Quantum-selected configuration interaction using time-evolved states

A major goal in quantum computing is the solution of quantum many-body problems with applications in quantum chemistry being of particular industrial relevance. In the last decade, quantum-classical hybrid algorithms that can perform calculations even on noisy devices such as the Variational Quantum Eigensolver (VQE) has attracted attention. VQE in the naive form has a number of shortcomings in practical applications, however, such as the difficulty of optimization, the so-called Baren Plateau, and the huge number of quantum circuit runs required for highly accurate quantum chemistry calculations. Quantum-selected configuration interaction (QSCI) is a recently proposed alternative quantum-classical hybrid algorithm which utilizes an input quantum state on a near-term quantum device to select important basis states (electron configurations in quantum chemistry) which defines a subspace in which to diagonalize a target Hamiltonian on classical computers.

One of the main issues in this proposal is the preparation of an input state which has important basis states in common with e.g. the ground state. In this work we propose using a time-evolved state by the target Hamiltonian from an initial state, usually the Hatree-Fock (HF) state, as the input state for QSCI. Our proposal is based on the intuition that time-evolution by the Hamiltonian creates electron excitations of various orders when applied to the initial state. We numerically investigate the energy precision of the proposed method for several quantum chemistry Hamiltonians describing electronic states of a variety of molecules. Numerical results reveals that our method can yield sufficiently precise ground state energies based on the time-evolved HF state. We also show that such results are better than diagonalizing based on important configurations selected by sampling a unitary coupled cluster singles and doubles anzats (UCCSD) with parameters determined by a classical CCSD calculation for complicated problems. Finally we analyze the scaling of required quantum and classical resources with system size for the hydrogen chain. Our proposal provides a systematic and optimization-free method to prepare input states for QSCI and could contribute to taking advantage of near-term quantum computing devices in quantum chemistry calculations.