Related papers: Exact Spin Elimination in Ising Hamiltonians and E…
The three-dimensional (3D) Ising model is mapped into a 3D spinless fermionic model by the Jordan-Wigner transformation. The exact solution of the 3D model for spinless fermions is derived analytically by performing a diagonalization…
Advancing quantum technologies requires precise and robust coherent control of quantum systems. Robust higher-order Hamiltonian engineering is essential for high-precision control and for accessing effective dynamics absent at zeroth order.…
Solving intractable mathematical problems in simulators composed of atoms, ions, photons or electrons has recently emerged as a subject of intense interest. Here we extend this concept to phonons that are localised in spectrally pure…
We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wavefunctions. Our approach directly determines system-specific representations of qubit…
We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and try to characterize the relevant…
We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic…
Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians,…
Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the…
We present an alternative scheme to the widely used method of representing the basis of one-band Hubbard model through the relation $I=I_{\uparrow}+2^{M}I_{\downarrow}$ given by H. Q. Lin and J. E. Gubernatis [Comput. Phys. 7, 400 (1993)],…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the…
Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
The paper discusses the transformation of decorated Ising models into an effective \textit{undecorated} spin models, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The…
We design two variational algorithms to optimize specific 2-local Hamiltonians defined on graphs. Our algorithms are inspired by the Quantum Approximate Optimization Algorithm. We develop formulae to analyze the energy achieved by these…
Quantum annealing is a promising algorithm for solving combinatorial optimization problems. However, various hardware restrictions significantly impede its efficient performance. Size-reduction methods provide an effective approach for…
A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the…
We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular momentum eigenstates. We split, from the total angular momentum operator, a proper part which can be separately…
In this work, we consider a fundamental task in quantum many-body physics - finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value…