We analyze the dynamics of multiparticle discrete-time quantum walk on the

two-dimensional lattice, with an interaction inspired on a classical model for

gas collision, called HPP model. In this classical model, the direction of

motion changes only when the particles collide head-on, preserving momentum and

energy. In our quantum model, the dynamics is driven by the usual quantum-walk

evolution operator if the particles are on different nodes, and is driven by

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Floquet engineering or coherent time periodic driving of quantum systems has

been successfully used to synthesize Hamiltonians with novel properties. In

ultracold atomic systems, this has led to experimental realizations of

artificial gauge fields, topological band structures, and observation of

dynamical localization, to name just a few. Here we present a Floquet-based

framework to stroboscopically engineer Hamiltonians with spatial features and

periodicity below the diffraction limit of light used to create them by

History dependent discrete time quantum walks (QWs) are often studied for

their lattice traversal properties. A particular model in the literature uses

the state of a memory qubit at each site to record visits and to control the

dynamics of the walk. We generalize this model to the neighborhood-history

quantum walk (NHQW), in which the walk dynamics and the state of the memory

qubits in a neighborhood of the particle's position are interdependent. To

demonstrate it, we construct an NHQW on a one-dimensional lattice, with a

Quantum annealing is a heuristic algorithm for solving combinatorial

optimization problems, and D-Wave Systems Inc. has developed hardware for

implementing this algorithm. The current version of the D-Wave quantum annealer

can solve unconstrained binary optimization problems with a limited number of

binary variables, although cost functions of many practical problems are

defined by a large number of integer variables. To solve these problems with

the quantum annealer, the integer variables are generally binarized with

We propose and discuss a method to engineer stroboscopically arbitrary

one-dimensional optical potentials with subwavelength resolution. Our approach

is based on subwavelength optical potential barriers for atoms in the dark

state in an optical \Lambda system, which we use as a stroboscopic drawing tool

by controlling their amplitude and position by changing the amplitude and the

phase of the control Rabi frequency in the \Lambda system. We demonstrate the

We theoretically analyze the performance of the nuclear magnetic resonance

(NMR) spectroscopy with a superconducting flux qubit (FQ). Such NMR with the FQ

is attractive because of the possibility to detect the relatively small number

of nuclear spins in a local region ($\sim\mu$m) with low temperatures ($\sim$

mK) and low magnetic fields ($\sim$ mT), in which other types of quantum

sensing schemes cannot easily access. A sample containing nuclear spins is

Squeezed states of light have received renewed attention due to their

applicability to quantum-enhanced sensing. To take full advantage of their

reduced noise properties to enhance atomic-based sensors, it is necessary to

generate narrowband near or on atomic resonance single-mode squeezed states of

light. We have previously generated bright two-mode squeezed states of light,

or twin beams, that can be tuned to resonance with the D1 line of $^{87}$Rb

with a non-degenerate four-wave mixing (FWM) process in a double-lambda

We present a novel continuous-time control strategy to exponentially

stabilize an eigenstate of a Quantum Non-Demolition (QND) measurement operator.

In open-loop, the system converges to a random eigenstate of the measurement

operator. The role of the feedback is to prepare a prescribed QND eigenstate

with unit probability. To achieve this we introduce the use of Brownian motion

to drive the unitary control actions; the feedback loop just adapts the

amplitude of this Brownian noise input as a function of the system state.

We looked into the algorithm for calculating Betti numbers presented by

Lloyd, Garnerone, and Zanardi (LGZ). We present a new algorithm in the same

spirit as LGZ with the intent of clarifying quantum algorithms for computing

Betti numbers. Our algorithm is simpler and slightly more efficient than that

presented by LGZ. We present a thorough analysis of our algorithm, pointing out

reasons that both our algorithm and that presented by LGZ do not run in

polynomial time for most inputs. However, the algorithms do run in polynomial

We derive the full linear-response theory for non-relativistic quantum

electrodynamics in the long wavelength limit, show quantum modifications of the

well-known Maxwell's equation in matter and provide a practical framework to

solve the resulting equations by using quantum-electrodynamical

density-functional theory. We highlight how the coupling between quantized

light and matter changes the usual response functions and introduces new types

of cross-correlated light-matter response functions. These cross-correlation