arXiv subjects

Miguel Angel Garcia-March

Publications and source records attributed to Miguel Angel Garcia-March.

11 recordsLinked to original sources

arXiv2026

Emergence of a Macroscopic Cat State and Multi-Channel Entanglement in a Frustrated Cluster Spin Chain

We study a one-dimensional frustrated spin chain, which combines cluster-Ising and anisotropic next-nearest neighbor Ising models. We first offer a historical perspective that justifies the studied model. Then we study in detail the two quantum phases and prove that they are separated by a first order quantum phase transition. On one side, the ground state corresponds to a ferromagnetic phase, shows the presence of macroscopic cat states, and a small gap that closes in the thermodynamic limit. On the other phase, competing interactions avoid the establishment of a topological phase, though it conserves large incommensurate quantum correlations. We prove it is fundamentally distinct from a simple paramagnet, and we name it an incommensurate phase. This is a gapped phase, which gap does not close in the thermodynamic limit. While in the ferromagnetic phase there are two dominant Schmidt coefficients, in the incommensurate phase there are four. This corresponds to four distinct bipartite entanglement channels contributing substantially to the ground state. Finally, we discuss the utility of the macroscopic cat states for quantum metrology applications and the experimental feasibility of the system.

quant-ph↗

arXiv2026

Adaptive time Compressed QITE (ACQ) and its geometrical interpretation

Imaginary time evolution (ITE) is a well-established method for ground-state preparation, a fundamental problem in many fields such as materials science, chemistry, and optimization. Quantum ITE (QITE) approximates this evolution on quantum hardware but suffers from high circuit depth and numerous measurements. In this work we introduce adaptive-time compressed QITE (ACQ), a novel algorithm that reduces resource-cost by combining adaptive time steps with circuit compression. This approach leverages geometric insights by characterizing its relationship to geodesic trajectories with a measure that distinguishes trajectories in CPN. Recalling that ITE is a gradient flow on the complex projective plane $\mathbb{CP}^N$, such trajectory measures allow one to measure the deviation from geodesicity of said flow. For Hamiltonians with only two distinct eigenvalues (spectral cardiality), ITE and QITE exactly trace geodesics, this fact motivates an adaptive strategy for systems whose corresponding spectral cardinality is greater than 2, where QITE unitaries are reused until an energy increase signals departure from the ITE path. This is implemented via a line search for energy minimization. Circuit compression is achieved by approximating the sequence of QITE unitaries with a single element of a one-parameter group. Numerical simulations on the transverse field Ising model and the Heisenberg model demonstrate that ACQ achieves comparable fidelity to standard QITE while significantly reducing the number of QITE optimizations and maintaining fixed circuit depth during propagation. Gate-count estimates and an analysis of the fidelity scaling with truncation parameters are provided. A gate count and performance comparison with the state of the art method double bracket QITE is also performed.

quant-ph↗

arXiv2025

Understanding Quantum Imaginary Time Evolution and its Variational form

Many computationally hard problems can be encoded in quantum Hamiltonians. The solution to these problems is given by the ground states of these Hamiltonians. A state-of-the-art algorithm for finding the ground state of a Hamiltonian is the so-called Quantum Imaginary Time Evolution (QITE) which approximates imaginary time evolution by a unitary evolution that can be implemented in quantum hardware. In this paper, we review the original algorithm together with a comprehensive computer program, as well as, the variational version of it.

quant-ph↗

arXiv2025

Objective comparison of methods to decode anomalous diffusion

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

physics.data-an↗

arXiv2023

Preface: Characterisation of Physical Processes from Anomalous Diffusion Data

Preface to the special issue "Characterisation of Physical Processes from Anomalous Diffusion Data" associated with the Anomalous Diffusion Challenge ( https://andi-challenge.org ) and published in Journal of Physics A: Mathematical and Theoretical. The list of articles included in the special issue can be accessed at https://iopscience.iop.org/journal/1751-8121/page/Characterisation-of-Physical-Processes-from-Anomalous-Diffusion-Data .

cond-mat.stat-mech↗

arXiv2022

Haake-Lewenstein-Wilkens approach to spin-glasses revisited

We revisit the Haake-Lewenstein-Wilkens (HLW) approach to Edwards-Anderson (EA) model of Ising spin glass [Phys. Rev. Lett. 55, 2606 (1985)]. This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, qEA. We use saddle point/steepest descent method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that qEA >0 at 0 <T <Tc in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts spin glass order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; ii) There is (no) spin glass transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak.

cond-mat.dis-nn↗

arXiv2020

AnDi: The Anomalous Diffusion Challenge

The deviation from pure Brownian motion generally referred to as anomalous diffusion has received large attention in the scientific literature to describe many physical scenarios. Several methods, based on classical statistics and machine learning approaches, have been developed to characterize anomalous diffusion from experimental data, which are usually acquired as particle trajectories. With the aim to assess and compare the available methods to characterize anomalous diffusion, we have organized the Anomalous Diffusion (AnDi) Challenge (\url{http://www.andi-challenge.org/}). Specifically, the AnDi Challenge will address three different aspects of anomalous diffusion characterization, namely: (i) Inference of the anomalous diffusion exponent. (ii) Identification of the underlying diffusion model. (iii) Segmentation of trajectories. Each problem includes sub-tasks for different number of dimensions (1D, 2D and 3D). In order to compare the various methods, we have developed a dedicated open-source framework for the simulation of the anomalous diffusion trajectories that are used for the training and test datasets. The challenge was launched on March 1, 2020, and consists of three phases. Currently, the participation to the first phase is open. Submissions will be automatically evaluated and the performance of the top-scoring methods will be thoroughly analyzed and compared in an upcoming article.

cond-mat.stat-mech↗

arXiv2020

Machine learning method for single trajectory characterization

In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion, and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate even very short trajectories to the underlying diffusion mechanism with a high accuracy. In addition, the method is able to classify the motion according to normal or anomalous diffusion, and determine its anomalous exponent with a small error. The method provides highly accurate outputs even when working with very short trajectories and in the presence of experimental noise. We further demonstrate the application of transfer learning to experimental and simulated data not included in the training/testing dataset. This allows for a full, high-accuracy characterization of experimental trajectories without the need of any prior information.

cond-mat.stat-mech↗

arXiv2014

Measure synchronization in quantum many-body systems

The concept of measure synchronization between two coupled quantum many-body systems is presented. In general terms we consider two quantum many-body systems whose dynamics gets coupled through the contact particle-particle interaction. This coupling is shown to produce measure synchronization, a generalization of synchrony to a large class of systems which takes place in absence of dissipation. We find that in quantum measure synchronization, the many-body quantum properties for the two subsystems, e.g. condensed fractions and particle fluctuations, behave in a coordinated way. To illustrate the concept we consider a simple case of two species of bosons occupying two distinct quantum states. Measure synchronization can be readily explored with state-of-the-art techniques in ultracold atomic gases and, if propertly controlled, be employed to share quantum correlations between different degrees of freedom.

cond-mat.quant-gas↗

arXiv2014

The key role of off-axis singularities in free-space vortex transmutation

We experimentally demonstrate the generation of off-axis phase singularities in a vortex transmutation process induced by the breaking of rotational symmetry. The process takes place in free space by launching a highly-charged vortex, owning full rotational symmetry, into a linear thin diffractive element presenting discrete rotational symmetry. It is shown that off-axis phase singularities follow straight dark rays bifurcating from the symmetry axis. This phenomenon may provide new routes towards the spatial control of multiple phase singularities for applications in atom trapping and particle manipulation.

physics.optics↗

arXiv2012

Quantum gas mixtures in different correlation regimes

We present a many-body description for two-component ultracold bosonic gases when one of the species is in the weakly interacting regime and the other is either weakly or strongly interacting. In the one-dimensional limit the latter case system is a hybrid in which a Tonks-Girardeau gas is immersed in a Bose-Einstein condensate, which is an example of a new class of quantum system involving a tunable, superfluid environment. We describe the process of phase separation microscopically and semiclassically in both situations and show that the quantum correlations are maintained in the separated phase.

cond-mat.quant-gas↗