Related papers: Loop Charges and Fragmentation in Pairwise Differe…
In complex electronic materials, coupling between electrons and the atomic lattice gives rise to remarkable phenomena, including colossal magnetoresistance and metal-insulator transitions. Charge-ordered phases are a prototypical…
We describe new spaces and maps. Our graphical map is a visual and numerical correspondence between spaces of circular electrical networks and circular planar split systems. When restricted to the planar circular electrical case, this…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial…
We develop a novel holographic framework to study dynamical phases in random quantum circuits with a global symmetry $G$. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent…
Hilbert space fragmentation is an ergodicity breaking phenomenon, in which Hamiltonian shatters into exponentially many dynamically disconnected sectors. In many fragmented systems, these sectors can be labelled by statistically localized…
Quantum low-density parity-check (qLDPC) codes have emerged as a promising approach for realizing low-overhead logical quantum memories. Recent theoretical developments have established shift automorphisms as a fundamental building block…
We attempt to extract a homological structure of two kinds of graphs by the Grover walk. The first one consists of a cycle and two semi-infinite lines and the second one is assembled by a periodic embedding of the cycles in $\mathbb{Z}$. We…
Photonic circuits, engineered to couple optical modes according to a specific map, serve as processors for classical and quantum light. The number of components typically scales with that of processed modes, thus correlating system size,…
Motivated by the co-existing charge and spin order found in strongly correlated ladder systems, we study an effective pseudospin model on a coupled two-leg ladder. A bosonisation analysis yields a rich phase diagram showing Wigner/Peierls…
We describe a charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids. Charge conservation is obtained from first principles, i.e., without the need for any post-processing or correction steps. This…
Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four…
The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract…
Parameterized quantum circuits play an essential role in the performance of many variational hybrid quantum-classical (HQC) algorithms. One challenge in implementing such algorithms is to choose an effective circuit that well represents the…
We undertake a detailed analysis of ergodicity for homogeneous discrete-time quantum walks on the integer lattice. The most significant result of our paper holds in dimension one, and gives a complete equivalence between the absolutely…
In this paper we reexamine the problem of the separation of spin and charge degrees of freedom in two dimensional strongly correlated systems. We establish a set of sufficient conditions for the occurence of spin and charge separation.…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
Deep generative models (DGMs) have recently demonstrated remarkable success in capturing complex probability distributions over graphs. Although their excellent performance is attributed to powerful and scalable deep neural networks, it is,…
We study the spectral stability of a 2D discrete Schr\"{o}dinger equation on a square lattice, in the simultaneous presence of a fractional Laplacian and $\cal{PT}$ symmetry. For that purpose, we compute the plane-wave spectrum in closed…
We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular…