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In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap,…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
The Hamiltonian of a quantum system is represented in terms of operators corresponding to the kinetic and potential energies of the system. The expectation value of a Hamiltonian and Hamiltonian simulation are two of the most fundamental…
Variational quantum eigensolvers (VQEs) combine classical optimization with efficient cost function evaluations on quantum computers. We propose a new approach to VQEs using the principles of measurement-based quantum computation. This…
Variational quantum algorithms (VQAs) have enabled a wide range of applications on near-term quantum devices. However, their scalability is fundamentally limited by barren plateaus, where the probability of encountering large gradients…
Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There…
Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks---generalised time evolution with…
Variational Quantum optimization algorithms, such as the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an…
Quantum variational optimization has been posed as an alternative to solve optimization problems faster and at a larger scale than what classical methods allow. In this paper we study systematically the role of entanglement, the structure…
The variational quantum eigensolver (VQE) is one of the most promising quantum algorithms for the near-term noisy intermediate-scale quantum (NISQ) devices. The VQE typically involves finding the minimum energy of a quantum Hamiltonian…
Exploring the potential application of quantum computers in material design and drug discovery has attracted a lot of interest in the age of quantum computing. However, the quantum resource requirement for solving practical electronic…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Variational quantum eigensolver (VQE), aiming at determining the ground state energy of a quantum system described by a Hamiltonian on noisy intermediate scale quantum (NISQ) devices, is among the most significant applications of…
The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenvalues and eigenvectors of a given Hamiltonian on noisy intermediate-scale quantum (NISQ) devices. A particular application is to obtain ground…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Variational Quantum Algorithms (VQAs) are promising methods for solving combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) devices. However, benchmarking VQAs is difficult due to their stochastic behavior and the…