Spin swap vs. double occupancy in quantum gates

We propose an approach to realize quantum gates with electron spins localized in a semiconductor that uses double occupancy to advantage. With a fast (non-adiabatic) time control of the tunnelling, the probability of double occupancy is first increased and then brought back exactly to zero. The quantum phase built in this process can be exploited to realize fast quantum operations. We illustrate the idea focusing on the half-swap operation, which is the key two-qubit operation needed to build a CNOT gate.Comment: 5 pages, 2 figure

Variational Monte Carlo for spin-orbit interacting systems

Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a general variational Monte Carlo approach is here introduced that treats in an efficient and very accurate way the spin degrees of freedom in atoms when spin orbit effects are included in the Hamiltonian describing the electronic structure. We illustrate the algorithm on the evaluation of the spin-orbit splittings of isolated carbon and lead atoms. In the case of the carbon atom, we investigate the differences between the inclusion of spin-orbit in its realistic and effective spherically symmetrized forms. The method exhibits a very good accuracy in describing the small energy splittings, opening the way for a systematic quantum Monte Carlo studies of spin-orbit effects in atomic systems.Comment: 7 pages, 0 figure

A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

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

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.Comment: 15 pages (2-column

Exchange between deep donors in semiconductors: a quantum defect approach

Exchange interactions among defects in semiconductors are commonly treated within effective-mass theory using a scaled hydrogenic wave-function. However such a wave-function is only applicable to shallow impurities; here we present a simple but robust generalization to treat deep donors, in which we treat the long-range part of the wavefunction using the well established quantum defect theory, and include a model central-cell correction to fix the bound-state eigenvalue at the experimentally observed value. This allows us to compute the effect of binding energy on exchange interactions as a function of donor distance; this is a significant quantity given recent proposals to carry out quantum information processing using deep donors. As expected, exchange interactions are suppressed (or increased), compared to the hydrogenic case, by the greater localization (or delocalization) of the wavefunctions of deep donors (or `super-shallow' donors with binding energy less then the hydrogenic value). The calculated results are compared with a simple scaling of the Heitler-London hydrogenic exchange; the scaled hydrogenic results give the correct order of magnitude but fail to reproduce quantitatively our calculations. We calculate the donor exchange in silicon including inter-valley interference terms for donor pairs along the $\{100\}$ direction, and also show the influence of the donor type on the distribution of nearest-neighbour exchange constants at different concentrations. Our methods can be used to compute the exchange interactions between two donor electrons with arbitrary binding energy.Comment: 11 pages, 10 figures, RevTeX

Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions

We investigate a microscopic motor based on an externally controlled two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two-level system is in contact with a given thermal bath and its energy levels are driven with a constant rate. The time evolution of the occupation probabilities of the two states are controlled by one rate equation and represent the system's response with respect to the external driving. We give the exact solution of the rate equation for the limit cycle and discuss the emerging thermodynamics: the work done on the environment, the heat exchanged with the baths, the entropy production, the motor's efficiency, and the power output. Furthermore we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. The exact calculation of the evolution operator for the augmented process allows us to discuss in detail the probability density for the performed work during the limit cycle. In the strongly irreversible regime, the density exhibits important qualitative differences with respect to the more common Gaussian shape in the regime of weak irreversibility.Comment: 21 pages, 7 figure

Rapid, multiplexed microfluidic phage display

The development of a method for high-throughput, automated proteomic screening could impact areas ranging from fundamental molecular interactions to the discovery of novel disease markers and therapeutic targets. Surface display techniques allow for efficient handling of large molecular libraries in small volumes. In particular, phage display has emerged as a powerful technology for selecting peptides and proteins with enhanced, target-specific binding affinities. Yet, the process becomes cumbersome and time-consuming when multiple targets are involved.Here we demonstrate for the first time a microfluidic chip capable of identifying high affinity phage displayed peptides for multiple targets in just a single round and without the need for bacterial infection. The chip is shown to be able to yield well-established control consensus sequences while simultaneously identifying new sequences for clinically important targets. Indeed, the confined parameters of the device allow not only for highly controlled assay conditions but also introduce a significant time-reduction to the phage display process. We anticipate that this easily-fabricated, disposable device has the potential to impact areas ranging from fundamental studies of protein, peptide, and molecular interactions, to applications such as fully automated proteomic screening

Bures distance between two displaced thermal states

The Bures distance between two displaced thermal states and the corresponding geometric quantities (statistical metric, volume element, scalar curvature) are computed. Under nonunitary (dissipative) dynamics, the statistical distance shows the same general features previously reported in the literature by Braunstein and Milburn for two--state systems. The scalar curvature turns out to have new interesting properties when compared to the curvature associated with squeezed thermal states.Comment: 3 pages, RevTeX, no figure

Volume of the quantum mechanical state space

The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of the determinant in the general setting too. The case when the state space is endowed with a monotone metric or a pull-back metric is considered too, we give formulas to compute the volume of the state space with respect to the given Riemannian metric. We present the volume of the space of qubits with respect to various monotone metrics. It turns out that the volume of the space of qubits can be infinite too. We characterize those monotone metrics which generates infinite volume.Comment: 17 page

Ground state of two electrons on concentric spheres

We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several electronic structure models are analyzed, ranging from the mean-field approximation (restricted and unrestricted Hartree-Fock solutions) to configuration interaction expansion, leading to near-exact wave functions and energies. The M{\o}ller-Plesset energy corrections (up to third-order) and the asymptotic expansion for the large-spheres regime are also considered. We also study the position intracules derived from approximate and exact wave functions. We find evidence for the existence of a long-range Coulomb hole in the large-spheres regime, and infer that unrestricted Hartree-Fock theory over-localizes the electrons.Comment: 10 pages, 10 figure