Engineering Quantum Boltzmann States through Variational Quantum Algorithms

Quantum algorithms have been proposed to address a wide array of problems, including classical optimization. Variational quantum algorithms represent a promising avenue for near-term quantum computers to exhibit quantum advantages over classical approaches in optimization and machine learning tasks. One notable framework among them is the Quantum Approximate Optimization Algorithm (QAOA), designed specifically for solving combinatorial optimization problems. In this talk, we will introduce variational quantum algorithms, with a particular focus on QAOA. Furthermore, we will provide extensive analytical and numerical evidence indicating that increasing the depth of the QAOA circuit applied to universal spin-glass models generates states resembling thermal distributions. To be specific, we demonstrate that a single layer of QAOA produces well-defined and unique temperature Boltzmann states. However, as the circuit depth increases, we observe signs of bimodal behavior. We will also offer a comprehensive and intuitive explanation for the finite-size scaling of the temperatures generated in a p-layer QAOA protocol. These findings hold significant potential for applications in quantum machine learning and quantum simulators.