相关论文: Back to the Origins. Using Matrix Functions of H\"…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
Quantum computing has recently been emerging in theoretical chemistry as a realistic avenue meant to offer computational speedup to challenging eigenproblems in the context of strongly-correlated molecular systems or extended materials.…
H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated {\pi}-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based…
Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our newcomputational toolbo x…
Starting from the Fock space representation of hadron bound states in a quark model, a change of representation is implemented by a unitary transformation such that the composite hadrons are redescribed by elementary-particle field…
Quantum interference is proposed as a tool to augment Quantum Computation.
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally…
Heisenberg's matrix formulation of quantum mechanics can be generalized to relativistic systems by evolving in light-front time tau = t+z/c. The spectrum and wavefunctions of bound states, such as hadrons in quantum chromodynamics, can be…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.
A proposal for an experiment to look at some possibly novel aspects of quantum interference is presented, along with some Engineering applications that might result.
We continue here to study simple matrix models of quantum mechanical Hamiltonians. The eigenvalues and eigenfunctions were associated energy levels and wave functions. Whereas previously we considered the weak coupling limits of our models,…
Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only…