Norm-Aware Product Formulas for Hamiltonian Simulations

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.