A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles

Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We present a framework for hybrid quantum-classical algorithms which utilise quantum computers significantly smaller than the problem size. Given an arbitrarily small ratio of the quantum computer to the instance size, we achieve polynomial speedups for classical divide-and-conquer algorithms, provided that certain criteria on the time- and space-efficiency are met. We demonstrate how this approach can be used to enhance Eppstein's algorithm for the cubic Hamiltonian cycle problem, and achieve a polynomial speedup for any ratio of the number of qubits to the size of the graph.Comment: 20+2 page

PT-symmetry breaking and laser-absorber modes in optical scattering systems

Using a scattering matrix formalism, we derive the general scattering properties of optical structures that are symmetric under a combination of parity and time-reversal (PT). We demonstrate the existence of a transition beween PT-symmetric scattering eigenstates, which are norm-preserving, and symmetry-broken pairs of eigenstates exhibiting net amplification and loss. The system proposed by Longhi, which can act simultaneously as a laser and coherent perfect absorber, occurs at discrete points in the broken symmetry phase, when a pole and zero of the S-matrix coincide.Comment: 4 pages, 4 figure

Characterisation of pressure-concentration-temperature profiles for metal hydride hydrogen storage alloys with model development

Metal hydride (MH) alloys have been applied to hydrogen storage and various energy conversion systems such as refrigeration, heat pump and heat transformer. However, to facilitate and efficiently investigate efficiently a particular application, an MH alloy must firstly be characterised with a purposely built test facility to measure profiles of pressure, MH hydrogen concentration and temperature (PCT). Obtaining detailed PCT profiles or curves could be an arduous and expensive task as each isothermal hydrogen absorption or desorption line requires hundreds of measurement points. It is thus desirable to develop an accurate correlative model for the PCT profiles with limited measurements of thermophysical property data for the purpose of characterisation of each MH alloy. This correlative model or characterisation process has been developed and is described in detail in this article. The correlative PCT MH alloy profiles can cover all applicable hydrogen storage phase regions of α, α + β and β as well as the phase transition dome curve and critical point such that a PCT phase diagram for a particular MH alloy can be depicted and characterised. As an application example, the correlative model is applied to predict an MH alloy's hydrogen storage capacity and hysteresis at a specific MH temperature. It has been discovered that each of these two parameters shows comparative trends in variation with reduced temperature. Correspondingly, for each parameter, a correlative function with reduced temperature has been produced. The MH alloy characterisation process is an essential step towards a detailed dynamic MH energy system modelling, simulation and optimisation as well as experimental investigation

Chiral structures of lander molecules on Cu(100)

Supramolecular assemblies of lander molecules (C$_{90}$H$_{98}$) on Cu(100) are investigated with low-temperature scanning tunneling microscopy. The energetically most favourable conformation of the adsorbed molecule is found to exist in two mirror symmetric enantiomers or conformers. At low coverage, the molecules align in enantiomerically pure chains along the chiral directions $[01\bar{2}],[02\bar{1}],[012]$ and $[021]$. The arrangement is proposed to be mainly governed by intermolecular van-der-Waals interaction. At higher coverages, the molecular chains arrange into chiral domains, for which a structural model is presented.Comment: to appear in Nanotechnology vol. 15 (2004

Alloy selections in high-temperature metal hydride heat pump systems for industrial waste heat recovery

In an energy intensive industrial site such as a steel plant, there are plenty of medium and low temperature waste heat which could be recovered for heating purposes with advanced and feasible technologies for example metal hydride (MH) heat pumps. Compared to other heat pump systems such as those with compression and absorption cycles, the MH heat pump has some distinctive advantages including low carbon system in terms of less electricity input and environmentally friendly working mediums, compactness, and most importantly achievable heat output with relatively high temperature. However, the applicable alloys for the high-temperature MH heat pump systems are critical and need to be purposely selected. Accordingly, in this paper, a comprehensive procedure to select alloys for the high-temperature MH heat pump systems is explained based on the operating temperatures, system efficiencies and thermodynamic equilibriums. From the database of literatures, totally 82 alloys are potentially used for this special application of which 1560 alloy pairs are formed and each pair consists of one high-temperature alloy and another low-temperature alloy. Subsequently, a number of applicable alloys are selected for each designed temperature of heat pump output and one pair is ultimately finalised. The alloy can be further examined considering of its thermophysical properties, heat transfer behaviours, costs and safety issues

Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures

We analyze the optical properties of one-dimensional (1D) PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT-symmetry breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT-symmetry and of PT-symmetry breaking transitions. The uniqueness of PT-symmetry breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.Comment: 10 pages, 10 figure

Coherent Perfect Absorbers: Time-reversed Lasers

We show that an arbitrary body or aggregate can be made perfectly absorbing at discrete frequencies if a precise amount of dissipation is added under specific conditions of coherent monochromatic illumination. This effect arises from the interaction of optical absorption and wave interference, and corresponds to moving a zero of the elastic S-matrix onto the real wavevector axis. It is thus the time-reversed process of lasing at threshold. The effect is demonstrated in a simple Si slab geometry illuminated in the 500-900 nm range. Coherent perfect absorbers are novel linear optical elements, absorptive interferometers, which may be useful for controlled optical energy transfer.Comment: 4 pages, 4 figure