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In this paper we show that all nodes can be found optimally for almost all

random Erd\H{o}s-R\'enyi ${\mathcal G}(n,p)$ graphs using continuous-time

quantum spatial search procedure. This works for both adjacency and Laplacian

matrices, though under different conditions. The first one requires

$p=\omega(\log^8(n)/n)$, while the seconds requires $p\geq(1+\varepsilon)\log

(n)/n$, where $\varepsilon>0$. The proof was made by analyzing the convergence

of eigenvectors corresponding to outlying eigenvalues in the $\|\cdot\|_\infty

We obtain coincidence rates for passive optical interferometry by exploiting

the permutational symmetries of partially distinguishable input photons, and

our approach elucidates qualitative features of multi-photon coincidence

landscapes. We treat the interferometer input as a product state of any number

of photons in each input mode with photons distinguished by their arrival time.

Detectors at the output of the interferometer count photons from each output

We recently introduced a method to approximate functions of Hermitian Matrix

Product Operators or Tensor Trains that are of the form $\mathsf{Tr} f(A)$.

Functions of this type occur in several applications, most notably in quantum

physics. In this work we aim at extending the theoretical understanding of our

method by showing several properties of our algorithm that can be used to

detect and correct errors in its results. Most importantly, we show that there

In this technical paper we introduce the Tensor Network Theory (TNT) library

-- an open-source software project aimed at providing a platform for rapidly

developing robust, easy to use and highly optimised code for TNT calculations.

The objectives of this paper are (i) to give an overview of the structure of

TNT library, and (ii) to help scientists decide whether to use the TNT library

in their research. We show how to employ the TNT routines by giving examples of

- Read more about The Tensor Network Theory. (arXiv:1610.02244v2 [quant-ph] UPDATED)
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We analytically evaluate the entanglement spectra of the superconductivity

states in graphene, primarily focusing on the s-wave and chiral $

d_{x^{2}-y^{2}}+id_{xy} $ superconductivity states. We demonstrate that the

topology of the entanglement Hamiltonian can differ from that of the subsystem

Hamiltonian. In particular, the topological properties of the entanglement

Hamiltonian of the chiral $ d_{x^{2}-y^{2}}+id_{xy} $ superconductivity state

obtained by tracing out one spin direction clearly differ from those of the

The simulation of lattice gauge theories with tensor network (TN) methods is

becoming increasingly fruitful. The vision is that such methods will,

eventually, be used to simulate theories in $(3+1)$ dimensions in regimes

difficult for other methods. So far, however, TN methods have mostly simulated

lattice gauge theories in $(1+1)$ dimensions. The aim of this paper is to

explore the simulation of quantum electrodynamics (QED) on infinite lattices

with TNs, i.e., fermionic matter fields coupled to a $U(1)$ gauge field,

By applying invariant-based inverse engineering in the small-oscillations

regime, we design the time dependence of the control parameters of an overhead

crane (trolley displacement and rope length), to transport a load between two

positions at different heights with minimal final energy excitation for a

microcanonical ensemble of initial conditions. The analogies between ion

transport in multisegmented traps or neutral atom transport in moving optical

Nonlinear modifications of quantum mechanics have a troubled history. They

were initially studied for many promising reasons: resolving the measurement

problem, testing the limits of standard quantum mechanics, and reconciling it

with gravity. Two results substantially undermined the credibility of

non-linear theories. Some have been experimentally refuted, and more

importantly, all deterministic non-linear theories can be used for superluminal

communication. However, these results are unconvincing because they overlook

A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from

a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic

equation also yields the Klein-Gordon wave equation with a covariant

(space-time dependent) mass. This mass is quantized and is given by

$m_{*n}^2=m_\omega^2\left(n_r^2-1-\beta\,\left(n+1\right)\right)\,,$ where

$m_\omega=\frac{\hbar\omega}{c^2}\,,$ $\beta=\frac{2mc^2}{\hbar\,\omega}\, $,

$n$, is the oscillator index, and $n_r$ is the refractive index in which the

- Read more about On relativistic harmonic oscillator. (arXiv:1709.06865v1 [physics.gen-ph])
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We improve the number of T gates needed to perform an n-bit adder from 8n +

O(1) to 4n + O(1). We do so via a "temporary logical-AND" construction, which

uses four T gates to store the logical-AND of two qubits into an ancilla and

zero T gates to later erase the ancilla. Temporary logical-ANDs are a generally

useful tool when optimizing T-counts. They can be applied to integer

arithmetic, modular arithmetic, rotation synthesis, the quantum Fourier

transform, Shor's algorithm, Grover oracles, and many other circuits. Because T

- Read more about Halving the cost of quantum addition. (arXiv:1709.06648v1 [quant-ph])
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