Related papers: Representation of the Fermionic Boundary Operator

Based on local unitary operators acting on a n-dimensional Hilbert-space, we investigate selective and collective operator basis sets for N-particle quantum networks. Selective cluster operators are used to derive the properties of general…

Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics. Although qubit-based quantum computers can potentially tackle this…

Various universal features of relativistic rotating strings depend on the organization of allowed local operators on the worldsheet. In this paper, we study the set of Neumann boundary operators in effective string theory, which are…

In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…

In this paper we provide a novel and general way to construct the result of the action of any bosonic or fermionic operator represented in second quantized form on a state vector, without resorting to the matrix representation of operators…

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group…

Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…

We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…

We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…

We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…

Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational…

Wiring diagrams are given for a quantum algorithm processor in CMOS to compute, in parallel, all divisors of an n-bit integer. Lines required in a wiring diagram are proportional to n. Execution time is proportional to the square of n.

In this paper the old problem of determining the discrete spectrum of a multi-particle Hamiltonian is reconsidered. The aim is to bring a fermionic Hamiltonian for large numbers N of particles by analytical means into a shape such that…

We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to Hermitian operators. In the class of Hamiltonian operators discussed here the transformation is given by a…

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…

We provide a framework for learning of dynamical systems rooted in the concept of representations and Koopman operators. The interplay between the two leads to the full description of systems that can be represented linearly in a finite…

We discuss the construction of real matrix representations of PT-symmetric operators. We show the limitation of a general recipe presented some time ago for non-Hermitian Hamiltonians with antiunitary symmetry and propose a way to overcome…

Finite plane geometry is associated with finite dimensional Hilbert space. The association allows mapping of q-number Hilbert space observables to the c-number formalism of quantum mechanics in phase space. The mapped entities reflect…

The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…

Particular complexity of linear quantum optical networks is deserved recently certain attention due to possible implications for theory of quantum computation. Two relevant models of bosons are discussed in presented work. Symmetric product…