Variational quantum algorithms for energy optimization and the thermal-state preparation of a many-body system.

Quantum computing has emerged as a powerful paradigm for solving complex problems that are intractable with classical computers, but limitations of available quantum hardware hinder the use of pure quantum algorithms. In the current noisy intermediate-scale quantum (NISQ) era, variational quantum algorithms (VQAs) represent a valid alternative: a set of classically optimized tunable parameters controls the quantum computation. In this presentation, we show how a Quantum Approximate Optimization Algorithm (QAOA) can be used to tackle the NP-Hard prosumer problem, which consists in identifying the most economical combinations for the production, purchase, and sale of energy in a community. Moreover, we develop a VQA for preparing a Gibbs state of a many-body system on a quantum computer, which represents a fundamental ingredient for investigating thermalization and out-of-equilibrium thermodynamics, and providing helpful initial resources for other quantum algorithms. To overtake the constraints of existing hardware, we implement an innovative, efficient, and accurate readout measurement scheme for single- and multi-qubit states, based on Bayesian inference.