We present a $2\mathrm{-dimensional}$ quantum walker on curved discrete

surfaces with dynamical geometry. This walker extends the quantum walker over

the fixed triangular lattice introduced in

\cite{quantum_walk_triangular_lattice}. We write the discrete equations of the

walker on an arbitrary triangulation, whose flat spacetime limit recovers the

Dirac equation in (2+1)-dimension. The geometry is changed through Pachner

moves, allowing the surface to transform into any topologically equivalent

# All

Universal properties of a critical quantum spin chain are encoded in the

underlying conformal field theory (CFT). This underlying CFT is fully

characterized by its conformal data. We propose a method to extract the

conformal data from a critical quantum spin chain with both periodic and

anti-periodic boundary conditions (PBC and APBC) based on low-energy

eigenstates, generalizing previous work on spin chains with only PBC. First,

scaling dimensions and conformal spins are extracted from the energies and

We introduce quantum circuits in two and three spatial dimensions which are

classically simulable, despite producing a high degree of operator

entanglement. We provide a partial characterization of these "automaton"

quantum circuits, and use them to study operator growth, information spreading,

and local charge relaxation in quantum dynamics with subsystem symmetries,

which we define as overlapping symmetries that act on lower-dimensional

submanifolds. With these symmetries, we discover the anomalous subdiffusion of

A powerful tool for studying the behavior of classical field theories is

Derrick's theorem: one may rule out the existence of localized inhomogeneous

stable field configurations (solitons) by inspecting the Hamiltonian and making

scaling arguments. For example, the theorem can be used to rule out compact

domain wall configurations for the classic $\phi^4$ theory in $3+1$ dimensions

and greater. We argue no such obstruction to constructing solitons exists in

One of the stunning consequences of quantum correlations in thermodynamics is

the reversal of the arrow of time, recently shown experimentally in [K.

Micadei, et al., Nat. Commun. 10:2456 (2019)], and manifesting itself by a

reversal of the heat flow (from the cold system to the hot one). Here, we show

that contrary to what could have been expected, heat flow reversal can happen

without reversal of the arrow of time. Moreover, contrasting with previous

We investigate the computational hardness of spin-glass instances on a square

lattice, generated via a recently introduced tunable and scalable approach for

planting solutions. The method relies on partitioning the problem graph into

edge-disjoint subgraphs, and planting frustrated, elementary subproblems that

share a common local ground state, which guarantees that the ground state of

the entire problem is known a priori. Using population annealing Monte Carlo,

We investigate the patterns in distributions of localizable entanglement over

a pair of qubits for random multi-qubit pure states. We observe that the mean

of localizable entanglement increases gradually with increasing the number of

qubits of random pure states while the standard deviation of the distribution

decreases. The effects on the distributions, when the random pure multi-qubit

states are subjected to local as well as global noisy channels, are also

investigated. Unlike the noiseless scenario, the average value of the

Number state filtered coherent states are a class of nonclassical states

obtained by removing one or more number states from a coherent state. Phase

sensitivity of an interferometer is enhanced if these nonclassical states are

used as input states. The optimal phase sensitivity, which is related to the

quantum Cramer-Rao bound (QCRB) for the input state, improves beyond the

standard quantum limit. It is argued that removal of more than one suitable

number state leads to better phase sensitivity. As an important limiting case

The so-called stellar formalism allows to represent the non-Gaussian

properties of single-mode quantum states by the distribution of the zeros of

their Husimi Q-function in phase-space. We use this representation in order to

derive an infinite hierarchy of single-mode states based on the number of zeros

of the Husimi Q-function, the stellar hierarchy. We give an operational

characterisation of the states in this hierarchy with the minimal number of

single-photon additions needed to engineer them, and derive equivalence classes

The L\"uders rule provides a way to define a quantum channel given a quantum

measurement. Using this construction, we establish an if-and-only-if condition

for the existence of a $d$-dimensional Symmetric Informationally Complete

quantum measurement (a SIC) in terms of a particular depolarizing channel.

Moreover, the channel in question satisfies two entropic optimality criteria.