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

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