arXiv subjects

Juan Román-Roche

Publications and source records attributed to Juan Román-Roche.

14 recordsLinked to original sources

arXiv2026

Robustness of quantized Hall resistivity under cavity coupling at zero temperature

Recent experiments have shown that strong light-matter coupling in electromagnetic cavities can modify transport properties of quantum Hall systems through the formation of Landau polaritons, prompting questions about the robustness of topological protection. While earlier theory demonstrated that the Hall conductivity can be modified at finite temperature and finite polariton lifetime (or finite broadening), experiments primarily probe the resistivity tensor. Our phenomenological model reveals an asymmetry between conductivity and resistivity in quantum Hall systems under strong light-matter interaction, showing that at zero temperature the Hall resistivity remains completely immune to cavity-induced modifications arising from polariton broadening, independent of the light-matter coupling strength. These results provide a deeper explanation for the absence of renormalization in the von Klitzing constant in experiments probing the even QH plateaus through the Hall resistivity at low temperature, and clarify the distinct roles of dissipation and strong light-matter coupling in hybrid light-matter systems.

cond-mat.mes-hall↗

arXiv2025

A genetic algorithm to generate maximally orthogonal frames in complex space

A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that can generate maximally orthogonal frames of arbitrary size $n$ in $d$-dimensional complex space. First, we formalize the concept of maximally orthogonal frame and demonstrate that it depends on the choice of an energy function to weigh the different pairwise overlaps between vectors. Then, we discuss the relation between different energy functions and well-known frame varieties such as tight and Grassmannian frames and complex projective $p$-designs. Obtaining maximally orthogonal frames poses a global non-convex minimization problem. We discuss the relation with established numerical problems such as the Thomson problem and the problem of finding optimal packings in complex projective space. To tackle the minimization, we design a hybrid genetic algorithm that features local optimization of the parents. To assess the performance of the algorithm, we propose two visualization techniques that allow us to analyze the coherence and uniformity of high-dimensional frames. The genetic algorithm is able to produce highly-symmetric universal frames, such as equiangular tight frames, symmetric, informationally complete, positive operator-valued measurements (SIC-POVMs) and maximal sets of mutually unbiased bases, for configurations of up to $d=6$ and $n=36$, with runtimes of the order of several minutes on a regular desktop computer for the largest configurations.

physics.comp-ph↗

arXiv2025

Qudit Machine Learning

We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST datasets. We explore various learning models in the metric learning framework, along with different encoding strategies. In particular, we employ data re-uploading techniques and maximally orthogonal states to accommodate input data within low-dimensional systems. Our findings reveal optimal strategies, indicating that when the dimension of input feature data and the number of classes are not significantly larger than the qudit's dimension, our results show favorable comparisons against the best classical models. This trend holds true even for small quantum systems, with dimensions d<5 and utilizing algorithms with a few layers (L=1,2). However, for high-dimensional data such as MNIST, we adopt a hybrid approach involving dimensional reduction through a convolutional neural network. In this context, we observe that small quantum systems often act as bottlenecks, resulting in lower accuracy compared to their classical counterparts.

quant-ph↗

arXiv2025

First- and second-order quantum phase transitions in the long-range unfrustrated antiferromagnetic Ising chain

We study the ground-state phase diagram of an unfrustrated antiferromagnetic Ising chain with longitudinal and transverse fields in the full range of interactions: from all-to-all to nearest-neighbors. First, we solve the model analytically in the strong long-range regime, confirming in the process that a mean-field treatment is exact for this model. We compute the order parameter and the correlations and show that the model exhibits a tricritical point where the phase transition changes from first to second order. This is in contrast with the nearest-neighbor limit where the phase transition is known to be second order. To understand how the order of the phase transition changes from one limit to the other, we tackle the analytically-intractable interaction ranges numerically, using a variational quantum Monte Carlo method with a neural-network-based ansatz, the visual transformer. We show how the first-order phase transition shrinks with decreasing interaction range and establish approximate boundaries in the interaction range for which the first-order phase transition is present. Finally, we establish that the key ingredient to stabilize a first-order phase transition and a tricritical point is the presence of ferromagnetic interactions between spins of the same sublattice on top of antiferromagnetic interactions between spins of different sublattices. Tunable-range unfrustrated antiferromagnetic interactions are just one way to implement such staggered interactions.

quant-ph↗

arXiv2025

Linear response theory for cavity QED materials at arbitrary light-matter coupling strengths

We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling, including symmetry-broken phases. We present and compare two different approaches. First, using a coherent path integral formulation for the partition function to obtain thermal Green functions. This approach relies on a saddle point expansion for the action, that can be truncated in the thermodynamic limit. Second, by formulating the equations of motion for the retarded Green functions and solving them. We use a mean-field decoupling of high-order Green functions in order to obtain a closed, solvable system of equations. Both approaches yield identical results in the calculation of response functions for the cavity and material. These are obtained in terms of the bare cavity and material responses. In combination, the two techniques clarify the validity of a mean-field decoupling in correlated light-matter systems and provide complementary means to compute finite-size corrections to the thermodynamic limit. The theory is formulated for a general model that encompasses most of the systems typically considered in the field of cavity QED materials. Finally, we provide a detailed application of the theory to the Quantum Hall effect and to a collection of spin models.

quant-ph↗

arXiv2025

Bound polariton states in the Dicke-Ising model

We present a study of hybrid light-matter excitations in cavity QED materials using the Dicke-Ising model as a theoretical framework. Leveraging linear response theory, we derive the exact excitations of the system in the thermodynamic limit. Our results demonstrate that the cavity can localize spin excitations, leading to the formation of bound polaritons, where the cavity acts as an impurity of the two-excitation band, localizing spin-wave pairs around single-spin domains. We derive the condition for the existence of these bound states and discuss its satisfiability in different regimes. Finally, we show that these effects persist in finite systems using exact-diagonalization calculations.

quant-ph↗

arXiv2024

Mumax3-cQED: an extension of Mumax3 to simulate magnon-photon interactions in cavity QED

We present an extension of the well-known micromagnetic package Mumax3 to simulate magnon-polaritons in realistic magnetic materials and nanostructures. Mumax3-cQED leverages the full GPU-accelerated capabilities of Mumax3 to model standard spin-spin interactions and the coupling of magnetic moments to external space- and time-dependent magnetic fields, with the additional unique feature of including the coupling to a cavity. We validate the code against results obtained from the Dicke model in both the paramagnetic and the superradiant phases. We show that hybrid magnon-light states can be calculated, as well as the non-equilibrium dynamics and their approach to equilibrium. In addition, we demonstrate the potential of Mumax3-cQED to reproduce experimental results and design magnon-cavity experiments, including three-dimensional and coplanar waveguide resonators. The code is fully available and will be useful for designing experiments involving microscopic saturated ferromagnets as well as systems featuring spin textures such as domain walls, vortices, or skyrmions.

quant-ph↗

arXiv2023

Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation

We present an exact analytical solution for quantum strong long-range models in the canonical ensemble by extending the classical solution proposed in [Campa et al., J. Phys. A 36, 6897 (2003)]. Specifically, we utilize the equivalence between generalized Dicke models and interacting quantum models as a generalization of the Hubbard-Stratonovich transformation. To demonstrate our method, we apply it to the Ising chain in transverse field and discuss its potential application to other models, such as the Fermi-Hubbard model, combined short and long-range models and models with antiferromagnetic interactions. Our findings indicate that the critical behaviour of a model is independent of the range of interactions, within the strong long-range regime, and the dimensionality of the model. Moreover, we show that the order parameter expression is equivalent to that provided by mean-field theory, thus confirming the exactness of the latter. Finally, we examine the algebraic decay of correlations and characterize its dependence on the range of interactions in the full phase diagram.

quant-ph↗

arXiv2023

Circuit Complexity through phase transitions: consequences in quantum state preparation

In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.

quant-ph↗

arXiv2022

Quantum kernels to learn the phases of quantum matter

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here, we exploit quantum kernels instead. They are naturally related to the \emph{fidelity} and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent $ν$. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor.

quant-ph↗

arXiv2022

Effective theory for matter in non-perturbative cavity QED

Starting from a general material system of $N$ particles coupled to a cavity, we use a coherent-state path integral formulation to produce a non-perturbative effective theory for the material degrees of freedom. We tackle the effects of image charges, the $A^2$ term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large-$N$ limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature.

quant-ph↗

arXiv2021

Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ansätze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.

quant-ph↗

arXiv2021

Photon Condensation and Enhanced Magnetism in Cavity QED

A system of magnetic molecules coupled to microwave cavities ($LC$ resonators) undergoes the equilibrium superradiant phase transition. The transition is experimentally observable. The effect of the coupling is first illustrated by the vacuum-induced ferromagnetic order in a quantum Ising model and then by the modification of the magnetic phase diagram of ${\rm Fe_8}$ dipolar crystals, exemplifying the cooperation between intrinsic and photon-induced spin-spin interactions. Finally, a transmission experiment is shown to resolve the transition, measuring the quantum electrodynamical control of magnetism.

quant-ph↗

arXiv2020

Bound states in ultrastrong waveguide QED

We discuss the properties of bound states in finite-bandwidth waveguide QED beyond the Rotating Wave Approximation or excitation number conserving light-matter coupling models. Therefore, we extend the \emph{standard} calculations to a broader range of light-matter strengths, in particular, in the so-called ultrastrong coupling regime. We do this using the Polaron technique. Our main results are as follows. We compute the spontaneous emission rate, which is renormalized as compared to the Fermi Golden Rule formula. We generalise the existence criteria for bound states, their properties and their role in the qubits thermalization. We discuss effective spin-spin interactions through both vacuum fluctuations and bound states. Finally, we sketch a perfect state-transfer protocol among distant emitters.

quant-ph↗