A simple encoding of a quantum circuit amplitude as a matrix permanent

A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This opens up some interesting classical monte-carlo algorithms for approximating quantum circuits.Comment: 6 figure

The Kaon B-parameter from Quenched Domain-Wall QCD

We present numerical results for the kaon B-parameter, B_K, determined in the quenched approximation of lattice QCD. Our simulations are performed using domain-wall fermions and the renormalization group improved, DBW2 gauge action which combine to give quarks with good chiral symmetry at finite lattice spacing. Operators are renormalized non-perturbatively using the RI/MOM scheme. We study scaling by performing the simulation on two different lattices with a^{-1} = 1.982(30) and 2.914(54) GeV. We combine this quenched scaling study with an earlier calculation of B_K using two flavors of dynamical, domain-wall quarks at a single lattice spacing to obtain B_K(MS,NDR,mu=2GeV)=0.563(21)(39)(30), were the first error is statistical, the second systematic (without quenching errors) and the third estimates the error due to quenching.Comment: 77 pages, 44 figures, to be published in Phys. Rev.

Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86 (22), 5188-5191 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, arXiv:quant-ph/0402005, accepted to appear in Phys. Rev. Lett.]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which non-deterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space.Comment: 31 pages, 54 figure

Proton decay matrix elements with domain-wall fermions

Hadronic matrix elements of operators relevant to nucleon decay in grand unified theories are calculated numerically using lattice QCD. In this context, the domain-wall fermion formulation, combined with non-perturbative renormalization, is used for the first time. These techniques bring reduction of a large fraction of the systematic error from the finite lattice spacing. Our main effort is devoted to a calculation performed in the quenched approximation, where the direct calculation of the nucleon to pseudoscalar matrix elements, as well as the indirect estimate of them from the nucleon to vacuum matrix elements, are performed. First results, using two flavors of dynamical domain-wall quarks for the nucleon to vacuum matrix elements are also presented to address the systematic error of quenching, which appears to be small compared to the other errors. Our results suggest that the representative value for the low energy constants from the nucleon to vacuum matrix elements are given as |alpha| simeq |beta| simeq 0.01 GeV^3. For a more reliable estimate of the physical low energy matrix elements, it is better to use the relevant form factors calculated in the direct method. The direct method tends to give smaller value of the form factors, compared to the indirect one, thus enhancing the proton life-time; indeed for the pi^0 final state the difference between the two methods is quite appreciable.Comment: 56 pages, 17 figures, a comment and two references added in the introduction, typo corrected in Eq.1

Hysteresis of spectral evolution in the soft state of black-hole binary LMC X-3

We report the discovery of hysteresis between the x-ray spectrum and luminosity of black-hole binary LMC X-3. Our observations, with the Proportional Counter Array on the Rossi X-ray Timing Explorer, took place entirely within the soft spectral state, dominated by a spectral component that was fitted well with a multicolor disk blackbody. A power-law component was seen only during times when the luminosity of the disk blackbody was declining. The x-ray luminosity at these times was comparable to that seen in transient systems (x-ray novae) when they return to the hard state at the end of an outburst. Our observations may represent partial transitions to the hard state; complete transitions have been seen in this system by Wilms et al. (2001). If they are related to the soft-to-hard transition in transients, then they demonstrate that hysteresis effects can appear without a full state transition. We discuss these observations in the context of earlier observations of hysteresis within the hard state of binaries 1E 1740.7-2942 and GRS 1758-258 and in relation to published explanations of hysteresis in transients.Comment: 14 pages, 6 figures, accepted by The Astrophysical Journa

Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging

A size-dependent strain relaxation and its effects on the optical properties of InGaN/GaN multiple quantum wells (QWs) in micro-pillars have been investigated through a combination of high spatial resolution cathodoluminescence (CL) hyperspectral imaging and numerical modeling. The pillars have diameters (d) ranging from 2 to 150 μm and were fabricated from a III-nitride light-emitting diode (LED) structure optimized for yellow-green emission at ∼560 nm. The CL mapping enables us to investigate strain relaxation in these pillars on a sub-micron scale and to confirm for the first time that a narrow (≤2 μm) edge blue-shift occurs even for the large InGaN/GaN pillars (d > 10 μm). The observed maximum blue-shift at the pillar edge exceeds 7 nm with respect to the pillar centre for the pillars with diameters in the 2–16 μm range. For the smallest pillar (d = 2 μm), the total blue-shift at the edge is 17.5 nm including an 8.2 nm “global” blue-shift at the pillar centre in comparison with the unetched wafer. By using a finite element method with a boundary condition taking account of a strained GaN buffer layer which was neglected in previous simulation works, the strain distribution in the QWs of these pillars was simulated as a function of pillar diameter. The blue-shift in the QWs emission wavelength was then calculated from the strain-dependent changes in piezoelectric field, and the consequent modification of transition energy in the QWs. The simulation and experimental results agree well, confirming the necessity for considering the strained buffer layer in the strain simulation. These results provide not only significant insights into the mechanism of strain relaxation in these micro-pillars but also practical guidance for design of micro/nano LEDs

Multi-qubit compensation sequences

The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.Comment: 9 pages, 5 figures; corrected reference formattin

Assessment of Flood Losses with Household Responses: Agent-Based Simulation in an Urban Catchment Area

Densely populated coastal urban areas are often exposed to multiple hazards, in particular floods and storms. Flood defenses and other engineering measures contribute to the mitigation of flood hazards, but a holistic approach to flood risk management should consider other interventions from the human side, including warning information, adaptive behavior, people/property evacuation, and the multilateral relief in local communities. There are few simulation approaches to consider these factors, and these typically focus on collective human actions. This paper presents an agent-based model that simulates flood response preferences and actions taken within individual households to reduce flood losses. The model implements a human response framework in w hich agents assess different flood scenarios according to warning information and decide whether and how much they invest in response measures to reduce potential inun- dation damages. A case study has been carried out in the Ng Tung River basin, an urbanized watershed in northern Hong Kong. Adopting a digital elevation model (DEM) as the modeling environment and a building map of household locations in the case area, the model considers the characteristics of households and the flood response behavior of their occupants. We found that property value, warning information, and storm conditions all influence household losses, with downstream and high density areas being particularly vulnerable. Results further indicate (i) that a flood warning system, which provides timely, accurate, and broad coverage rainstorm warning, can reduce flood losses by 30–40%; and (ii) to reduce losses, it is more effective and cheaper to invest early in response measures than late actions. This dynamic agent-based modeling approach is an innovative attempt to quantify and model the role of human responses in flood loss assessments. The model is demonstrated being useful for analyzing household scale flood losses and responses and it has the potential to contribute to flood emergency planning resource allocation in pluvial flood incidents

Fluctuation limits of strongly degenerate branching systems

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures.Comment: 15 page