrary nodes. We found optimal parameters of atoms in the circuit and self quantum modes for quantum processing. The predicted perfect storage has been observed experimentally for microwave radiation on the lithium phthalocyaninate molecule ensemble. Then also, for the first time we show a realization of the efficient basic two-qubit gate with direct coupling of two arbitrary nodes by using appropriate atomic frequency shifts in the circuit nodes. Proposed two-qubit gate runs with a speed drastically accelerated proportionally to the number of atoms in the node. The direct coupling and accelerated two-qubit gate can be realized for large number of the circuit nodes. Finally, we describe two and three-dimensional scalable architectures that pave the road to construction of universal multi-qubit quantum computer operating at room temperatures.

Abstract:
A solid-state implementation of a quantum computer composed entirely of silicon is proposed. Qubits are Si-29 nuclear spins arranged as chains in a Si-28 (spin-0) matrix with Larmor frequencies separated by a large magnetic field gradient. No impurity dopants or electrical contacts are needed. Initialization is accomplished by optical pumping, algorithmic cooling, and pseudo-pure state techniques. Magnetic resonance force microscopy is used for readout. This proposal takes advantage of many of the successful aspects of solution NMR quantum computation, including ensemble measurement, RF control, and long decoherence times, but it allows for more qubits and improved initialization.

Abstract:
We present a systematic and realistic simulation for single and double phosphorous donors in a silicon-based quantum computer design. A two-valley equation is developed to describe the ground state of phosphorous donors in strained silicon quantum well (QW), with the central cell effect treated by a model impurity potential. We find that the increase of quantum well confinement leads to shrinking charge distribution in all 3 dimensions. Using an unrestricted Hartree-Fock method with Generalized Valence Bond (GVB) single-particle wave functions, we are able to solve the two-electron Sch${\ddot o}$dinger equation with quantum well confinement and realistic gate potentials. The effects of QW width, gate voltages, donor separation, and donor position are calculated and analyzed. The gate tunability and gate fidelity are defined and evaluated, for a typical QC design. Estimates are obtained for the duration of $\sqrt{SWAP}$ gate operation and the required accuracy in voltage control. A strong exchange oscillation is observed as both donors are shifted along [001] axis but with their separation unchanged. Applying a gate potential tends to suppress the oscillation. The exchange oscillation as a function of donor position along [100] axis is found to be completely suppressed as the donor separation is decreased. The simulation presented in this paper is of importance to the practical design of an exchange-based silicon quantum computer.