Quantum computing

This section assumes the reader is already familiar with the relation of the NMR response function to the correlator of spin operators. Otherwise, we recommend reading the NMR and Maths chapters first.

The use of quantum computers to measure time-resolved correlation functions is well established, for example to measure the Green's function with respect to a ground state prepared on a quantum computer (see for example Wecker et. al, doi:10.1103/PhysRevA.92.062318). This use case typically assumes an ideal quantum computer. The correlator is measured with respect to a pure state and all noise present in the system is a source of error.

In calculating NMR response functions, we do not aim for a quantum computer operating on pure states. We are in fact aiming for the infinite-temperature limit, where we start from a fully-mixed-state density matrix and run the correlation measurement in the presence of noise.

While the traditional way to measure correlators (Wecker et. al) would still be applicable, the infinite-temperature initial state allows us to further simplify the algorithm and eliminate the need for an additional ancilla qubit.