arXiv subjects

Luca A. Nutricati

Publications and source records attributed to Luca A. Nutricati.

13 recordsLinked to original sources

arXiv2026

Calabi-Yau Metrics with Full Moduli Dependence

Recent advances in numerical and machine-learning methods have enabled highly accurate constructions of Ricci-flat metrics on compact Calabi-Yau three-folds. For phenomenological applications it is crucial to understand how these metrics vary across moduli space. In this work, we construct approximate analytic expressions for Ricci-flat Calabi-Yau metrics with explicit complex-structure and Kähler moduli dependence by combining machine-learned numerical data with symbolic regression. Our approach is based on an explicit Ansatz for the Kähler potential with moduli-dependent coefficients. Fitting this Ansatz to numerical data and applying symbolic regression allows us to reconstruct analytic formulae for these coefficients, thereby obtaining approximate Ricci-flat metrics with explicit moduli dependence. We apply the construction to a one-parameter family of bi-cubic three-folds in $\mathbb{P}^2 \times \mathbb{P}^2$, achieving percent-level agreement with the underlying numerical data.

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arXiv2026

Calabi-Yau Metrics with Kähler Moduli Dependence

We present a method to construct approximate analytic expressions for Ricci-flat Kähler metrics on Calabi-Yau threefolds with explicit dependence on the Kähler moduli. Our strategy combines numerical data obtained from machine learning with an explicit analytic Ansatz for the Kähler potential and symbolic regression methods. Specifically, we use neural networks to learn the Kähler potential at selected points in Kähler moduli space, fit this data to analytic expressions with Kähler moduli-dependent parameters, and determine an analytic form of these coefficients as functions of the Kähler moduli using symbolic regression. In this way, we reconstruct closed-form approximations to the Ricci-flat metric that retain explicit Kähler-moduli dependence. We apply this method to two Calabi-Yau threefolds with $h^{1,1}=2$, namely a bicubic hypersurface in $\mathbb{P}^2 \times \mathbb{P}^2$ and a bi-degree $(2,4)$ hypersurface in $\mathbb{P}^1 \times \mathbb{P}^3$, both of which admit nontrivial discrete symmetry groups that simplify the structure of the metric. In both cases, the resulting analytic expressions reproduce the numerically learned Kähler potentials with percent-level accuracy and yield a Ricci-flatness measure that remains sufficiently small across the sampled region. Our results represent a concrete bridge between purely numerical results for Calabi-Yau metrics and analytic constructions, opening the door to a systematic study of their dependence on Kähler moduli.

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arXiv2026

Quantum Annealing: Optimisation, Sampling, and Many-Body Dynamics

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.

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arXiv2025

Enhancement of quantum annealing via n-local catalysts

The potential quantum speedup in solving optimization problems via adiabatic quantum annealing is often hindered by the closing of the energy gap during the anneal, especially when this gap scales exponentially with system size. In this work, we alleviate this bottleneck by demonstrating that for the NP-complete Maximum Weighted Independent Set (MWIS) problem, an informed choice of $n-$local catalysts (operators involving $n$ qubits) can re-open the gap during the annealing process. By analyzing first-order phase transitions in toy instances of the MWIS problem, we first identify direct-tunneling catalysts that effectively eliminate the transition and provide an analytical discussion on when the sign of the catalyst influences its impact. We then reveal that $n-$local catalysts exponentially improve gap scaling and in certain scenarios are as effective as direct tunnel coupling between two minima. Utilizing this understanding, we show that they also increase the efficiency of ground state preparation via adiabatic quantum annealing in random graphs and analytically demonstrate the necessity of their placement across unfrustrated loops in the graph for effective performance in MWIS problems. Additionally, using a circuit implementation of the $n$-local catalyst (requiring $2n$ nearest-neighbour gates), we demonstrate that both the circuit depth and the total number of gates required to solve the problem are reduced by several orders of magnitude when compared to the discrete-time version of traditional quantum annealing using local drivers. Our analysis suggests that non-local quantum fluctuations entangling multiple qubits as a catalyst are key to achieving the desired quantum advantage.

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arXiv2025

Reproducing Standard Model Fermion Masses and Mixing in String Theory: A Heterotic Line Bundle Study

Deriving the Yukawa couplings and the resulting fermion masses and mixing angles of the Standard Model (SM) from a more fundamental theory remains one of the central outstanding problems in theoretical high-energy physics. It has long been recognised that string theory provides a framework within which this question can, at least in principle, be addressed. While substantial progress has been made in studying flavour physics in string compactifications over the past few decades, a concrete string construction that reproduces the full set of observed SM flavour parameters remains unknown. Here, we take a significant step in this direction by identifying two explicit $E_8 \times E_8$ heterotic string models compactified on a Calabi-Yau threefold with abelian, holomorphic, and poly-stable vector bundles with an (MS)SM spectrum. Subject to reasonable assumptions about the moduli, we show that these models reproduce the correct values of the quark and charged lepton masses, as well as the quark mixing parameters, at some point in their moduli spaces. The resulting four-dimensional theories are $\mathcal{N}=1$ supersymmetric, contain no exotic fields and realise a $μ$-term suppressed to the electroweak scale. While the issues of moduli stabilisation and supersymmetry breaking are not addressed here, our main result constitutes a proof of principle: there exist choices of topology and moduli within heterotic string compactifications which allow for an MSSM spectrum with the correct flavour parameters.

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arXiv2025

Quantum Annealing Feature Selection on Light-weight Medical Image Datasets

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. As problem sizes grow, classical approaches struggle to scale efficiently. Quantum computers, particularly quantum annealers, are well-suited for such problems, offering potential advantages in specific formulations. We present a method to solve larger feature selection instances than previously presented 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. 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.

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arXiv2024

Enhancing the Energy Gap of Random Graph Problems via XX-catalysts in Quantum Annealing

One of the bottlenecks in solving combinatorial optimisation problems using quantum annealers is the emergence of exponentially-closing energy gaps between the ground state and the first excited state during the annealing, which indicates that a first-order phase transition is taking place. The minimum energy gap scales inversely with the exponential of the system size, ultimately resulting in an exponentially large time required to ensure the adiabatic evolution. In this paper we demonstrate that employing multiple XX-catalysts 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 more severe the first-order phase transition, the more effective the catalyst is in opening the gap. This result is based on a detailed statistical analysis performed on a large number of randomly generated MWIS problem instances on both Erdős-Rényi and Barabási-Albert graphs. We also observe that similar performance cannot be achieved by the non-stoquastic version of the same catalyst, with the stoquastic catalyst being the preferred choice in this context.

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arXiv2024

A New Non-Renormalization Theorem from UV/IR Mixing

In this paper, we prove a new non-renormalization theorem which arises from UV/IR mixing. This theorem and its corollaries are relevant for all four-dimensional tachyon-free closed string theories which can be realized from higher-dimensional theories via geometric compactifications. As such, they therefore apply 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.

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arXiv2023

String Model Building on Quantum Annealers

We explore for the first time the direct construction of string models on quantum annealers, and investigate their efficiency and effectiveness in the model discovery process. Through a thorough comparison with traditional methods such as simulated annealing, random scans, and genetic algorithms, we highlight the potential advantages offered by quantum annealers, which in this study promised to be roughly fifty times faster than random scans and genetic algorithm and approximately four times faster than simulated annealing.

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arXiv2023

Decoding Nature with Nature's Tools: Heterotic Line Bundle Models of Particle Physics with Genetic Algorithms and Quantum Annealing

The string theory landscape may include a multitude of ultraviolet embeddings of the Standard Model, but identifying these has proven difficult due to the enormous number of available string compactifications. Genetic Algorithms (GAs) represent a powerful class of discrete optimisation techniques that can efficiently deal with the immensity of the string landscape, especially when enhanced with input from quantum annealers. In this letter we focus on geometric compactifications of the $E_8\times E_8$ heterotic string theory compactified on smooth Calabi-Yau threefolds with Abelian bundles. We make use of analytic formulae for bundle-valued cohomology to impose the entire range of spectrum requirements, something that has not been possible so far. For manifolds with a relatively low number of Kahler parameters we compare the GA search results with results from previous systematic scans, showing that GAs can find nearly all the viable solutions while visiting only a tiny fraction of the solution space. Moreover, we carry out GA searches on manifolds with a larger numbers of Kahler parameters where systematic searches are not feasible.

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arXiv2023

On the Running of Gauge Couplings in String Theory

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.

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arXiv2022

A Genetic Quantum Annealing Algorithm

A genetic algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. We present an algorithm which enhances the classical GA with input from quantum annealers. As in a classical GA, the algorithm works by breeding a population of possible solutions based on their fitness. However, the population of individuals is defined by the continuous couplings on the quantum annealer, which then give rise via quantum annealing to the set of corresponding phenotypes that represent attempted solutions. This introduces a form of directed mutation into the algorithm that can enhance its performance in various ways. Two crucial enhancements come from the continuous couplings having strengths that are inherited from the fitness of the parents (so-called nepotism) and from the annealer couplings allowing the entire population to be influenced by the fittest individuals (so-called quantum-polyandry). We find our algorithm to be significantly more powerful on several simple problems than a classical GA.

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arXiv2022

Ising Machines for Diophantine Problems in Physics

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.

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