We discuss the relations between restricted Boltzmann machine (RBM) states

and the matrix product states (MPS) for the ground states of 1D translational

invariant stabilizer codes. A generic translational invariant and finitely

connected RBM state can be expressed as an MPS, and the matrices of the

resulting MPS are of rank 1. We dub such an MPS as an RBM-MPS. This provides a

necessary condition for exactly realizing a quantum state as an RBM state, if

the quantum state can be written as an MPS. For generic 1D stabilizer codes

# All

In the tensor network representation, a deformed $Z_{2}$ topological ground

state wave function is proposed and its norm can be exactly mapped to the

two-dimensional solvable Ashkin-Teller (AT) model. Then the topological (toric

code) phase with anyonic excitations corresponds to the partial order phase of

the AT model, and possible topological phase transitions are precisely

determined. With the electric-magnetic self-duality, a novel gapless Coulomb

We study the relaxation dynamics of a one-dimensional quantum spin-1/2 chain

obtained by joining two semi-infinite halves supporting ballistic transport,

the XX model and the XXZ model. We initialize the system in a pure state with

either a strong energy or magnetization imbalance and employ a matrix-product

state ansatz of the wavefunction to numerically assess the long-time dynamics.

We show that the relaxation process takes place inside a light cone, as in

Quantum computing is a growing field at the intersection of physics and

computer science. This module introduces three of the key principles that

govern how quantum computers work: superposition, quantum measurement, and

entanglement. The goal of this module is to bridge the gap between popular

science articles and advanced undergraduate texts by making some of the more

technical aspects accessible to motivated high school students. Problem sets

and simulation based labs of various levels are included to reinforce the

Using dyadic representations elaborated from vectors of Jones, and

calculating relations of anti-commutation of these tensorial forms, we obtain

in shape explicit the Pauli spin matrices.

We introduce a binary temperature classifier quantum model operates in a

thermal environment. Proper measurement and sensing of temperature are of

central importance to the realization of nanoscale quantum devices. More

significantly, minimal classifiers may constitute the basic units for the

physical quantum neural networks. In the present study, first, the mathematical

model was introduced through a two-level quantum system weakly coupled to the

thermal reservoirs and demonstrate that the model faithfully classifies the

Quantum error-correcting codes are used to protect quantum information from

decoherence. A raw state is mapped, by an encoding circuit, to a codeword so

that the most likely quantum errors from a noisy quantum channel can be removed

after a decoding process.

Compiling quantum circuits lends itself to an elegant formulation in the

language of rewriting systems on non commutative polynomial algebras $\mathbb

Q\langle X\rangle$. The alphabet $X$ is the set of the allowed hardware 2-qubit

gates. The set of gates that we wish to implement from $X$ are elements of a

free monoid $X^*$ (obtained by concatenating the letters of $X$). In this

setting, compiling an idealized gate is equivalent to computing its unique

normal form with respect to the rewriting system $\mathcal R\subset \mathbb

Can normal science-in the Kuhnian sense-add something substantial to the

discussion about the measurement problem? Does an extended Wigner's-friend

Gedankenexperiment illustrate new issues? Or a new quality of known issues? Are

we led to new interpretations, new perspectives, or do we iterate the

previously known? The recent debate does, as we argue, neither constitute a

turning point in the discussion about the measurement problem nor fundamentally

challenge the legitimacy of quantum mechanics. Instead, the measurement problem

Models are developed to estimate properties of relic cosmic perturbations

with "spooky" nonlocal correlations on the inflationary horizon, analogous to

those previously posited for information on black hole event horizons. Scalar

curvature perturbations are estimated to emerge with a dimensionless power

spectral density $\Delta_S^2\approx H t_P$, the product of inflationary

expansion rate $H$ with Planck time $t_P$, larger than standard inflaton

fluctuations. Current measurements of the spectrum are used to derive