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

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

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