The calculation of transition probabilities is necessary for determining quantities such as light absorption spectra and condensed phase correlation functions. Though there have been methods proposed for simulating transition amplitudes on quantum computers, most of these use the expensive Hadamard test as a subroutine. Building on previous work by Ibe et al (arXiv:2002.11724) we present methods and resource counts for a class of algorithms that do not require the Hadamard test, leading to approaches that are more amenable to near-term quantum hardware. We apply our methods to the calculation of Franck-Condon factors with the inclusion of non-Condon effects. Importantly, we show that one can trade-off circuit depth for quantum circuit repetitions, making the algorithm adaptable to an arbitrary quantum device.

Quantum algorithms for transition probabilities

ACS Spring 2022

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