相关论文: Permanents in linear optical networks
This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems.…
We propose a measure of quantum efficiency of a multimode state of light that quantifies the amount of optical loss this state has experienced, and prove that this efficiency cannot increase in any linear-optical processing with destructive…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad…
Consider the regular representation of the sum over all permutations weighted by the sum of their descent, inversion, and fixed point multinomials. We compute the spectrum and the multiplicities of its elements of that matrix. Note that…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering their wide…
Most observables at particle colliders involve physics at a wide variety of distance scales. Due to asymptotic freedom of the strong interaction, the physics at short distances can be calculated reliably using perturbative techniques, while…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
Scalable and efficient quantum computation with photonic qubits requires (i) deterministic sources of single-photons, (ii) giant nonlinearities capable of entangling pairs of photons, and (iii) reliable single-photon detectors. In addition,…
The desire to understand the interaction between light and matter has stimulated centuries of research, leading to technological achievements that have shaped our world. One contemporary frontier of research into light-matter interaction…
The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. By Minc's conjecture, there exists a reachable upper bound on the permanent of 2-dimensional (0,1)-matrices. In this paper we obtain some…
We introduce unitary network, an oriented architecture for tensor network unitaries. Compared to existing architectures, in a unitary network each local tensor is required to be a unitary matrix upon suitable reshaping. Global unitarity is…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
Physically motivated quantum algorithms for specific near-term quantum hardware will likely be the next frontier in quantum information science. Here, we show how many of the features of neural networks for machine learning can naturally be…
In this article, we study permanental varieties, i.e. varieties defined by the vanishing of permanents of fixed size of a generic matrix. Permanents and their varieties play an important, and sometimes poorly understood, role in…
Quantum networks, capable of transmitting arbitrary quantum states, provide a foundation for a wide range of quantum applications, including distributed quantum computing, distributed quantum sensing, and quantum communication. Photons are…