33,158 research outputs found
Parallelizing Quantum Circuits
We present a novel automated technique for parallelizing quantum circuits via
forward and backward translation to measurement-based quantum computing
patterns and analyze the trade off in terms of depth and space complexity. As a
result we distinguish a class of polynomial depth circuits that can be
parallelized to logarithmic depth while adding only polynomial many auxiliary
qubits. In particular, we provide for the first time a full characterization of
patterns with flow of arbitrary depth, based on the notion of influencing paths
and a simple rewriting system on the angles of the measurement. Our method
leads to insightful knowledge for constructing parallel circuits and as
applications, we demonstrate several constant and logarithmic depth circuits.
Furthermore, we prove a logarithmic separation in terms of quantum depth
between the quantum circuit model and the measurement-based model.Comment: 34 pages, 14 figures; depth complexity, measurement-based quantum
computing and parallel computin
On measuring alpha in B(t)-> rho^\pm pi^\mp
Defining a most economical parametrization of time-dependent B-> rho^\pm
pi^\mp decays, including a measurable phase alpha_{eff} which equals the weak
phase alpha in the limit of vanishing penguin amplitudes, we propose two ways
for determining alpha in this processes. We explain the limitation of one
method, assuming only that two relevant tree amplitudes factorize and that
their relative strong phase, delta_t, is negligible. The other method, based on
broken flavor SU(3), permits a determination of alpha in B^0-> rho^\pm pi^\mp
in an overconstrained system using also rate measurements of B^{0,+}-> K^* pi
and B^{0,+}->rho K. Current data are shown to restrict two ratios of penguin
and tree amplitudes, r_\pm, to a narrow range around 0.2, and to imply an upper
bound |alpha_{eff} - alpha| < 15 degrees. Assuming that delta_t is much smaller
than 90 degrees, we find alpha =(93\pm 16) degrees and (102 \pm 20) degrees
using BABAR and BELLE results for B(t)-> rho^\pm pi^mp. Avoiding this
assumption for completeness, we demonstrate the reduction of discrete
ambiguities in alpha with increased statistics, and show that SU(3) breaking
effects are effectively second order in r_\pm.Comment: 23 pages, 2 figures, data and references updated, to be published in
Phys. Rev.
Space-time autocoding
Prior treatments of space-time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval-in which case there is a nonzero “outage capacity”-or multiple fading intervals-in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In short, space-time signals are their own channel codes. We call this phenomenon space-time autocoding, and the accompanying capacity the space-time autocapacity. Let an M-transmitter antenna, N-receiver antenna Rayleigh flat fading channel be characterized by an M×N matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a T-symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of transmitter antennas be related as T=βM for some constant β. A T×M matrix-valued signal, associated with R·T bits of information for some rate R is transmitted during the T-symbol coherence interval. Then there is a positive space-time autocapacity Ca such that for all R<Ca, the block probability of error goes to zero as the pair (T, M)→∞ such that T/M=β. The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and Ca=Nlog(1+ρ) in either case, independently of β, where ρ is the expected signal-to-noise ratio (SNR) at each receiver antenna. Lower bounds on the cutoff rate derived from random unitary space-time signals suggest that the autocoding effect manifests itself for relatively small values of T and M. For example, within a single coherence interval of duration T=16, for M=7 transmitter antennas and N=4 receiver antennas, and an 18-dB expected SNR, a total of 80 bits (corresponding to rate R=5) can theoretically be transmitted with a block probability of error less than 10^-9, all without any training or knowledge of the propagation matrix
Computing the Shapley value in allocation problems: approximations and bounds, with an application to the Italian VQR research assessment program
In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money compensation to perform a fair allocation taking into account the actual contribution of all agents to the social welfare. Coalitional games provide a formal mathematical framework to model such problems, in particular the Shapley value is a solution concept widely used for assigning worths to agents in a fair way. Unfortunately, computing this value is a #P-hard problem, so that applying this good theoretical notion is often quite difficult in real-world problems.
We describe useful properties that allow us to greatly simplify the instances of allocation problems,
without affecting the Shapley value of any player. Moreover, we propose algorithms for computing lower bounds and upper bounds of the Shapley value, which in some cases provide the exact result and that can be combined with approximation algorithms.
The proposed techniques have been implemented and tested on a real-world application of allocation problems, namely, the Italian research assessment program known as VQR (Verifica della Qualità della Ricerca, or Research Quality Assessment)1. For the large university considered in the experiments, the
problem involves thousands of agents and goods (here, researchers and their research products). The
algorithms described in the paper are able to compute the Shapley value for most of those agents, and to
get a good approximation of the Shapley value for all of the
On the exciton binding energy in a quantum well
We consider a model describing the one-dimensional confinement of an exciton
in a symmetrical, rectangular quantum-well structure and derive upper and lower
bounds for the binding energy of the exciton. Based on these bounds, we
study the dependence of on the width of the confining potential with a
higher accuracy than previous reports. For an infinitely deep potential the
binding energy varies as expected from at large widths to at
small widths. For a finite potential, but without consideration of a mass
mismatch or a dielectric mismatch, we substantiate earlier results that the
binding energy approaches the value for both small and large widths,
having a characteristic peak for some intermediate size of the slab. Taking the
mismatch into account, this result will in general no longer be true. For the
specific case of a quantum-well
structure, however, and in contrast to previous findings, the peak structure is
shown to survive.Comment: 32 pages, ReVTeX, including 9 figure
Error suppression in Hamiltonian based quantum computation using energy penalties
We consider the use of quantum error detecting codes, together with energy
penalties against leaving the codespace, as a method for suppressing
environmentally induced errors in Hamiltonian based quantum computation. This
method was introduced in [1] in the context of quantum adiabatic computation,
but we consider it more generally. Specifically, we consider a computational
Hamiltonian, which has been encoded using the logical qubits of a single-qubit
error detecting code, coupled to an environment of qubits by interaction terms
that act one-locally on the system. Energy penalty terms are added that
penalize states outside of the codespace. We prove that in the limit of
infinitely large penalties, one-local errors are completely suppressed, and we
derive some bounds for the finite penalty case. Our proof technique involves
exact integration of the Schrodinger equation, making no use of master
equations or their assumptions. We perform long time numerical simulations on a
small (one logical qubit) computational system coupled to an environment and
the results suggest that the energy penalty method achieves even greater
protection than our bounds indicate.Comment: 26 pages, 7 figure
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