Related papers: Representation of the Fermionic Boundary Operator
Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since a variety of strong highly nonlinear operations are unavailable in the existing physical…
For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data, including solution values and normal derivatives, rather…
In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum…
In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
It is known that it is a very restrictive condition for a frame $\{f_k\}_{k=1}^\infty$ to have a representation $ \{T^n \varphi\}_{n=0}^\infty$ as the orbit of a bounded operator $T$ under a single generator $\varphi\in\mathcal{H}.$ In this…
We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…
A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…
We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is…
The aim of this brief note is to demonstrate that the boundary pair of a dissipative operator is determined by the unitary boundary pair of its symmetric part.
A bosonic operator of U_q(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of U_q(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
The photon creation and annihilation operators are cornerstones of the quantum description of the electromagnetic field. They signify the isomorphism of the optical Hilbert space to that of the harmonic oscillator and the bosonic nature of…
The O$(N)$ vector model in the presence of a boundary has a non-trivial fixed point in $(4-\epsilon)$ dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is…
To be able to solve operator equations numerically a discretization of those operators is necessary. In the Galerkin approach bases are used to achieve discretized versions of operators. In a more general set-up, frames can be used to…
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…
A representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. It stems from noting that the zeros in a product qubit state do not contribute to the number. They serve only as…
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with…
The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their…