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Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and…

We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We start by providing a hybrid numeric-symbolic…

In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is…

It is shown that the Hamiltonian formalism proposed previously in [1] to describe the nonlinear dynamics of only {\it soft} fermionic and bosonic excitations contains much more information than initially assumed. In this paper, we have…

Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…

Using the operator formulation we discuss the bosonization of the two-dimensional derivative-coupling model. The fully bosonized quantum Hamiltonian is obtained by computing the composite operators as the leading terms in the Wilson short…

The symmetry-projected Hartree--Fock ansatz for the electronic structure problem can efficiently account for static correlation in molecules, yet it is often unable to describe dynamic correlation in a balanced manner. Here, we consider a…

This work proposes a computational multiscale method for the mixed formulation of a second-order linear elliptic equation subject to a homogeneous Neumann boundary condition, based on a stable localized orthogonal decomposition (LOD) in…

Exponentiation of Hamiltonians refers to a mathematical operation to a Hamiltonian operator, typically in the form e^(-i.t.H), where H is the Hamiltonian and t is a time parameter. This operation is fundamental in quantum mechanics,…

We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…

We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This…

A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…

We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…

We study the least-squares (LS) functional of the canonical polyadic (CP) tensor decomposition. Our approach is based on the elimination of one factor matrix which results in a reduced functional. The reduced functional is reformulated into…

This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…

There is growing interest to investigate states of matter with topological order, which support excitations in the form of anyons, and which underly topological quantum computing. Examples of such systems include lattice spin models in two…

The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in…

The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…