Steven Abel

Steven Abel, Andrei Constantin, Luca A. Nutricati

Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing.

Shehu AbdusSalam, Steven Abel, Deaglan Bartlett et al.

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density, and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focussed on the promising regions in order to be equally performant.

Steven Abel, David G. Cerdeno, Sandra Robles

Genetic Algorithms (GAs) are explored as a tool for probing new physics with high dimensionality. We study the 19-dimensional pMSSM, including experimental constraints from all sources and assessing the consistency of potential signals of new physics. We show that GAs excel at making a fast and accurate diagnosis of the cross-compatibility of a set of experimental constraints in such high dimensional models. In the case of the pMSSM, it is found that only ${\cal O}(10^4)$ model evaluations are required to obtain a best fit point in agreement with much more costly MCMC scans. This efficiency allows higher dimensional models to be falsified, and patterns in the spectrum identified, orders of magnitude more quickly. As examples of falsification, we consider the muon anomalous magnetic moment, and the Galactic Centre gamma-ray excess observed by Fermi-LAT, which could in principle be explained in terms of neutralino dark matter. We show that both observables cannot be explained within the pMSSM, and that they provide the leading contribution to the total goodness of the fit, with $χ^2_{δa_μ^{\mathrm{SUSY}}}\approx12$ and $χ^2_{\rm GCE}\approx 155$, respectively.