Related papers: An alternating-minimization method for preparing l…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…
Quantum coherence profoundly alters classical thermodynamic expectations by modifying the structure and accessibility of probability distributions. Classically, transitions to lower-entropy states (local second-law violations) are…
One promising application of near-term quantum devices is to prepare trial wavefunctions using short circuits for solving different problems via variational algorithms. For this purpose, we introduce a new circuit design that combines…
We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based…
Nature is governed by precise physical laws, which can inspire the discovery of new computer-run simulation algorithms. Thermal states are the most ubiquitous for they are the equilibrium states of matter. Simulating thermal states of…
The preparation of thermal equilibrium states is important for the simulation of condensed-matter and cosmology systems using a quantum computer. We present a method to prepare such mixed states with unitary operators, and demonstrate this…
The ground state energy and the free energy of Quantum Local Hamiltonians are fundamental quantities in quantum many-body physics, however, it is QMA-Hard to estimate them in general. In this paper, we develop new techniques to find…
While the preparation of a general quantum state is challenging, realistic problem instances, such as those encountered in quantum chemistry and quantum machine learning-typically exhibit hierarchical amplitude structures, consisting of a…
We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity (with complexity measured by the quantum circuit depth…
I describe a simple algorithm for numerically finding the ground state and low-lying excited states of a quantum system. The algorithm is an adaptation of the relaxation method for solving Poisson's equation, and is fundamentally based on…
The variational quantum eigensolver (VQE) and its variants, which is a method for finding eigenstates and eigenenergies of a given Hamiltonian, are appealing applications of near-term quantum computers. Although the eigenenergies are…
A computational method is presented which is capable to obtain low lying energy structures of topological amorphous systems. The method merges a differential mutation genetic algorithm with simulated annealing. This is done by incorporating…
Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate…
We present a method to formulate the unit commitment problem in energy production as quadratic unconstrained binary optimization (QUBO) problem, which can be solved by classical algorithms and quantum computers. We suggest a first approach…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
A procedure for calculation of rotation-vibration states of medium sized molecules is presented. It combines the advantages of variational calculations and perturbation theory. The vibrational problem is solved by diagonalizing a…
Calculating the molecular ground-state energy is a central challenge in computational chemistry. Conventional methods such as the Complete Active Space Configuration Interaction scale exponentially with molecular size, limiting their…
A Hamiltonian based approach using spatially localized projection operators is introduced to give precise meaning to the chemically intuitive idea of the electronic energy on a quantum subsystem. This definition facilitates the study of…