A comparative study of iterative Chebyshev and Lanczos implementations of the boundary inhomogeneity method for quantum scattering

We have recently developed a scaleable Artificial Boundary Inhomogeneity (ABI) method [Chem. Phys. Lett.366, 390–397 (2002)] based on the utilization of the Lanczos algorithm, and in this work explore an alternative iterative implementation based on the Chebyshev algorithm. Detailed comparisons between the two iterative methods have been made in terms of efficiency as well as convergence behavior. The Lanczos subspace ABI method was also further improved by the use of a simpler three-term backward recursion algorithm to solve the subspace linear system. The two different iterative methods are tested on the model collinear H+H2 reactive state-to-state scattering.

Scaling of decoherence effects in quantum computers

The scaling of decoherence rates with qubit number N is studied for a simple model of a quantum computer in the situation where N is large. The two state qubits are localized around well-separated positions via trapping potentials and vibrational centre of mass motion of the qubits occurs. Coherent one and two qubit gating processes are controlled by external classical fields and facilitated by a cavity mode ancilla. Decoherence due to qubit coupling to a bath of spontaneous modes, cavity decay modes and to the vibrational modes is treated. A non-Markovian treatment of the short time behaviour of the fidelity is presented, and expressions for the characteristic decoherence time scales obtained for the case where the qubit/cavity mode ancilla is in a pure state and the baths are in thermal states. Specific results are given for the case where the cavity mode is in the vacuum state and gating processes are absent and the qubits are in (a) the Hadamard state (b) the GHZ state.

Iterative quantum computations of HO2 bound states and resonances for J=4 and 5

Bound and resonance states of HO2 have been calculated by both the complex Lanczos homogeneous filter diagonalisation (LHFD) method(1,2) and the real Chebyshev filter diagonalisation method(3,4) for non-zero total angular momentum J = 4 and 5. For bound states, the agreement between the two methods is quite satisfactory; for resonances while the energies are in good agreement, the widths are only in general agreement. The relative performances of the two iterative FD methods have also been discussed in terms of efficiency as well as convergence behaviour for such a computationally challenging problem. A helicity quantum number Ohm assignment (within the helicity conserving approximation) is performed and the results indicate that Coriolis coupling becomes more important as J increases and the helicity conserving approximation is not a good one for the HO2 resonance states.

Coherent-state linear optical quantum computing gates using simplified diagonal superposition resource states

In this paper we explore the possibility of fundamental tests for coherent-state optical quantum computing gates [ T. C. Ralph et al. Phys. Rev. A 68 042319 (2003)] using sophisticated but not unrealistic quantum states. The major resource required in these gates is a state diagonal to the basis states. We use the recent observation that a squeezed single-photon state [S(r)∣1⟩] approximates well an odd superposition of coherent states (∣α⟩−∣−α⟩) to address the diagonal resource problem. The approximation only holds for relatively small α, and hence these gates cannot be used in a scalable scheme. We explore the effects on fidelities and probabilities in teleportation and a rotated Hadamard gate.

Quantum phase-space simulations of fermions and bosons

We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations of the dynamics and thermal equilibrium states of many-body quantum systems from first principles. As an example, we numerically calculate finite-temperature correlation functions for the Fermi Hubbard model, with no evidence of the Fermi sign problem. (c) 2005 Elsevier B.V. All rights reserved.

Hydrothermal Synthesis of Layered Double Hydroxides (LDHs) from Mixed MgO and Al2O3: LDH Formation Mechanism

The formation of MgA1 layered double hydroxide (LDH) from physically mixed MgO and Al2O3 oxides upon hydrothermal treatment has been extensively investigated, and a formation mechanism has been proposed. We observed that the formation of LDH from the oxide mixture occurs upon heating at 110 degreesC. In general, LDH is the major component while the minor phases are mainly determined by the initial pH of the oxide suspension as well as the MgO/Al2O3 ratio. The neutrality in the initial suspension results in a minor Mg(OH)(2) as the impure phase, while the alkalinity in the suspension keeps some MgO unreacted throughout the whole hydrothermal treatment. We suggest that MgO and Al2O3 be hydrated into Mg(OH)(2) and Al(OH)(3), respectively, in the initial stage for all samples. We further Suggest that in the neutral condition Mg(OH)2 be quickly dissociated to Mg2+ and OH- which then deposit on the surface of Al(OH)(3)/Al2O3 to form a M-Al pre-LDH material. Al(OH)(4)(-), ionized from Al(OH)(3) in the basic solution, deposits on the surface of Mg(OH)(2)/MgO to result in a similar MgAl pre-LDH material. Such a pre-LDH material is then well crystallized upon continuous heating via the diffusion of metal ions in the solid lattice. Such a dissociation-deposition-diffusion mechanism via two pathways has been supported by the phase composition, morphological features of crystallites, and [Mg]/[Al] ratios on the crystallite surface. and presumably applied to the general formation of LDHs with various synthetic methods. Such as coprecipitation, homogeneous preparation, and reconstruction.

CDP571, a humanized monoclonal antibody to tumour necrosis factor-alpha, for steroid-dependent Crohn's disease: a randomized, double-blind, placebo-controlled trial

Background More than 50% of patients with Crohn's disease become either steroid resistant or dependent. Accordingly, development of new treatments for steroid-dependent Crohn's disease is a research priority. Aim To evaluate CDP571, a humanized antibody to tumour necrosis factor-α, for the treatment of steroid-dependent Crohn's disease. Methods Patients with steroid-dependent Crohn's disease (n = 271) were enrolled in a 36-week, double-blind, placebo-controlled trial. Steroid dependence was defined as use of prednisolone or prednisone (15–40 mg/day) or budesonide (9 mg/day) for ≥8 weeks, a previous failed attempt to decrease or discontinue steroids within 8 weeks of screening, and a Crohn's Disease Activity Index score of ≤150 points. Patients were randomized to receive intravenous CDP571 10 mg/kg or placebo 8-weekly through to week 32. Steroids were then tapered using a defined schedule. The primary efficacy endpoint was the percentage of patients with steroid sparing, defined as discontinuation of steroid therapy without a disease flare (Crohn's Disease Activity Index score ≥220 points) at week 36. Results Steroid sparing occurred in 53 of 181 (29.3%) CDP571 patients and 33 of 90 (36.7%) placebo patients (P = 0.24). Adverse events occurred at similar frequencies in both treatment groups. Conclusions CDP571 was ineffective for sparing steroids in patients with steroid-dependent Crohn's disease. CDP571 was well tolerated.

Conditional quantum-state engineering using ancillary squeezed-vacuum states

We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection, and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of n

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

Modelling photo-detectors in quantum optics

Photo-detection plays a fundamental role in experimental quantum optics and is of particular importance in the emerging field of linear optics quantum computing. Present theoretical treatment of photo-detectors is highly idealized and fails to consider many important physical effects. We present a physically motivated model for photo-detectors which accommodates for the effects of finite resolution, bandwidth and efficiency, as well as dark counts and dead-time. We apply our model to two simple well-known applications, which illustrates the significance of these characteristics.

Quantum gate based on Stark tunable nanocrystal interactions with ultrahigh-Q/V field modes in fused silica microcavities

We investigate the use of nanocrystal quantum dots as a quantum bus element for preparing various quantum resources for use in photonic quantum technologies. Using the Stark-tuning property of nanocrystal quantum dots as well as the biexciton transition, we demonstrate a photonic controlled-NOT (CNOT) interaction between two logical photonic qubits comprising two cavity field modes each. We find the CNOT interaction to be a robust generator of photonic Bell states, even with relatively large biexciton losses. These results are discussed in light of the current state of the art of both microcavity fabrication and recent advances in nanocrystal quantum dot technology. Overall, we find that such a scheme should be feasible in the near future with appropriate refinements to both nanocrystal fabrication technology and microcavity design. Such a gate could serve as an active element in photonic-based quantum technologies.

Quantum optical systems for the implementation of quantum information processing

We review the field of quantum optical information from elementary considerations to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the minimum needed to understand the key theoretical and experimental results.