Quantum Computing: Shell model for Ni-58

We (Bharti Bhoy and I) have been working on developing quantum computing algorithms to tackle the nuclear shell model.

This is the picture of the nucleus which assumes a set of single particle levels that each neutron or proton moves in, with the levels arranged in “shells”.
To calculate properties of a particular nucleus you then look at which shells are filled with protons or neutrons and ignore those as being part of an inert core of particles.

Any nucleons in part-filled shells are treated specially and allowed to interact with a “residual interaction” (= the bit of the nuclear interaction left over after working out the single particle levels).

This interaction gives rise to a range of different allowed states according to the Schrödinger equation, and the main job of the shell model is to find these levels, and perhaps extract some information from them, like how a nucleus might decay from one level to another.

In classical calculations of the shell model, a lot of the hard work is in finding the levels once the problem has been set up.

This is because the interaction of the nucleons in the partially-filled shell involves many possible combinations that get represented in a very large matrix (with millions or billions of rows) and then there is a laborious task of solving a matrix equation.

On a quantum computer, the idea is to manipulate the qubits in such a way as to drive them to a wave function that maps to the nuclear wave function, and so avoid the difficulties of the ever-increasing matrix size.

We have done this for the nucleus nickel-58. It’s a simple case because it only has two neutrons outside the nickel-56 fully-closed-shell nucleus, but it allowed us to test our methods, borrowed mainly from quanutm chemistry and show that we can get the right results.

The work has just been published as Bharti Bhoy and Paul Stevenson, New Journal of Physics 26 075001 (2024)