# PhD Studentship: SPINDRIFT—Finite Temperature Neural Quantum States for Quantum Monte Carlo
Location: Imperial College London, London, UK.
Supervisor: Assoc. Prof. Jarvist Moore Frost (Department of Chemistry, Department of Physics).
Funding: Fully funded for 48 months, Royal Society London-weighted tax-free PhD stipend, £25,000 today, inflating ~2% by tax year. Open to UK/Home fee status students only.
Start date: Available immediately; applications will be evaluated on a rolling basis until the position is filled.
At thermonuclear temperatures (imaginary time β → 0), quantum mechanics is trivial. Kinetic energy dominates, and electrons purely diffuse through space as Gaussian heat kernels.
The trouble begins when you cool down.
As you project along imaginary time exp(-β Ĥ), quantum correlations condense, and the antisymmetrisation of the many-body Fermionic density matrix forms an intricate nodal manifold. Most modern Neural Quantum States attempt to directly learn the highly entangled ground state from a standing start, variationally optimising a zero-temperature wavefunction.
SPINDRIFT ([2607.29590] Spindrift: Learning quantum degeneracy from thermal purity in restricted path integral Monte Carlo) takes a radically different route. Rather than trying to guess the ground state immediately, we learn the continuous appearance of quantum structure along a descending temperature curriculum. We use the nodal surface learnt at the higher temperatures to systematically increase the signal-to-noise of learning at the next, lower, temperature.
We implement this in Julia, using a restricted path integral Monte Carlo (RPIMC) algorithm. Quite astonishingly, we can directly calculate the pointwise residual error on path-integral samples, as the density matrix satisfies the operator Bloch equation (a finite-temperature analogue of the Schrödinger equation). The simulation feeds this mismatch as a ‘loss’ to the neural network representation of the density matrix, allowing the nodes to learn their own geometry from first principles - exerting a literal pressure which sculpts the nodal surface.
The plan for your PhD is to extend the architecture to the fully spin-polarised uniform electron gas (UEG). This requires implementing periodic boundary conditions for the neural Ansatz, and some established PIMC tricks to reach lower temperatures. The initial goal is to map the emergence of spontaneous symmetry breaking, such as the formation of the Wigner crystal, as the system cools. Once the foundation is proven and extended to unpolarised systems, we will analyse the fitted thermal density matrix directly to calculate off-diagonal long-range order and thereby probe the mechanism of pairing in correlated matter as we pass through symmetry breaking transitions.
## Who we are looking for
You do not need to know how to program an equivariant normalizing flow, or even be familiar with every technical term in this advert. You do need to be mathematically adventurous, and intrinsically curious about how quantum matter organises itself. In this project we are quite intentionally doing something a little out of the mainstream.
We require a degree (integrated Master’s or equivalent; Upper Second Class (2:1) Honours or above) in Physics, Applied Mathematics, Theoretical Chemistry or Computer Science. The key theory is based in quantum mechanics and statistical mechanics.
A lot of the PhD will involve coding; currently our Halcyon.jl (GitHub - Frost-group/Halcyon.jl: General PIMC working directory · GitHub) codebase is written entirely in Julia, which allows for both the highly efficient low-level Monte Carlo updates and high-level neural ODEs to be present in the same context. Julia is easy to learn if coming from a C, Fortran, or Python background.
## How to apply
To apply, email jarvist.frost@imperial.ac.uk with your CV, a link to any code you have written (GitHub, GitLab, or past project work), and a brief note explaining what caught your attention in the SPINDRIFT preprint: what seemed interesting, puzzling, dubious, “not even wrong”, or an open question you would want to explore.
((I’m not sure how many UK Julia quantum mechanics undergraduates there are out there - but just in case, I thought I would cross-post this advert here! The codebase is entirely Julia, and it really plays to its strengths: tightly optimised low level Monte Carlo moves, then more high level specification of the Machine Learning.))