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Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor…
We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…
We present classical and quantum algorithms for approximating partition functions of classical Hamiltonians at a given temperature. Our work has two main contributions: first, we modify the classical algorithm of \v{S}tefankovi\v{c},…
MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually…
We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our work generalizes previous known results for…
Preparing the ground state of a Hamiltonian is a problem of great significance in physics with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
Recent successes in producing rigorous approximation algorithms for local Hamiltonian problems such as Quantum Max Cut have exploited connections to unconstrained classical discrete optimization problems. We initiate the study of…
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…
Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a…
Determining the energy gap in a quantum many-body system is critical to understanding its behavior and is important in quantum chemistry and condensed matter physics. The challenge of determining the energy gap requires identifying both the…
In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
We present quantum algorithms for the loading of probability distributions using Hamiltonian simulation for one dimensional Hamiltonians of the form ${\hat H}= \Delta + V(x) \mathbb{I}$. We consider the potentials $V(x)$ for which the…
We propose a scheme to distribute graph states over quantum networks in the presence of noise in the channels and in the operations. The protocol can be implemented efficiently for large graph sates of arbitrary (complex) topology. We…
Realizing photonic graph states, crucial in various quantum protocols, is challenging due to the absence of deterministic entangling gates in linear optics. To address this, emitter qubits have been leveraged to establish and transfer the…
A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer,…