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THE SELFADJOINT LIE–TROTTER–KATO PRODUCT FORMULA IN OPERATOR NORM AND TIME-SLICED APPROXIMATION TO IMAGINARY-TIME PATH INTEGRAL

Takashi Ichinose

Published Sep 1, 2004• 0 citations
Publisher
DOI
10.1142/9789812702364_0003

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With the target of efficiently solving the quantum-mechanical Schrödinger equation on future quantum computers, first- and second-order product formulas for the time-evolution operator are proposed, designed to exploit hierarchies in the operator norms of the individual Hamiltonian components. Inspired by the THRIFT product formula, these decomposition schemes achieve a suppression of the leading error term by a factor of alpha<1 with respect to the standard Lie--Trotter--Suzuki splitting of the same order, where alpha quantifies the norm ratio between the dominant and subdominant parts of the Hamiltonian. Unlike THRIFT, the proposed formulas retain the general product-formula structure, making them applicable to Hamiltonians whose terms act on an arbitrary number of qubits. The advantages of this approach are demonstrated through numerical experiments on engineered two-dimensional spin-1/2 XY model systems and isolated molecules within the double-factorization framework.