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Combinatorial optimization is regarded as a potentially promising application of near and long-term quantum computers. The best-known heuristic quantum algorithm for combinatorial optimization on gate-based devices, the Quantum Approximate…
We resolve the approximability of the maximum energy of the Quantum Max Cut (QMC) problem using product states. A classical 0.498-approximation, using a basic semidefinite programming relaxation, is known for QMC, paralleling the celebrated…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
We introduce a $0.611$-approximation algorithm for Quantum MaxCut and a $\frac{1+\sqrt{5}}{4} \approx 0.809$-approximation algorithm for the EPR Hamiltonian of [arXiv:2209.02589]. A novel ingredient in both of these algorithms is to…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…
In this work, we introduce three algorithmic improvements to reduce the cost and improve the scaling of orbital space variational Monte Carlo (VMC). First, we show that by appropriately screening the one- and two-electron integrals of the…
Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of…
We present a polynomial-time $(\alpha_{GW} + \varepsilon)$-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where $\alpha_{GW} \approx 0.878$ is the approximation guarantee of the Goemans-Williamson…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
Utilizing quantum computer to investigate quantum chemistry is an important research field nowadays. In addition to the ground-state problems that have been widely studied, the determination of excited-states plays a crucial role in the…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
We introduce an architecture for variational quantum algorithms that can be efficiently trained via parameter updates along exact geodesics on the Riemannian state manifold. This features a parameter-optimal circuit ansatz which supersedes…
Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of p steps; in each step a…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
Of late, we are witnessing spectacular developments in Quantum Information Processing with the availability of Noisy Intermediate-Scale Quantum devices of different architectures and various software development kits to work on quantum…
Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. While they have demonstrated considerable promise in solving problems of practical interest, efficiently determining the minimal…
Measuring the expectation value of the molecular electronic Hamiltonian is one of the challenging parts of the variational quantum eigensolver. A widely used strategy is to express the Hamiltonian as a sum of measurable fragments using…