Examinando por Materia "Entrelazamiento cuántico"

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    Architecture dependence in the many-body entanglement structure of local quantum circuits
    (Universidad del Valle, 2025) Valencia Fonseca, Andrés Felipe; Madronero, Javier
    This work studies the architecture dependence on the entanglement structure in quantum circuits with at most two-qubit local gates, using the minimal cut formalism [1]. In the first stage, a cut growth model is developed to establish a classical upper bound for the estimation of Rényi entropies in random Clifford circuits [2]. Subsequently, an original graph-based computational algorithm proposed by the author is developed to efficiently compute minimal cuts in local quantum circuits, and numerical simulations are carried out to compare these results with those obtained through the direct calculation of Rényi entropies. A consistent numerical correspondence is observed between both approaches, which validates the minimal cut as an efficient method for characterizing entanglement dynamics and for recovering the characteristic fluctuations of the Kardar–Parisi–Zhang (KPZ) universality class. The results show that the dependence on architecture is reflected in the saturation scale of entanglement, which is reached in circuits whose area grows proportionally to the cube of the number of qubits. In this way, a scaling law is established that links the geometry of the circuit with the efficiency of entanglement generation. Overall, the study presented here contributes to a deeper understanding of the generic behavior of entanglement in quantum many-body systems.
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    Tensor network-based ansatz for the analysis of a spin-1 system quadrupolar phases
    (Universidad del Valle, 2024) Enríquez Zamudio, Ana María; Rodriguez-Ramirez, Karen
    The precision achieved by experimental techniques with ultracold atoms has enabled the creation of quantum simulators, facilitating the exploration of one-dimensional systems in the laboratory. In these systems, fluctuations are inherently collective and propagate over large distances due to frequent collisions. As a result, theoretical frameworks have been developed that leverage these fluctuations to describe such systems. Ultracold gases confined in optical lattices not only serve as quantum simulators for traditional condensed matter systems but also act as platforms to create new many-body quantum systems. In this work, two numerical techniques are proposed to explore a spin-1 bosonic gas contained in a one-dimensional optical lattice, in the strongly interacting phase and in the Mott insulator regime. The first technique is a mean-field approach, known as the Gutzwiller ansatz, which approximates the many-body wave function as the product of individual contributions at each site. Additionally, a more advanced ansatz has been developed that considers pairs of coupled sites, allowing for the exploration of regions in the phase space that are not accessible with the traditional ansatz. The second technique is based on tensor networks, specifically representing the state as a Matrix Product State (MPS), combined with the Time-Evolving Block Decimation (TEBD) algorithm. This technique is used to analyze the ground state properties and magnetic behavior of the system under the influence of an external magnetic field. Both techniques were evaluated within the context of a Bilinear-Biquadratic Heisenberg Hamiltonian, incorporating perturbative corrections to account for the quadratic Zeeman effect. The results of this work demonstrate that tensor networks, particularly MPS, provide a robust numerical technique for capturing the quantum phenomena exhibited by spin-1 bosons. The calculations of ground state energy and magnetization profiles confirm the effectiveness of tensor networks in representing the essential physics of the system. Furthermore, the investigation of entanglement properties reveals that the system’s entanglement entropy obeys an area law, characteristic of gapped one-dimensional systems. Chirality and spin correlation observables were also explored, revealing relevant information about the system’s behavior under various interaction parameters. The results are consistent with previous theoretical and numerical studies, highlighting the potential of tensor networks to address challenges in many-body quantum physics. This work introduces a novel numerical perspective within the context of Solid State research at the University of Valle, paving the way for future studies utilizing advanced tensor network techniques.