# All

For a native gate set which includes all single-qubit gates, we apply results

from symplectic geometry to analyze the spaces of two-qubit programs accessible

within a fixed number of gates. These techniques yield an explicit description

of this subspace as a convex polytope, presented by a family of linear

inequalities themselves accessible via a finite calculation. We completely

describe this family of inequalities in a variety of familiar example cases,

We sketch a recipe to define renormalization group transformations based on

Kadanoff-Wilson block packing using a quantum error correction code. In such a

case the RG transformations of the couplings are determined by the error matrix

of the QEC code. In order to define the RG transformation of couplings we use

Weinberg's sum rule for an error Kallen Lehmann function. We define an error

beta function that for holographic AdS codes is conjectured to be zero. For

When can quantum information be localized to each of a collection of

spacetime regions, while also excluded from another collection of regions? We

answer this question by defining and analyzing the localize-exclude task, in

which a state must be localized to a collection of authorized regions while

also being excluded from a set of unauthorized regions. This task is a

spacetime analogue of quantum secret sharing, with authorized and unauthorized

regions replacing authorized and unauthorized sets of parties. Our analysis

We discuss how, in appropriately designed configurations, solenoids carrying

a semifluxon can be used as topological energy barriers for charged quantum

systems. We interpret this phenomenon as a consequence of the fact that such

solenoids induce nodal lines in the wave function describing the charge, which

on itself is a consequence of the Aharonov-Bohm effect. Moreover, we present a

thought experiment with a cavity where just two solenoids are sufficient to

create topological bound states.

Being comparable in quantum systems makes it possible for spaces with varying

dimensions to attribute each other using special conversions can attribute

schrodinger equation with like-hydrogen atom potential in defined dimensions to

a schrodinger equation with other certified dimensions with isotropic

oscillator potential. Applying special transformation provides a relationship

between different dimensions of two quantum systems. The result of the

quantized isotropic oscillator can be generalized to like-hydrogen atom problem

In this work we show how constructing Wigner functions of heterogeneous

quantum systems leads to new capability in the visualization of quantum states

of atoms and molecules. This method allows us to display quantum correlations

(entanglement) between spin and spatial degrees of freedom (spin-orbit

coupling) and between spin degrees of freedom, as well as more complex

combinations of spin and spatial entanglement for the first time. This is

important as there is growing recognition that such properties affect the

Quantum simulations of Fermi-Hubbard models have been attracting considerable

efforts in the optical lattice research, with the ultracold anti-ferromagnetic

atomic phase reached at half filling in recent years. An unresolved issue is to

dope the system while maintaining the low thermal entropy. Here we propose to

achieve the low temperature phase of the doped Fermi-Hubbard model using

incommensurate optical lattices through adiabatic quantum evolution. In this

In this paper, we have proposed and demonstrated a new method of atomic

population transfer. Transition dynamic of a two-level system is studied in a

full quantum description of the Jaynes-Cummings model. Solving the

time-dependent Schr\"odinger equation, we have investigated the transition

probabilities numerically and analytically by using a sudden boost of the laser

frequency. The results show that complete population transfer can be achieved

by adjusting the time of the frequency boost.

In this paper we consider to use the quantum stabilizer codes as secret

sharing schemes for classical secrets. We give necessary and sufficient

conditions for qualified and forbidden sets in terms of quantum stabilizers.

Then we give a Gilbert-Varshamove-type sufficient condition for existence of

secret sharing schemes with given parameters, and by using that sufficient

condition, we show that roughly 19% of participants can be made forbidden

independently of the size of classical secret, in particular when an $n$-bit

Quantum computing technologies promise to revolutionize calculations in many

areas of physics, chemistry, and data science. Their power is expected to be

especially pronounced for problems where direct analogs of a quantum system

under study can be encoded coherently within a quantum computer. A first step

toward harnessing this power is to express the building blocks of known

physical systems within the language of quantum gates and circuits. In this

paper, we present a quantum calculation of an archetypal quantum system: