Quantum Information Informed Quantum Algorithms

Quantum computing presents promising solutions for electronic structure and excited state problems, yet traditional methods like the Variational Quantum Eigensolver (VQE) encounter difficulties such as deep quantum circuits and optimization challenges for quantum chemistry problems. In this talk, I present quantum information-informed algorithms that significantly enhance the efficiency of quantum chemistry calculations by reducing the circuit complexity. The PermVQE [1] approach leverages quantum information to optimize qubit permutations to localize correlations, thereby reducing circuit depth and improving noise resilience. ClusterVQE [2] utilizes mutual information and graph theory to partition qubit space into entangled clusters, enabling precise simulations of larger systems with fewer qubits. Finally, the Quantum Davidson algorithm [3-4] extends the quantum Krylov subspace method, employing a pre-conditioned iterative expansion that accelerates convergence on excited states with shallower circuits.



References:

1. PRX Quantum, 2, 020337 (2021).

2. npj Quantum Inf. 8, 1 (2022)

3. Quantum Sci. Technol. 9, 035012 (2024).

4. arXiv:2406.08675.