Abstract
This chapter reviews quantum algorithms for exact molecular energy calculations, that is, quantum analogs of the full configuration interaction (FCI) calculations. First, the chapter provides the necessary basics of quantum computing including the quantum Fourier transform (QFT), the phase estimation algorithm (PEA), and their semiclassical variants. Next, it presents details of the quantum algorithm for the FCI method (qFCI). It discusses the application to molecular Born–Oppenheimer electronic Hamiltonians. The chapter briefly mentions the initial state preparation and deals with the crucial part of the algorithm, namely the implementation of controlled powers of the exponential of molecular Hamiltonians. It further demonstrates an application of the qFCI method to non-relativistic ground and excited state energy calculations on the example of the methylene molecule. Finally, the chapter talks about the qFCI method for four-component (4c) relativistic computations.
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