Descubriendo el potencial de la computación cuántica

@unpublished{nokey,

title = {Reducing the number of qubits in quantum simulations of one dimensional many-body Hamiltonians},

author = {Mehrabankar, S. and García-March, M.A. and Almudéver, C.G. and Pérez, A. },

url = {https://arxiv.org/abs/2308.01545},

doi = {doi.org/10.48550/arXiv.2308.01545},

abstract = {We investigate the Ising and Heisenberg models using the Block Renormalization Group Method (BRGM), focusing on its behavior across different system sizes. The BRGM reduces the number of spins by a factor of 1/2 (1/3) for the Ising (Heisenberg) model, effectively preserving essential physical features of the model while using only a fraction of the spins. Through a comparative analysis, we demonstrate that as the system size increases, there is an exponential convergence between results obtained from the original and renormalized Ising Hamiltonians, provided the coupling constants are redefined accordingly. Remarkably, for a spin chain with 24 spins, all physical features, including magnetization, correlation function, and entanglement entropy, exhibit an exact correspondence with the results from the original Hamiltonian. The study of the Heisenberg model also shows this tendency, although complete convergence may appear for a size much larger than 24 spins, and is therefore beyond our computational capabilities. The success of BRGM in accurately characterizing the Ising model, even with a relatively small number of spins, underscores its robustness and utility in studying complex physical systems, and facilitates its simulation on current NISQ computers, where the available number of qubits is largely constrained.},

howpublished = {Preprint},

keywords = {UV},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{nokey,

title = {Role of coherence in many-body Quantum Reservoir Computing},

author = {Palacios, A. and Martínez-Pena, R. and Soriano, M.C. and Giorgi, G.L. and Zambrini, R. },

url = {https://arxiv.org/pdf/2409.17734},

doi = {doi.org/10.48550/arXiv.2409.17734},

abstract = {Quantum Reservoir Computing (QRC) offers potential advantages over classical reservoir computing, including inherent processing of quantum inputs and a vast Hilbert space for state exploration. Yet, the relation between the performance of reservoirs based on complex and many-body quantum systems and non-classical state features is not established. Through an extensive analysis of QRC based on a transverse-field Ising model we show how different quantum effects, such as quantum

coherence and correlations, contribute to improving the performance in temporal tasks, as measured by the Information Processing Capacity. Additionally, we critically assess the impact of finite measurement resources and noise on the reservoir’s dynamics in different regimes, quantifying the limited ability to exploit quantum effects for increasing damping and noise strengths. Our results reveal a monotonic relationship between reservoir performance and coherence, along with the importance of quantum effects in the ergodic regime.},

howpublished = {Preprint},

keywords = {uib},

pubstate = {published},

tppubtype = {unpublished}

}

@unpublished{nokey,

title = {Unbounded Quantum Advantage in Communication with Minimal Input Scaling},

author = {Rout, S. and Sakharwade, N. and Bhattacharya, S.S. and Ramanathan, R. and Horodecki, P.},

url = {https://arxiv.org/pdf/2305.10372},

doi = {doi.org/10.48550/arXiv.2305.10372},

abstract = {In communication complexity-like problems, previous studies have shown either an exponential quantum advantage or an unbounded quantum advantage with an exponentially large input set Θ(2n) bits with respect to classical communication Θ(n) bits. In the former, the quantum and classical separation grows exponentially in input while the latter's quantum communication resource is a constant. Remarkably, it was still open whether an unbounded quantum advantage exists while the inputs do not scale exponentially. Here we answer this question affirmatively using an input size of optimal order. Considering two variants as tasks: 1) distributed computation of relation and 2) {it relation reconstruction}, we study the one-way zero-error communication complexity of a relation induced by a distributed clique labelling problem for orthogonality graphs. While we prove no quantum advantage in the first task, we show an {it unbounded quantum advantage} in relation reconstruction without public coins. Specifically, for a class of graphs with order m, the quantum complexity is Θ(1) while the classical complexity is Θ(logm). Remarkably, the input size is Θ(logm) bits and the order of its scaling with respect to classical communication is {it minimal}. This is exponentially better compared to previous works. Additionally, we prove a lower bound (linear in the number of maximum cliques) on the amount of classical public coin necessary to overcome the separation in the scenario of restricted communication and connect this to the existence of Orthogonal Arrays. Finally, we highlight some applications of this task to semi-device-independent dimension witnessing as well as to the detection of Mutually Unbiased Bases.},

howpublished = {Preprint},

keywords = {UAB},

pubstate = {published},

tppubtype = {unpublished}

}