Adapting the HHL algorithm to quantum many-body theory

• DOI: 10.48550/arxiv.2212.14781
• Publication Date: 2022-01-01
• Authors: Nishanth Baskaran; Abhishek Singh Rawat; Dibyajyoti Chakra...; Akshaya Jayashankar; K. Sugisaki; D. Mukherjee; V. S. Prasannaa
• Keywords: Chemical Physics (physics.chem-ph); Quantum Physics; Atomic Physics (physics.atom-ph); Physics - Chemical Physics; 0103 physical sciences; FOS: Physical sciences; Quantum Physics (quant-ph); 01 natural sciences; Physics - Atomic Physics

Rapid progress in developing near- and long-term quantum algorithms for chemistry has provided us with an impetus to move beyond traditional approaches explore new ways apply computing electronic structure calculations. In this work, we identify the connection between many-body theory a linear solver, implement Harrow-Hassidim-Lloyd (HHL) algorithm make precise predictions of correlation energies light molecular systems via (non-unitary) linearised coupled cluster theory. We alter HHL integrate two novel aspects- (a) prescribe scaling approach that allows one scale any arbitrary symmetric positive definite matrix A, solve Ax = b achieve x reasonable precision, all while without having compute eigenvalues (b) devise techniques reduce depth overall circuit. context, introduce following variants different eras computing- AdaptHHLite its appropriate forms noisy intermediate (NISQ), late-NISQ, early fault-tolerant eras, as well AdaptHHL era. demonstrate ability NISQ variant capture energy precisely, simultaneously being resource-lean, using simulation 11-qubit IonQ hardware.