Related papers: A Remarkable Application of Zassenhaus Formula to …
The Zassenhaus formula finds many applications in theoretical physics or mathematics, from fluid dynamics to differential geometry. The non-commutativity of the elements of the algebra implies that the exponential of a sum of operators…
This paper studies the exponential of the sum of two non-commuting operators as an infinite product of exponential operators involving repeated commutators of increasing order. It will be shown how to determine two coefficients in front of…
We propose and analyze a symmetric version of the Zassenhaus formula for disentangling the exponential of two non-commuting operators. A recursive procedure for generating the expansion up to any order is presented which also allows one to…
A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are…
The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of fermionic Gaussian circuits and Ising…
An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutators of the respective matrices. The procedure is shown to…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
In this paper, we contribute operator-splitting methods improved by the Zassenhaus product for the numerical solution of linear partial differential equations. We address iterative splitting methods, that can be improved by means of the…
We study the applicability of composite fermion theory to electrons in two-dimensional parabolically-confined quantum dots in a strong perpendicular magnetic field in the limit of low Zeeman energy. The non-interacting composite fermion…
In this contribution we present calculations performed for interacting electron systems within a non-perturbative formulation of the cluster theory. Extrapolation of the model to describe the time dependence of the interacting systems is…
A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and thus containing the minimum number of…
In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used $ab~initio$ methods, which is critically limited by its non-unitary nature. The unitary modification as an ideal solution to the problem is,…
A full coupled-cluster expansion suitable for sparse algebraic operations is developed by expanding the commutators of the Baker-Campbell-Hausdorff series explicitly for cluster operators in binary representations. A full coupled-cluster…
On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…
The structure and dynamics of an n-particle system are described with coupled nonlinear Heisenberg's commutator equations where the nonlinear terms are generated by the two-body interaction that excites the reference vacuum via…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
We study entanglement in a system of three coupled quantum harmonic oscillators. Specifically, we use the Schmidt decomposition to analyze how the entanglement is distributed among the three subsystems. The Schmidt decomposition is a…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
We use, for the first time, ab initio coupled-cluster theory to compute the spectral function of the uniform electron gas at a Wigner-Seitz radius of $r_\mathrm{s}=4$. The coupled-cluster approximations we employ go significantly beyond the…