Walking through Hilbert Space with Quantum Computers

Understand

Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers.

• This review highlights the recent advancements of quantum algorithms tackling complex sampling tasks in the key areas of computational chemistry: ground state, thermal state properties, and quantum dynamics calculations.
• We review a broad range of quantum algorithms, from hybrid quantum-classical to fully quantum, focusing on the traditional Monte Carlo family, including Markov chain Monte Carlo, variational Monte Carlo, projector Monte Carlo, path integral Monte Carlo, etc.
• We also cover other relevant techniques involving complex sampling tasks, such as quantum-selected configuration interaction, minimally entangled typical thermal states, entanglement forging, and Monte Carlo-flavored Lindbladian dynamics.