Related papers: Exact closed-form expression for unitary spin-adap…
We generalized a class of non-Hermitian Hamiltonians which introduced previously by us in such a way in which every member in the class is non-\textit{PT}-symmetric. For every member of the class, the ground state is a constant with zero…
We derive a formalism to express the spin algebra $\mathfrak{su}(2)$ in a spin $s$ representation in terms of the algebra of $L$ fermionic operators that obey the Canonical Anti-commutation Relations. We also give the reverse direction of…
We consider quantum error-correcting subsystem codes whose gauge generators realize a translation-invariant, free-fermion-solvable spin model. In this setting, errors are suppressed by a Hamiltonian whose terms are the gauge generators of…
The Cayley-Hamilton problem of expressing functions of matrices in terms of only their eigenvalues is well-known to simplify to finding the inverse of the confluent Vandermonde matrix. Here, we give a highly compact formula for the inverse…
Exact analytic expression is derived for the matrix elements of the Coulomb interaction in two dimensions in the form of a closed finite sum expression. The orthonormal complete set of eigenfunctions of the harmonic oscillator is used as…
We show that each unitary representation of the N=2 superVirasoro algebra can be realized in terms of ``collective excitations'' over a filled Dirac sea of fermionic operators satisfying a generalized exclusion principle. These are…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…
We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…
Recently it has been shown that the quantum spin-1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [\cite{JW1}], and 2D [\cite{JW2}] as well. In this paper, using the…
We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator…
Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the $SU(2)$ total-spin symmetry, remains a major challenge.…
In a companion paper, we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators…
Using some modification of the standard fermion technique we derive factorized formula for spin operator matrix elements (form-factors) between general eigenstates of the Hamiltonian of quantum Ising chain in a transverse field of finite…
We consider quantum spin chains with a hidden free fermionic structure, distinct from the Jordan-Wigner transformation and its generalizations. We express selected local operators with the hidden fermions. This way we can exactly solve the…
We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has…
Expressions are given for the exponential of a hermitian matrix, A. Replacing A by iA these are explicit formulas for the Fourier transform of exp(iA). They extend to any size matrix the previous results for the 2 X 2, 3 X 3, and 4 X 4…
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
In this paper, we evaluate the accuracy of the Hermitian form of the downfolding procedure utilizing the double unitary coupled cluster Ansatz (DUCC) on the H6 and H8 benchmark systems. The computational infrastructure employs the…
In this paper, we report on a correctly scaling novel coupled cluster singles and doubles (CCSD) implementation for arbitrary high-spin open-shell states. The chosen cluster operator is completely spin-free, i.e. employs spatial…
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…