Related papers: Improved approximation algorithms for bounded-degr…
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state…
We present the meta-VQE, an algorithm capable to learn the ground state energy profile of a parametrized Hamiltonian. By training the meta-VQE with a few data points, it delivers an initial circuit parametrization that can be used to…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
We give an approximation algorithm for Quantum Max-Cut which works by rounding an SDP relaxation to an entangled quantum state. The SDP is used to choose the parameters of a variational quantum circuit. The entangled state is then…
Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…
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 present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…
Local Hamiltonians with topological quantum order exhibit highly entangled ground states that cannot be prepared by shallow quantum circuits. Here, we show that this property may extend to all low-energy states in the presence of an on-site…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…