Walking through Hilbert Space with Quantum Computers.

Area of Science:

• Quantum computing
• Computational chemistry
• Chemical physics

Background:

• Quantum computers are anticipated to revolutionize chemical system computations.
• Complex sampling tasks in computational chemistry, such as determining equilibrium and nonequilibrium properties, are computationally intensive for classical computers.

Purpose of the Study:

• To review recent advancements in quantum algorithms for complex sampling tasks in computational chemistry.
• To provide a comprehensive overview of quantum algorithms for ground state, thermal state properties, and quantum dynamics calculations.

Main Methods:

• Review of quantum algorithms, including hybrid quantum-classical and fully quantum approaches.
• Focus on Monte Carlo methods: Markov chain Monte Carlo, variational Monte Carlo, projector Monte Carlo, and path integral Monte Carlo.
• Inclusion of other techniques: quantum-selected configuration interaction, minimally entangled typical thermal states, entanglement forging, and Monte Carlo-flavored Lindbladian dynamics.

Main Results:

• Detailed theoretical frameworks of various quantum algorithms and their classical counterparts.
• Discussion of the potential for quantum advantage in computational chemistry tasks.
• Identification of challenges and limitations in current quantum algorithms for chemical simulations.

Conclusions:

• Quantum algorithms, particularly Monte Carlo-based methods, offer significant potential for advancing computational chemistry.
• Further development is needed to overcome challenges and fully realize quantum computational advantages for chemical system simulations.