Today our new paper appeared (as an "in press" draft) in the New Journal of Physics. In it, we develop quantum computing circuits that can produce eigenstates in the nuclear shell mode. This nuclear model, called "configuration interaction" in other areas of many-body quantum mechanics, such as quantum chemsitry, is probably the main approach that realistic calculations of nuclei have been attempted on quantum computers by various groups.
Our paper is by no means the first to explore how to apply quantum computing to the shell model. What we have done, though, is to use a circuit ansatz inspired by the nuclear physics and the symmetries involved to use a small number of gates, and a small number of variational parameters in order to turn the initial "zero" state of the quantum computer register into a state which simulates the nuclear wave function.
The result is that we are able to find, with relatively low-depth circuits, the ground state, lowest 2+ and 4+ states, on a simulated quantum computer with good accuracy.
We had some useful comments from the referees pointing us to how we might be able to reduce the circuit depth further, and we will look into that. We also would like to really test the circuits on a real quantum computer.
Here's an example circuit - probably our most complicated one - that finds the 2+ state of Nickel-58
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