Subspace confinement : how good is your qubit?

The basic operating element of standard quantum computation is the qubit, an isolated two-level system that can be accurately controlled, initialized and measured. However, the majority of proposed physical architectures for quantum computation are built from systems that contain much more complicated Hilbert space structures. Hence, defining a qubit requires the identification of an appropriate controllable two-dimensional sub-system. This prompts the obvious question of how well a qubit, thus defined, is confined to this subspace, and whether we can experimentally quantify the potential leakage into states outside the qubit subspace. We demonstrate how subspace leakage can be characterized using minimal theoretical assumptions by examining the Fourier spectrum of the oscillation experiment

Matterwave Transport Without Transit

Classically it is impossible to have transport without transit, i.e., if the points one, two and three lie sequentially along a path then an object moving from one to three must, at some point in time, be located at two. However, for a quantum particle in a three-well system it is possible to transport the particle between wells one and three such that the probability of finding it at any time in the classically accessible state in well two is negligible. We consider theoretically the analogous scenario for a Bose-Einstein condensate confined within a three well system. In particular, we predict the adiabatic transportation of an interacting Bose-Einstein condensate of 2000 Li atoms from well one to well three without transiting the allowed intermediate region. To an observer of this macroscopic quantum effect it would appear that, over a timescale of the order of one second, the condensate had transported, but not transited, a macroscopic distance of 20 microns between wells one and three.Comment: 6 pages, 4 figure

Stark tuning of the charge states of a two-donor molecule in silicon

Gate control of phosphorus donor based charge qubits in Si is investigated using a tight-binding approach. Excited molecular states of P2+ are found to impose limits on the allowed donor separations and operating gate voltages. The effects of surface (S) and barrier (B) gates are analyzed in various voltage regimes with respect to the quantum confined states of the whole device. Effects such as interface ionization, saturation of the tunnel coupling, sensitivity to donor and gate placement are also studied. It is found that realistic gate control is smooth for any donor separation, although at certain donor orientations the S and B gates may get switched in functionality. This paper outlines and analyzes the various issues that are of importance in practical control of such donor molecular systems.Comment: 8 pages, 9 figure

Orbital Stark effect and quantum confinement transition of donors in silicon

Adiabatic shuttling of single impurity bound electrons to gate induced surface states in semiconductors has attracted much attention in recent times, mostly in the context of solid-state quantum computer architecture. A recent transport spectroscopy experiment for the first time was able to probe the Stark shifted spectrum of a single donor in silicon buried close to a gate. Here we present the full theoretical model involving large-scale quantum mechanical simulations that was used to compute the Stark shifted donor states in order to interpret the experimental data. Use of atomistic tight-binding technique on a domain of over a million atoms helped not only to incorporate the full band structure of the host, but also to treat realistic device geometries and donor models, and to use a large enough basis set to capture any number of donor states. The method yields a quantitative description of the symmetry transition that the donor electron undergoes from a 3D Coulomb confined state to a 2D surface state as the electric field is ramped up adiabatically. In the intermediate field regime, the electron resides in a superposition between the states of the atomic donor potential and that of the quantum dot like states at the surface. In addition to determining the effect of field and donor depth on the electronic structure, the model also provides a basis to distinguish between a phosphorus and an arsenic donor based on their Stark signature. The method also captures valley-orbit splitting in both the donor well and the interface well, a quantity critical to silicon qubits. The work concludes with a detailed analysis of the effects of screening on the donor spectrum.Comment: 10 pages, 10 figures, journa

Coherent electronic transfer in quantum dot systems using adiabatic passage

We describe a scheme for using an all-electrical, rapid, adiabatic population transfer between two spatially separated dots in a triple-quantum dot system. The electron spends no time in the middle dot and does not change its energy during the transfer process. Although a coherent population transfer method, this scheme may well prove useful in incoherent electronic computation (for example quantum-dot cellular automata) where it may provide a coherent advantage to an otherwise incoherent device. It can also be thought of as a limiting case of type II quantum computing, where sufficient coherence exists for a single gate operation, but not for the preservation of superpositions after the operation. We extend our analysis to the case of many intervening dots and address the issue of transporting quantum information through a multi-dot system.Comment: Replaced with (approximately) the published versio

High precision quantum control of single donor spins in silicon

The Stark shift of the hyperfine coupling constant is investigated for a P donor in Si far below the ionization regime in the presence of interfaces using Tight-binding and Band Minima Basis approaches and compared to the recent precision measurements. The TB electronic structure calculations included over 3 million atoms. In contrast to previous effective mass based results, the quadratic Stark coefficient obtained from both theories agrees closely with the experiments. This work represents the most sensitive and precise comparison between theory and experiment for single donor spin control. It is also shown that there is a significant linear Stark effect for an impurity near the interface, whereas, far from the interface, the quadratic Stark effect dominates. Such precise control of single donor spin states is required particularly in quantum computing applications of single donor electronics, which forms the driving motivation of this work.Comment: 5 pages, 2 figure

Global control and fast solid-state donor electron spin quantum computing

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 naive 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 $T_{2}/T_{ops}$ approaching the $10^{6}$ level.Comment: 9 pages, 9 figure

Cross-talk compensation of hyperfine control in donor qubit architectures

We theoretically investigate cross-talk in hyperfine gate control of donor-qubit quantum computer architectures, in particular the Kane proposal. By numerically solving the Poisson and Schr\"{o}dinger equations 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 (20-30nm). The use of compensation protocols is investigated, whereby the extent of crosstalk is limited by the application of compensation bias to a series of gates. In light of these factors the architectural implications are then considered.Comment: 15 pages, 22 figures, submitted to Nanotechnolog

Mapping donor electron wave function deformations at sub-Bohr orbit resolution

Quantum wave function engineering of dopant-based Si nano-structures reveals new physics in the solid-state, and is expected to play a vital role in future nanoelectronics. Central to any fundamental understanding or application is the ability to accurately characterize the deformation of the electron wave functions in these atom-based structures through electromagnetic field control. We present a method for mapping the subtle changes that occur in the electron wave function through the measurement of the hyperfine tensor probed by 29Si impurities. Our results show that detecting the donor electron wave function deformation is possible with resolution at the sub-Bohr radius level.Comment: 4 pages, 3 figures, and 1 tabl

A hybrid double-dot in silicon

We report electrical measurements of a single arsenic dopant atom in the tunnel-barrier of a silicon SET. As well as performing electrical characterization of the individual dopant, we study series electrical transport through the dopant and SET. We measure the triple points of this hybrid double dot, using simulations to support our results, and show that we can tune the electrostatic coupling between the two sub-systems.Comment: 11 pages, 6 figure