We study quantum period finding algorithms such as Simon, Shor, and

Eker{\aa}-H{\aa}stad. For a periodic function $f$ these algorithms produce --

via some quantum embedding of $f$ -- a quantum superposition $\sum_x \vert

x\rangle\vert f(x)\rangle$, which requires a certain amount of output bits that

represent $\vert f(x)\rangle$. We show that we can lower this amount to a

single output qubit by hashing $f$ down to a single bit. Namely, we replace the

embedding of $f$ in quantum period finding circuits by several embeddings of

# All

We study the dynamics of coupled quantum spins one-half on a lattice with

nearest-neighbour "XY" (flip-flop) interactions, driven by external fields and

subject to dissipation. The meanfield limit of the model manifests bistable

parameter regions of two coexisting steady states with different

magnetizations. We introduce an efficient scheme accounting for the corrections

to meanfield by correlations at leading order, and benchmark this scheme using

high-precision numerics based on matrix-product-operators in one- and

In 1935, in a paper entitled "Can quantum-mechanical description of reality

be considered complete?", Einstein, Podolsky, and Rosen (EPR) formulated an

apparent paradox of quantum theory. They considered two quantum systems that

were initially allowed to interact, and were then later separated. A

measurement of a physical observable performed on one system then had to have

an immediate effect on the conjugate observable in the other system - even if

the systems were causally disconnected! The authors viewed this as a clear

The scalar product of two vectors with $K$ real components can be computed

using two quantum channels, that is, information transmission lines in the form

of spin-1/2 XX chains. Each channel has its own $K$-qubit sender and both

channels share a single two-qubit receiver. The $K$ elements of each vector are

encoded in the pure single-excitation initial states of the senders. After time

evolution, a bi-linear combination of these elements appears in the only matrix

We study two recent conjectures for holographic complexity: the

complexity=action conjecture and the complexity=volume conjecture. In

particular, we examine the structure of the UV divergences appearing in these

quantities, and show that the coefficients can be written as local integrals of

geometric quantities in the boundary. We also consider extending these

conjectures to evaluate the complexity of the mixed state produced by reducing

the pure global state to a specific subregion of the boundary time slice. The

Probing optical excitations with nanometer resolution is important for

understanding their dynamics and interactions down to the atomic scale.

Electron microscopes currently offer the unparalleled ability of rendering

spatially-resolved electron spectra with combined meV and sub-nm resolution,

while the use of ultrafast optical pulses enables fs temporal resolution and

exposure of the electrons to ultraintense confined optical fields. Here, we

theoretically investigate fundamental aspects of the interaction of fast

In this paper, we report a numerical method for analyzing optical radiation

from a two-level atom. The proposed method can consistently consider the

optical emission and absorption process of an atom, and also the interaction

between atoms through their interaction with a radiation field. The numerical

model is based on a damping oscillator description of a dipole current, which

is a classical model of atomic transition and is implemented with a

finite-difference time-domain method. Using the method, we successfully

Summoning is a task between two parties, Alice and Bob, with distributed

networks of agents in space-time. Bob gives Alice a random quantum state, known

to him but not her, at some point. She is required to return the state at some

later point, belonging to a subset defined by communications received from Bob

at other points. Many results about summoning, including the impossibility of

unrestricted summoning tasks and the necessary conditions for specific types of

An experiment to test for relativistic frame dragging effects with quantum

interferometry is proposed. The idea that the classical trajectories of the

interferometer surround a spherical mass source whose angular momentum is

perpendicular to the plane containing these trajectories. A simple analysis

allows one to find the phase shift for particles traveling in the innermost

stable circular orbit; the result can be easily generalized for more realistic

orbits. The phase difference goes like the source's angular momentum per mass

Bright squeezed vacuum (BSV) is a non-classical macroscopic state of light,

which can be generated through high-gain parametric down-conversion or

four-wave mixing. Although BSV is an important tool in quantum optics and has a

lot of applications, its theoretical description is still not complete. In

particular, the existing description in terms of Schmidt modes fails to explain

the spectral broadening observed in experiment as the mean number of photons