Abstract
AbstractThis study proposes a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, which is a recently proposed framework for quantum chemistry using probabilistic imaginary-time evolution (PITE). In this scheme, the nuclei in a molecule are treated as classical point charges while the electrons are treated as quantum mechanical particles. The electronic states and candidate geometries are encoded as a superposition of many-qubit states, for which a histogram created from repeated measurements gives the global minimum of the energy surface. We demonstrate that the circuit depth per step scales as $${{{\mathcal{O}}}}({n}_{{\rm {e}}}^{2}{{{\rm{poly}}}}(\log {n}_{{\rm {e}}}))$$
O
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poly
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for the electron number ne, which can be reduced to $${{{\mathcal{O}}}}({n}_{{\rm {e}}}{{{\rm{poly}}}}(\log {n}_{{\rm {e}}}))$$
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poly
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if extra $${{{\mathcal{O}}}}({n}_{{\rm {e}}}\log {n}_{{\rm {e}}})$$
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qubits are available. Moreover, resource estimation implies that the total computational time of our scheme starting from a good initial guess may exhibit overall quantum advantage in molecule size and candidate number. The proposed scheme is corroborated using numerical simulations. Additionally, a scheme adapted to variational calculations is examined that prioritizes saving circuit depths for noisy intermediate-scale quantum (NISQ) devices. A classical system composed only of charged particles is considered as a special case of the scheme. The new efficient scheme will assist in achieving scalability in practical quantum chemistry on quantum computers.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Computer Networks and Communications,Statistical and Nonlinear Physics,Computer Science (miscellaneous)
Cited by
6 articles.
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