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The adiabatic theorem of quantum mechanics states that the error between an

instantaneous eigenstate of a time-dependent Hamiltonian and the state given by

quantum evolution of duration $\tau$ is upper bounded by $C/\tau$ for some

positive constant $C$. It has been known for decades that this error can be

reduced to $C_{k}/\tau^{k+1}$ if the Hamiltonian has vanishing derivatives up

to order $k$ at the beginning and end of the evolution. Here we extend this

We present a hybrid quantum-classical algorithm for the time evolution of

out-of-equilibrium thermal states. The method depends upon classically

computing a sparse approximation to the density matrix, and then time-evolving

each matrix element via the quantum computer. For this exploratory study, we

investigate the time-dependent Heisenberg model with five spins on the Rigetti

Forest quantum virtual machine and a one spin system on the Rigetti 8Q-Agave

quantum processor.

For a discrimination problem $\Phi_\eta$ consisting of $N$ linearly

independent pure quantum states $\Phi=\{|\phi_i\rangle\}$ and the corresponding

occurrence probabilities $\eta=\{\eta_i\}$ we associate, up to a permutation

over the probabilities $\{\eta_i\}$, a unique pair of density matrices

$\boldsymbol{\rho_{_{T}}}$ and $\boldsymbol{\eta_{{p}}}$ defined on the

$N$-dimensional Hilbert space $\mathcal{H}_N$. The first one,

$\boldsymbol{\rho_{_{T}}}$, provides a representation of a generic full-rank

We investigate an explicitly time-dependent quantum system driven by a

secant-pulse external field. By solving the Schr\"odinger equation exactly, we

elucidate exotic properties of the system with respect to its dynamical

evolution: on the one hand, the system is shown to be innately nonadiabatic

which prohibits an adiabatic approximation for its dynamics, on the other hand,

the loop evolution of the model can induce a geometric phase which, analogous

to the Berry phase in the adiabatic cyclic evolution, associates to a solid

Information transfer rates in optical communications may be dramatically

increased by making use of spatially non-Gaussian states of light. Here we

demonstrate the ability of deep neural networks to classify

numerically-generated, noisy Laguerre-Gauss modes of up to 100 quanta of

orbital angular momentum with near-unity fidelity. The scheme relies only on

the intensity profile of the detected modes, allowing for considerable

simplification of current measurement schemes required to sort the states

Quantum state preparation in high-dimensional systems is an essential

requirement for many quantum-technology applications. The engineering of an

arbitrary quantum state is, however, typically strongly dependent on the

experimental platform chosen for implementation, and a general framework is

still missing. Here we show that coined quantum walks on a line, which

represent a framework general enough to encompass a variety of different

platforms, can be used for quantum state engineering of arbitrary

We study the effect of disorder on work exchange associated to quantum

Hamiltonian processes by considering an Ising spin chain in which the strength

of coupling between spins are randomly drawn from either Normal or Gamma

distributions. The chain is subjected to a quench of the external transverse

field which induces this exchange of work. In particular, we study the

irreversible work incurred by a quench as a function of the initial

temperature, field strength and magnitude of the disorder. While presence of

A defining feature of topologically ordered states of matter is the existence

of locally indistinguishable states on spaces with non-trivial topology. These

degenerate states form a representation of the mapping class group (MCG) of the

space, which is generated by braids of defects or anyons, and by Dehn twists

along non-contractible cycles. These operations can be viewed as fault-tolerant

logical gates in the context of topological quantum error correcting codes.

The discrete-time quantum walk dynamics can be generated by a time-dependent

Hamiltonian, repeatedly switching between the coin and the shift generators. We

change the model and consider the case where the Hamiltonian is

time-independent, including both the coin and the shift terms in all times. The

eigenvalues and the related Bloch vectors for the time-independent Hamiltonian

are then compared with the corresponding quantities for the effective

Hamiltonian generating the quantum walk dynamics. Restricted to the

Magnetic effects on free electron systems have been studied extensively in

the context of spin-to-orbital angular momentum conversion. Starting from the

Dirac equation, we derive a fully relativistic expression for the energy of

free electrons in the presence of a spatiotemporally constant, weak

electromagnetic field. The expectation value of the maximum energy shift, which

is completely independent of the electron spin-polarization coefficients, is

computed perturbatively to first order. This effect is orders of magnitude