Related papers: Quantum operations for Kramers-Wannier duality
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case $\kappa=t^{-1/N}$, using the intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated with…
We use superconducting qubit quantum annealing devices to determine the ground state of Ising models with algebraically decaying competing long-range interactions in the thermodynamic limit. This is enabled by a unit-cell-based optimization…
Quantum annealing aims to solve combinatorial optimization problems mapped on to Ising interactions between quantum spins. A critical factor that limits the success of a quantum annealer is its sensitivity to noise, and intensive research…
We propose the construction of equations of motion based on symmetries in quantum-mechanical systems, using Heisenberg's uncertainty principle as a minimal foundation. From canonical operators, two spaces of conjugate operators are…
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical…
We demonstrate how a one parameter family of interacting non-commuting Hamiltonians, which are physically equivalent, can be constructed in non-commutative quantum mechanics. This construction is carried out exactly (to all orders in the…
The iteration procedure of supersymmetric transformations for the two-dimensional Schroedinger operator is implemented by means of the matrix form of factorization in terms of matrix 2x2 supercharges. Two different types of iterations are…
The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interactions arise alongside bond-dependent couplings such as Kitaev ($K$) and $\Gamma$…
Kramers-Wannier dualities in lattice models are intimately connected with symmetries. We show that they can be found directly and explicitly from the symmetry transformations of the boundary states in the underlying conformal field theory.…
The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…
We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more…
We study a class of duality transformations in generalised Z(2) gauge theories and Ising models on two- and three-dimensional compact lattices. The theories are interpreted algebraically in terms of the structure constants of a…
A well-known theorem due to R. E. Curto and N. Salinas gives a necessary and sufficient condition for the unitary equivalence of commuting tuples of bounded linear operators acting on reproducing kernel Hilbert spaces. Inspired by this…
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…
Entanglement generated by Ising model has been studied for several authors in order to understand the relation between it and magnetic properties of materials, principally using one or two dimensional models for two or more particles. In…
A simple alternative scheme for implementing quantum gates with a single trapped cold two-level ion beyond the Lamb-Dicke (LD) limit is proposed. Basing on the quantum dynamics for the laser-ion interaction described by a generalized…
We generalize the gauging of $\mathbb{Z}_2$ symmetries by inserting Majorana fermions, establishing parallel duality correspondences for bosonic and fermionic lattice systems. Using this fermionic gauging, we construct fermionic analogs of…
The gate version of quantum computation exploits several quantum key resources as superposition and entanglement to reach an outstanding performance. In the way, this theory was constructed adopting certain supposed processes imitating…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…