arXiv subjects

Fernando J. Gómez-Ruiz

Publications and source records attributed to Fernando J. Gómez-Ruiz.

14 recordsLinked to original sources

arXiv2026

Universal Resources for QAOA and Quantum Annealing

The Quantum Approximate Optimization Algorithm (QAOA) is a variational ansatz that resembles the Trotterized dynamics of a Quantum Annealing (QA) protocol. This work formalizes this connection formally and empirically, showing the angles of a multilayer QAOA circuit converge to universal QA trajectories. Furthermore, the errors in both QAOA circuits and QA paths act as thermal excitations in pseudo-Boltzmann probability distributions whose temperature decreases with the invested resource -- i.e. integrated angles or total time -- and which in QAOA also contain a higher temperature arising from the Trotterization. This also means QAOA and QA are cooling protocols and simulators of partition functions whose target temperature can be tuned by rescaling the universal trajectory. The average cooling power of both methods exhibits favorable algebraic scalings with respect to the target temperature and problem size, whereby in QAOA the coldest temperature is inversely proportional to the number of layers, $T\sim 1/p$, and to the integrated angles -- or integrated interactions in QA.

quant-ph↗

arXiv2025

Spin Glass Dynamics on Complex Hardware Topologies: A Bond-Correlated Percolation Approach

Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin-glass models provide a natural framework to explore this connection, as their energy landscapes are governed by competing interactions and constrained topologies. We investigate the non-exponential relaxation behavior of spin glasses on network architectures relevant to quantum annealing hardware -- such as finite size Chimera, Pegasus, and Zephyr graphs -- where embedding constraints and finite connectivity strongly modulate the distribution of barriers and metastable states. This slow relaxation arises from the combined effects of frustration and disorder, which persist even beyond the conventional spin-glass transition. Within the Fortuin-Kasteleyn-Coniglio-Klein (FKCK) cluster formalism, the appearance of unfrustrated cluster regions gives rise to multiple relaxation scales, as distinct domains follow different dynamical pathways across a rugged energy landscape. This framework enables a more comprehensive characterization of spin-glass energy landscapes and offers valuable insight into how topological constraints and disorder jointly govern relaxation dynamics, providing quantitative benchmarks for evaluating the performance and limitations of quantum annealing architectures.

cond-mat.stat-mech↗

arXiv2025

Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States

We investigate the effects of coupling a local electromagnetic cavity to a segment of a topological Kitaev chain (KC), with particular emphasis on the interplay between photons and Majorana zero modes (MZMs). In addition to the well-known {\it scissor effect}-which effectively partitions the chain and isolates free MZMs in the bulk-we provide evidence of non-trivial fusion rules and braiding operations, hallmark signatures of non-Abelian anyons, enabled by spatially selective ultrastrong KC-cavity coupling. We propose that these distinctive MZM properties can be experimentally probed via fermionic parity measurements and photon-induced Berry phases. Furthermore, we demonstrate that, in the so-called sweet-spot regime, the coupled system can be mapped onto a Rabi-like model with a homodyne-rotated quadrature, offering a simplified yet powerful theoretical description. Exploiting the symmetry of fermionic modes within a two-site cavity configuration, we also show the feasibility of generating hybrid MZM-polariton Schrödinger cat states. Our findings offer a novel approach to manipulating topological quantum matter through local light-matter interactions and provide theoretical tools for future experimental realizations in platforms such as quantum materials or superconducting circuits.

quant-ph↗

arXiv2025

Squeezing generation crossing a mean-field critical point: Work statistics, irreversibility and critical fingerprints

Understanding the dynamical consequences of quantum phase transitions on thermodynamical quantities, such as work statistics and entropy production, is one of the most intriguing aspect of quantum many-body systems, pinpointing the emergence of irreversibility to critical features. In this work, we investigate the critical fingerprints appearing in these key thermodynamical quantities for a mean-field critical system undergoing a finite-time cycle, starting from a thermal state at a generic inverse temperature. In contrast to non-zero dimensional many-body systems, the presence of a mean-field critical point in a finite-time cycle leads to constant irreversible work even in the limit of infinitely slow driving. This links with the fact that a slow finite-time cycle results in a constant amount of squeezing, which enables us to derive analytical expressions for the work statistics and irreversible entropy, depending solely on the mean-field critical exponents and the functional form of the control parameter near the critical point. We find that the probability of observing negative work values, corresponding to negative irreversible entropy, is inversely proportional to the time the system remains near to the critical point, and this trend becomes less pronounced the lower the temperature of the initial thermal state. Finally, we determine the irreversibility traits under squeezing generation at zero-temperature using the relative entropy of coherence.

quant-ph↗

arXiv2025

Quantum Chaos in Random Ising Networks

We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erdős-Rényi network. This is achieved by studying local spectral measures such as the level spacing and the level velocity statistics. A spectral form factor analysis is also performed as a global measure, probing energy level correlations at arbitrary spectral distances. Our findings show that these measures capture the breakdown of chaotic behavior upon varying the connectivity and strength of the transverse field in various regimes. We demonstrate that the level spacing statistics and the spectral form factor signal this breakdown for sparsely and densely connected networks. The velocity statistics capture the surviving chaotic signatures in the sparse limit. However, these integrable-like regimes extend over a vanishingly small segment in the full range of connectivity.

cond-mat.dis-nn↗

arXiv2024

Quantum information scrambling in adiabatically-driven critical systems

Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Information scrambling is intimately linked to the thermalization of isolated quantum many-body systems, and has been typically studied in a sudden quench scenario. Here, we extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution. In particular, we analyze how the symmetry-breaking information of an initial state is scrambled in adiabatically driven integrable systems, such as the Lipkin--Meshkov--Glick and quantum Rabi models. Following a time-dependent protocol that drives the system from symmetry-breaking to a normal phase, we show how the initial information is scrambled, even for perfect adiabatic evolutions, as indicated by the expectation value of a suitable observable. We detail the underlying mechanism for quantum information scrambling, its relation to ground- and excited-state quantum phase transitions, and quantify the degree of scrambling in terms of the number of eigenstates that participate in the encoding of the initial symmetry-breaking information. While the energy of the final state remains unaltered in an adiabatic protocol, the relative phases among eigenstates are scrambled, and so is the symmetry-breaking information. We show that a potential information retrieval, following a time-reversed protocol, is hindered by small perturbations, as indicated by a vanishingly small Loschmidt echo and out-of-time-ordered correlators. The reported phenomenon is amenable for its experimental verification, and may help in the understanding of information scrambling in critical quantum many-body systems.

quant-ph↗

arXiv2024

Exploring Supersymmetry: Interchangeability Between Jaynes-Cummings and Anti-Jaynes-Cummings Models

The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated.

quant-ph↗

arXiv2024

Chapter: Vulnerability of Quantum Information Systems to Collective Manipulation

The highly specialist terms `quantum computing' and `quantum information', together with the broader term `quantum technologies', now appear regularly in the mainstream media. While this is undoubtedly highly exciting for physicists and investors alike, a key question for society concerns such systems' vulnerabilities -- and in particular, their vulnerability to collective manipulation. Here we present and discuss a new form of vulnerability in such systems, that we have identified based on detailed many-body quantum mechanical calculations. The impact of this new vulnerability is that groups of adversaries can maximally disrupt these systems' global quantum state which will then jeopardize their quantum functionality. It will be almost impossible to detect these attacks since they do not change the Hamiltonian and the purity remains the same; they do not entail any real-time communication between the attackers; and they can last less than a second. We also argue that there can be an implicit amplification of such attacks because of the statistical character of modern non-state actor groups. A countermeasure could be to embed future quantum technologies within redundant classical networks. We purposely structure the discussion in this chapter so that the first sections are self-contained and can be read by non-specialists.

quant-ph↗

arXiv2023

Energy transfer in $N$-component nanosystems enhanced by pulse-driven vibronic many-body entanglement

The processing of energy by transfer and redistribution plays a key role in the evolution of dynamical systems. At the ultrasmall and ultrafast scale of nanosystems, quantum coherence could in principle also play a role and has been reported in many pulse-driven nanosystems (e.g. quantum dots and even the microscopic Light-Harvesting Complex II (LHC-II) aggregate). Typical theoretical analyses cannot easily be scaled to describe these general $N$-component nanosystems; they do not treat the pulse dynamically; and they approximate memory effects. Here our aim is to shed light on what new physics might arise beyond these approximations. We adopt a purposely minimal model such that the time-dependence of the pulse is included explicitly in the Hamiltonian. This simple model generates complex dynamics: specifically, pulses of intermediate duration generate highly entangled vibronic (i.e. electronic-vibrational) states that spread multiple excitons -- and hence energy -- maximally within the system. Subsequent pulses can then act on such entangled states to efficiently channel subsequent energy capture. The underlying pulse-generated vibronic entanglement increases in strength and robustness as $N$ increases.

quant-ph↗

arXiv2022

Experimental validation of the Kibble-Zurek Mechanism on a Digital Quantum Computer

The Kibble-Zurek mechanism (KZM) captures the essential physics of nonequilibrium quantum phase transitions with symmetry breaking. KZM predicts a universal scaling power law for the defect density which is fully determined by the system's critical exponents at equilibrium and the quenching rate. We experimentally tested the KZM for the simplest quantum case, a single qubit under the Landau-Zener evolution, on an open access IBM quantum computer (IBM-Q). We find that for this simple one-qubit model, experimental data validates the central KZM assumption of the adiabatic-impulse approximation for a well isolated qubit. Furthermore, we report on extensive IBM-Q experiments on individual qubits embedded in different circuit environments and topologies, separately elucidating the role of crosstalk between qubits and the increasing decoherence effects associated with the quantum circuit depth on the KZM predictions. Our results strongly suggest that increasing circuit depth acts as a decoherence source, producing a rapid deviation of experimental data from theoretical unitary predictions.

quant-ph↗

arXiv2022

Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scale with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft anti-periodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except by an additive term, that becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.

cond-mat.stat-mech↗

arXiv2022

Benchmarking quantum annealing dynamics: the spin-vector Langevin model

The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the annealing dynamics in real-time.We introduce the spin-vector Langevin (SVL) model as an alternative benchmark in which the time evolution is described by Langevin dynamics. The SVL model is shown to provide a more stringent test than the SVMC model for the identification of quantum signatures in the performance of quantum annealing devices, as we illustrate by describing the Kibble-Zurek scaling associated with the dynamics of symmetry breaking in the transverse field Ising model, recently probed using D-Wave machines. Specifically, we show that D-Wave data are reproduced by the SVL model.

quant-ph↗

arXiv2020

Quantum Non-equilibrium Many-Body Spin-Photon Systems

In this Ph.D. thesis dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. The research is neither restricted to static properties or long-term relaxation evolutions nor does it neglect effects on any relevant subsystem as is frequently done with the environment in master equations approaches. The focus of this work is to explore different quantum systems during several regimes of operations, then discover results that might be of interest to quantum control, and hence to quantum computation and quantum information processing. Our main results can be summarized as follows in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.

cond-mat.quant-gas↗

arXiv2020

Full Counting Statistics of Topological Defects After Crossing a Phase Transition

We consider the number distribution of topological defects resulting from the finite-time crossing of a continuous phase transition and identify signatures of universality beyond the mean value, predicted by the Kibble-Zurek mechanism. Statistics of defects follows a binomial distribution with $\mathcal{N}$ Bernouilli trials associated with the probability of forming a topological defect at the locations where multiple domains merge. All cumulants of the distribution are predicted to exhibit a common universal power-law scaling with the quench time in which the transition is crossed. Knowledge of the distribution is used to discuss the onset of adiabatic dynamics and bound rare events associated with large deviations.

cond-mat.stat-mech↗