Luca Nutricati

Abstract:

One of the main challenges in solving combinatorial optimisation problems with quantum annealers is the emergence of extremely small energy gaps between the ground state and the first excited state of the annealing Hamiltonian. These small gaps may be symptoms of an underlying first-order phase transition, which, according to the adiabatic theorem, can significantly extend the required anneal time, making practical implementation effectively infeasible. In this paper we demonstrate that attaching an XX-catalyst on all the edges of a graph upon which a MWIS (Maximum Weighted Independent Set) problem is defined, significantly enhances the minimum energy gap. Remarkably, our analysis shows that the smaller the energy gap, the more effective the catalyst is in opening it. This result is based on a detailed statistical analysis performed on a large number of randomly generated MWIS problem instances on both Erdõs–Rényi and Barabáasi–Albert graphs. We perform the analysis using both stoquastic and non-stoquastic catalysts.

Abstract:

We investigate the use of quantum computing algorithms on real quantum hardware to tackle the computationally intensive task of feature selection for light-weight medical image datasets. Feature selection is often formulated as a k of n selection problem, where the complexity grows binomially with increasing k and n. Quantum computers, particularly quantum annealers, are well-suited for such problems, which may offer advantages under certain problem formulations. We present a method to solve larger feature selection instances than previously demonstrated on commercial quantum annealers. Our approach combines a linear Ising penalty mechanism with subsampling and thresholding techniques to enhance scalability. The method is tested in a toy problem where feature selection identifies pixel masks used to reconstruct small-scale medical images. We compare our approach against a range of feature selection strategies, including randomized baselines, classical supervised and unsupervised methods, combinatorial optimization via classical and quantum solvers, and learning-based feature representations. The results indicate that quantum annealing-based feature selection is effective for this simplified use case, demonstrating its potential in high-dimensional optimization tasks. However, its applicability to broader, real-world problems remains uncertain, given the current limitations of quantum computing hardware. While learned feature representations such as autoencoders achieve superior reconstruction performance, they do not offer the same level of interpretability or direct control over input feature selection as our approach.

Abstract:

In this paper, we prove a new nonrenormalization theorem which arises from UV/IR mixing. This theorem and its corollaries are relevant for all four-dimensional perturbative tachyon-free closed string theories which can be realized from higher-dimensional theories via geometric compactifications. As such, our theorem therefore holds regardless of the presence or absence of spacetime supersymmetry and regardless of the gauge symmetries or matter content involved. This theorem resolves a hidden clash between modular invariance and the process of decompactification, and enables us to uncover a number of surprising phenomenological properties of these theories. Chief among these is the fact that certain physical quantities within such theories cannot exhibit logarithmic or power-law running and instead enter an effective fixed-point regime above the compactification scale. This cessation of running occurs as the result of the UV/IR mixing inherent in the theory. These effects apply not only for gauge couplings but also for the Higgs mass and other quantities of phenomenological interest, thereby eliminating the logarithmic and/or power-law running that might have otherwise appeared for such quantities. These results illustrate the power of UV/IR mixing to tame divergences - even without supersymmetry - and reinforce the notion that UV/IR mixing may play a vital role in resolving hierarchy problems without supersymmetry.

Abstract:

In this paper we conduct a general, model-independent analysis of the running of gauge couplings within closed string theories. Unlike previous discussions in the literature, our calculations fully respect the underlying modular invariance of the string and include the contributions from the infinite towers of string states which are ultimately responsible for many of the properties for which string theory is famous, including an enhanced degree of finiteness and UV/IR mixing. In order to perform our calculations, we adopt a formalism that was recently developed for calculations of the Higgs mass within such theories, and demonstrate that this formalism can also be applied to calculations of gauge couplings. In general, this formalism gives rise to an "on-shell"effective field theory (EFT) description in which the final results are expressed in terms of supertraces over the physical string states, and in which these quantities exhibit an EFT-like "running"as a function of an effective spacetime mass scale. We find, however, that the calculation of the gauge couplings differs in one deep way from that of the Higgs mass: while the latter results depend on purely on-shell supertraces, the former results have a different modular structure which causes them to depend on off-shell supertraces as well. In some regions of parameter space, our results demonstrate how certain expected field-theoretic behaviors can emerge from the highly UV/IR-mixed environment. In other situations, by contrast, our results give rise to a number of intrinsically stringy behaviors that transcend what might be expected within an effective field theory approach.

Abstract:

Diophantine problems arise frequently in physics, in for example anomaly cancellation conditions, string consistency conditions and so forth. We present methods to solve such problems to high order on annealers that are based on the quadratic Ising Model. This is the intrinsic framework for both quantum annealing and for common forms of classical simulated annealing. We demonstrate the method on so-called Taxicab numbers (discovering some apparently new ones), and on the realistic problem of anomaly cancellation in U(1) extensions of the Standard Model.