Projective quantum eigensolver via adiabatically decoupled subsystem evolution: A resource efficient approach to molecular energetics in noisy quantum computers.

Quantum computers hold immense potential in the field of chemistry, ushering new frontiers to solve complex many-body problems that are beyond the reach of classical computers. However, noise in the current quantum hardware limits their applicability to large chemical systems. This work encompasses the development of a projective formalism that aims to compute ground-state energies of molecular systems accurately using noisy intermediate scale quantum (NISQ) hardware in a resource-efficient manner. Our approach is reliant upon the formulation of a bipartitely decoupled parameterized ansatz within the disentangled unitary coupled cluster framework based on the principles of nonlinear dynamics and synergetics. Such decoupling emulates total parameter optimization in a lower dimensional manifold, while a mutual synergistic relationship among the parameters is exploited to ensure characteristic accuracy via a non-iterative energy correction. Without any pre-circuit measurements, our method leads to a highly compact fixed-depth ansatz with shallower circuits and fewer expectation value evaluations. Through analytical and numerical demonstrations, we establish the method's superior performance under noise while concurrently ensuring requisite accuracy in future fault-tolerant systems. This approach enables rapid exploration of emerging chemical spaces by the efficient utilization of near-term quantum hardware resources.