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Quantum signal processing provides an optimal procedure for simulatingHamiltonian evolution on a quantum computer using calls to a block encoding ofthe Hamiltonian. In many situations it is possible to control between forwardand reverse steps with almost identical cost to a simple controlled operation.We show that it is then possible to reduce the cost of Hamiltonian simulationby a factor of 2 using the recent results of generalised quantum signalprocessing.

Doubling Efficiency of Hamiltonian Simulation via Generalized Quantum Signal Processing