Graph-|Q⟩⟨C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure.

Area of Science:

• Quantum Computing
• Computational Chemistry
• Molecular Dynamics

Background:

• Accurate chemical property determination is vital but hindered by computational scaling issues in electron correlation and quantum nuclear dynamics.
• Quantum computing offers a potential solution for exponentially complex challenges in quantum chemistry and molecular dynamics.

Purpose of the Study:

• To present a new quantum computing approach to significantly reduce quantum circuit depth for electron correlation energy calculations.
• To improve the accuracy of quantum computations for large molecular systems.

Main Methods:

• A graph-theoretic approach to molecular fragmentation is employed.
• This method generates projection operators to decompose quantum circuits into separate unitary processes.
• These processes are executed asynchronously and in parallel on quantum and classical hardware.

Main Results:

• The developed quantum algorithms drastically reduce quantum circuit depth by several orders of magnitude.
• Numerical benchmarks demonstrate the computation of accurate unitary coupled-cluster singles and doubles (UCCSD) energies for water clusters.

Conclusions:

• The new quantum fragmentation approach effectively reduces computational complexity for electron correlation energy calculations.
• This method shows promise for accurate and efficient quantum simulations of large molecular systems.