Paul D Stevenson

Paul D Stevenson

Nuclear Physics & Quantum Computing

Quantum Computing: Shell model for Ni-58

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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)

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Solving coupled non-linear differential equations on quantum computer

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This week, we (PhD student Lance, co-supervisor Jim, and me) have published a new paper on a method of solution of non-linear coupled Schrödinger equtions on quantum computer.
It’s the continuation of some previous work where we employed the quantum imaginary time method to solve nuclear density functional problems in a simple model. In the new work, we wanted to make the model more realistic and less simple, and this meant solving simultaneously for multiple single particle wave functions, each of which are subject to slightly different Schrödinger equations, but which couple together through a density-depedendent term. Rather than present this work as specifically a way to solve the nuclear physics problem, we decided to send it to a more general journal which was running a special issue on quantum computing technology in the hope of reaching a wider audience. I guess we will see if it gets widely read and cited, but the referee, at least, agreed that it was worth publishing, at least after a round of comments / updates. The paper does not yet have its final volume and article number designation, but is online at the EPJ Special Topics journal site.

A Comment on Li et al.

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A recent paper by Li et al. introduced a variance minimization quantum algorithm. As one of their examples, they took a much-used nuclear physics case: A one-body model of the deuteron. Unfortunately, their presentation was a bit problematic, so I wrote a comment to submit to the journal (Physica Scripta) to try to correct the record. The comment was rejected by the editor, so I present the comment here instead, for the record - link at end of post. I would have put it on the arXiv, but they don’t publish comments of papers unless those papers are in the arXiv.

New Paper in Phys. Lett. B

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A new paper appeared today in Physics Letters B, here, which features the work of now-graduated PhD student Iain Lee, on friction in heavy ion reactions. The reaction studied was 16O + 92Zr, prompted by a previous experimental study which suggested that the reaction mechanism was notably different to that of 16O + 90Zr because of the higher density of states caused by the two neutrons outside of the closed shell. I got involved in the calculations by providing some time-dependent Hartree-Fock calculations to see what this kind of microscopic approach said about the rate of developement of the neck during fusion. One unusual aspect of this paper is that it was submitted less than two weeks ago. The editors sent it out for review extremely quickly, and referee comments came back quickly. They were serious comments and the referee had clearly read the paper well, and was an expert in the area. My colleauge Alexis, who was the coresponding author, worked on the response straight away, and the editor and referee accepted the response, meaning that the paper was accepted within a week, and has since apperaed (as an uncorrected proof) today, less than two weeks since submission.
I have never experienced such a quick process in publishing a scientific research paper!

New Paper in Phys Rev C

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Congratulations to Lance Li, my PhD student on the publication of his first paper. It shows how the quantum imaginary time evolution operator can be used to solve nuclear density functional theory on a quantum computer. Physical Review C published the paper today at Phys. Rev. C. 109, 044322 (2024). It’s open access so viewable by all.