arXiv subjects

José I. Latorre

Publications and source records attributed to José I. Latorre.

At least 19 recordsLinked to original sources

arXiv2025

Arithmetic sequences as quantum states

We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical sequences that maximize entanglement entropy across all bipartitions and derive an analytical approximation as a function of the sequence length. This quantum-inspired approach offers a novel perspective for analyzing randomness in arithmetic sequences.

quant-ph↗

arXiv2024

The c-d conjecture

We conjecture a relation between the local dimension $d$ of a local nearest-neighbor critical Hamiltonian in one spatial dimension and the maximum central charge, $c_{\text{max}}$, that it can yield. Specifically, we propose that $c_{\text{max}} \leq d-1$, establishing a link between the short-distance lattice realization of a model and its emerging long-distance entanglement properties. This inequality can be viewed as a general form of a $c$-theorem establishing the reduction of effective degrees of freedom between the UV lattice and the IR conformal field theory. We support this conjecture with numerous examples.

cond-mat.stat-mech↗

arXiv2023

Hype in Science Communication: Exploring Scientists' Attitudes and Practices in Quantum Physics

An interpretive phenomenological approach is adopted to investigate scientists' attitudes and practices related to hype in science communication. Twenty-four active quantum physicists participated in 5 focus groups. Through a semi-structured questionnaire, their use of hype, attitudes, behaviours, and perspectives on hype in science communication were observed. The main results show that scientists primarily attribute hype generation to themselves, major corporations, and marketing departments. They see hype as crucial for research funding and use it strategically, despite concerns. Scientists view hype as coercive, compromising their work's integrity, leading to mostly negative feelings about it, except for collaborator-generated hype. A dissonance exists between scientists' involvement in hype, their opinions, and the negative emotions it triggers. They manage this by attributing responsibility to the academic system, downplaying their practices. This reveals hype in science communication as a calculated, persuasive tactic by academic stakeholders, aligning with a neoliberal view of science. Implications extend to science communication, media studies, regulation, and academia.

physics.soc-ph↗

arXiv2022

Variational Quantum Eigensolver for SU($N$) Fermions

Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum eigensolver is one of the aforementioned algorithms designed to determine the ground-state of many-body Hamiltonians. Here, we apply the variational quantum eigensolver to study the ground-state properties of $N$-component fermions. With such knowledge, we study the persistent current of interacting SU($N$) fermions, which is employed to reliably map out the different quantum phases of the system. Our approach lays out the basis for a current-based quantum simulator of many-body systems that can be implemented on noisy intermediate-scale quantum computers.

quant-ph↗

arXiv2022

Solving systems of Boolean multivariate equations with quantum annealing

Polynomial systems over the binary field have important applications, especially in symmetric and asymmetric cryptanalysis, multivariate-based post-quantum cryptography, coding theory, and computer algebra. In this work, we study the quantum annealing model for solving Boolean systems of multivariate equations of degree 2, usually referred to as the Multivariate Quadratic problem. We present different methodologies to embed the problem into a Hamiltonian that can be solved by available quantum annealing platforms. In particular, we provide three embedding options, and we highlight their differences in terms of quantum resources. Moreover, we design a machine-agnostic algorithm that adopts an iterative approach to better solve the problem Hamiltonian by repeatedly reducing the search space. Finally, we use D-Wave devices to successfully implement our methodologies on several instances of the Multivariate Quadratic problem.

quant-ph↗

arXiv2021

An Optimized Quantum Implementation of ISD on Scalable Quantum Resources

The security of code based constructions is usually assessed by Information Set Decoding (ISD) algorithms. In the quantum setting, amplitude amplification yields an asymptotic square root gain over the classical analogue. However, it is still unclear whether a real quantum circuit could yield actual improvements or suffer an enormous overhead due to its implementation. This leads to different considerations of these quantum attacks in the security analysis of code based proposals. In this work we clarify this doubt by giving the first quantum circuit design of the fully-fledged ISD procedure, an implementation in the quantum simulation library Qibo as well as precise estimates of its complexities. We show that against common belief, Prange's ISD algorithm can be implemented rather efficiently on a quantum computer, namely with only a logarithmic overhead in circuit depth compared to a classical implementation. As another major contribution, we leverage the idea of classical co-processors to design hybrid classical-quantum trade-offs, that allow to tailor the necessary qubits to any available amount, while still providing quantum speedups. Interestingly, when constraining the width of the circuit instead of its depth we are able to overcome previous optimality results on constraint quantum search.

quant-ph↗

arXiv2021

One qubit as a Universal Approximant

A single-qubit circuit can approximate any bounded complex function stored in the degrees of freedom defining its quantum gates. The single-qubit approximant presented in this work is operated through a series of gates that take as their parameterization the independent variable of the target function and an additional set of adjustable parameters. The independent variable is re-uploaded in every gate while the parameters are optimized for each target function. The output state of this quantum circuit becomes more accurate as the number of re-uploadings of the independent variable increases, i. e., as more layers of gates parameterized with the independent variable are applied. In this work, we provide two different proofs of this claim related to both the Fourier series and the Universal Approximation Theorem for Neural Networks, and we benchmark both methods against their classical counterparts. We further implement a single-qubit approximant in a real superconducting qubit device, demonstrating how the ability to describe a set of functions improves with the depth of the quantum circuit. This work shows the robustness of the re-uploading technique on Quantum Machine Learning.

quant-ph↗

arXiv2021

Platonic Entanglement

We present a construction of highly entangled states defined on the topology of a platonic solid using tensor networks based on ancillary Absolute Maximally Entangled (AME) states. We illustrate the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. We analyze the entropy of such states on many different partitions, and observe that they come on integer numbers and are almost maximal. We also observe that all platonic solids accept the construction of AME states based on Reed-Solomon codes since their number of facets, vertices and edges are always a prime number plus one.

quant-ph↗

arXiv2021

Quantum unary approach to option pricing

We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude distribution corresponding to the asset value at maturity is generated using a low depth circuit; second, the computation of the expected return is computed with simple controlled gates; and third, standard Amplitude Estimation is used to gain quantum advantage. On the positive side, unary representation remarkably simplifies the structure and depth of the quantum circuit. Amplitude distributions uses quantum superposition to bypass the role of classical Monte Carlo simulation. The unary representation also provides a post-selection consistency check that allows for a substantial mitigation in the error of the computation. On the negative side, unary representation requires linearly many qubits to represent a target probability distribution, as compared to the logarithmic scaling of binary algorithms. We compare the performance of both unary vs. binary option pricing algorithms using error maps, and find that unary representation may bring a relevant advantage in practice for near-term devices.

quant-ph↗

arXiv2020

Quantum Search for Scaled Hash Function Preimages

We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our implementation provides the means to assess with precision the scaling of the number of gates and depth of a full-fledged quantum circuit designed to find the preimages of a given hash digest. The detailed construction of the quantum oracle shows that the presence of AND gates, OR gates, shifts of bits and the reuse of the initial state along the computation, require extra quantum resources as compared with other hash functions based on modular additions, XOR gates and rotations. We also track the entanglement entropy present in the quantum register at every step along the computation, showing that it becomes maximal at the inner core of the first action of the quantum oracle, which implies that no classical simulation based on Tensor Networks would be of relevance. Finally, we show that strategies that suggest a shortcut based on sampling the quantum register after a few steps of Grover's algorithm can only provide some marginal practical advantage in terms of error mitigation.

quant-ph↗

arXiv2020

Quantum Singular Value Decomposer

We present a variational quantum circuit that produces the Singular Value Decomposition of a bipartite pure state. The proposed circuit, that we name Quantum Singular Value Decomposer or QSVD, is made of two unitaries respectively acting on each part of the system. The key idea of the algorithm is to train this circuit so that the final state displays exact output coincidence from both subsystems for every measurement in the computational basis. Such circuit preserves entanglement between the parties and acts as a diagonalizer that delivers the eigenvalues of the Schmidt decomposition. Our algorithm only requires measurements in one single setting, in striking contrast to the $3^n$ settings required by state tomography. Furthermore, the adjoints of the unitaries making the circuit are used to create the eigenvectors of the decomposition up to a global phase. Some further applications of QSVD are readily obtained. The proposed QSVD circuit allows to construct a SWAP between the two parties of the system without the need of any quantum gate communicating them. We also show that a circuit made with QSVD and CNOTs acts as an encoder of information of the original state onto one of its parties. This idea can be reversed and used to create random states with a precise entanglement structure.

quant-ph↗

arXiv2020

Scaling of variational quantum circuit depth for condensed matter systems

We benchmark the accuracy of a variational quantum eigensolver based on a finite-depth quantum circuit encoding ground state of local Hamiltonians. We show that in gapped phases, the accuracy improves exponentially with the depth of the circuit. When trying to encode the ground state of conformally invariant Hamiltonians, we observe two regimes. A finite-depth regime, where the accuracy improves slowly with the number of layers, and a finite-size regime where it improves again exponentially. The cross-over between the two regimes happens at a critical number of layers whose value increases linearly with the size of the system. We discuss the implication of these observations in the context of comparing different variational ansatz and their effectiveness in describing critical ground states.

quant-ph↗

arXiv2020

Data re-uploading for a universal quantum classifier

A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple data re-uploading. A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensions in the input and several categories in the output, to conform to a universal quantum classifier. The extension of this idea to several qubits enhances the efficiency of the strategy as entanglement expands the superpositions carried along with the classification. Extensive benchmarking on different examples of the single- and multi-qubit quantum classifier validates its ability to describe and classify complex data.

quant-ph↗

arXiv2020

Measuring the tangle of three-qubit states

We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal values for the parameters are learned in a variational fashion. Once this transformation is achieved, direct measurement of outcome probabilities in the computational basis provides an estimate of the tangle, which quantifies genuine tripartite entanglement. We perform simulations on a set of random states under different noise conditions to asses the validity of the method.

quant-ph↗

arXiv2017

Maximal Entanglement in High Energy Physics

We analyze how maximal entanglement is generated at the fundamental level in QED by studying correlations between helicity states in tree-level scattering processes at high energy. We demonstrate that two mechanisms for the generation of maximal entanglement are at work: i) $s$-channel processes where the virtual photon carries equal overlaps of the helicities of the final state particles, and ii) the indistinguishable superposition between $t$- and $u$-channels. We then study whether requiring maximal entanglement constrains the coupling structure of QED and the weak interactions. In the case of photon-electron interactions unconstrained by gauge symmetry, we show how this requirement allows reproducing QED. For $Z$-mediated weak scattering, the maximal entanglement principle leads to non-trivial predictions for the value of the weak mixing angle $θ_W$. Our results are a first step towards understanding the connections between maximal entanglement and the fundamental symmetries of high-energy physics.

hep-th↗

arXiv2017

Parton distributions from high-precision collider data

We present a new set of parton distributions, NNPDF3.1, which updates NNPDF3.0, the first global set of PDFs determined using a methodology validated by a closure test. The update is motivated by recent progress in methodology and available data, and involves both. On the methodological side, we now parametrize and determine the charm PDF alongside the light quarks and gluon ones, thereby increasing from seven to eight the number of independent PDFs. On the data side, we now include the D0 electron and muon W asymmetries from the final Tevatron dataset, the complete LHCb measurements of W and Z production in the forward region at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. We also include for the first time top-quark pair differential distributions and the transverse momentum of the Z bosons from ATLAS and CMS. We investigate the impact of parametrizing charm and provide evidence that the accuracy and stability of the PDFs are thereby improved. We study the impact of the new data by producing a variety of determinations based on reduced datasets. We find that both improvements have a significant impact on the PDFs, with some substantial reductions in uncertainties, but with the new PDFs generally in agreement with the previous set at the one sigma level. The most significant changes are seen in the light-quark flavor separation, and in increased precision in the determination of the gluon. We explore the implications of NNPDF3.1 for LHC phenomenology at Run II, compare with recent LHC measurements at 13 TeV, provide updated predictions for Higgs production cross-sections and discuss the strangeness and charm content of the proton in light of our improved dataset and methodology. The NNPDF3.1 PDFs are delivered for the first time both as Hessian sets, and as optimized Monte Carlo sets with a compressed number of replicas.

hep-ph↗

arXiv2016

Operational approach to Bell inequalities: applications to qutrits

Bell inequalities can be studied both as constraints in the space of probability distributions and as expectation values of multipartite operators. The latter approach is particularly useful when considering outcomes as eigenvalues of unitary operators. This brings the possibility of exploiting the complex structure of the coefficients in the Bell operators. We investigate this avenue of though in the known case of two outcomes, and find new Bell inequalities for the cases of three outcomes and $n=3,4,5$ and $6$ parties. We find their corresponding classical bounds and their maximum violation in the case of qutrits. We further propose a novel way to generate Bell inequalities based on a mapping from maximally entangled states to Bell operators and produce examples for different outcomes and number of parties.

quant-ph↗

arXiv2016

Towards the compression of parton densities through machine learning algorithms

One of the most fascinating challenges in the context of parton density function (PDF) is the determination of the best combined PDF uncertainty from individual PDF sets. Since 2014 multiple methodologies have been developed to achieve this goal. In this proceedings we first summarize the strategy adopted by the PDF4LHC15 recommendation and then, we discuss about a new approach to Monte Carlo PDF compression based on clustering through machine learning algorithms.

hep-ph↗