arXiv subjects

Jordi Tura

Publications and source records attributed to Jordi Tura.

At least 37 records · Page 2Linked to original sources

arXiv2025

Measuring multipartite entanglement efficiently by testing symmetries

Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of bipartite and multipartite entanglement can be obtained with symmetry tests. We propose and benchmark several efficient methods to estimate these measures, and derive near-optimal sampling strategies for each. Despite the nonlinearity of the methods, we demonstrate that the sampling error scales no worse than $O(N_{\mathrm{tot}}^{-1/2})$ with the total number of copies $N_{\mathrm{tot}}$, which suggests experimental feasibility. By exploiting symmetries we compute our measures for large number of copies, and derive the asymptotic decay exponents for relevant states in many-body systems. Using these results we identify tradeoffs between estimation complexity and sensitivity of the presented entanglement measures, oriented to practical implementations.

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arXiv2025

Distributed Quantum Information Processing: A Review of Recent Progress

Distributed quantum information processing seeks to overcome the scalability limitations of monolithic quantum devices by interconnecting multiple quantum processing nodes via classical and quantum communication. This approach extends the capabilities of individual devices, enabling access to larger problem instances and novel algorithmic techniques. Beyond increasing qubit counts, it also enables qualitatively new capabilities, such as joint measurements on multiple copies of high-dimensional quantum states. The distinction between single-copy and multi-copy access reveals important differences in task complexity and helps identify which computational problems stand to benefit from distributed quantum resources. At the same time, it highlights trade-offs between classical and quantum communication models and the practical challenges involved in realizing them experimentally. In this review, we contextualize recent developments by surveying the theoretical foundations of distributed quantum protocols and examining the experimental platforms and algorithmic applications that realize them in practice.

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arXiv2025

Characterizing Translation-Invariant Bell Inequalities using Tropical Algebra and Graph Polytopes

Nonlocality is one of the key features of quantum physics, which is revealed through the violation of a Bell inequality. In large multipartite systems, nonlocality characterization quickly becomes a challenging task. A common practice is to make use of symmetries, low-order correlators, or exploiting local geometries, to restrict the class of inequalities. In this paper, we characterize translation-invariant (TI) Bell inequalities with finite-range correlators in one-dimensional geometries. We introduce a novel methodology based on tropical algebra tensor networks and highlight its connection to graph theory. Surprisingly, we find that the TI Bell polytope has a number of extremal points that can be uniformly upper-bounded with respect to the system size. We give an efficient method to list all vertices of the polytope for a particular system size, and characterize the tightness of a given TI Bell inequality. The connections highlighted in our work allow us to re-interpret concepts developed in the fields of tropical algebra and graph theory in the context of Bell nonlocality, and vice-versa. This work extends a parallel article [M. Hu \textit{et al.}, arXiv: 2208.02798 (2022)] on the same subject.

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arXiv2025

Preparing low-variance states using a distributed quantum algorithm

Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The routine then acts as an effective filtering operation, reducing the energy variance of the initial state. In this work, we present a distributed quantum algorithm inspired by iterative phase estimation to prepare low-variance states. Our method uses a single auxiliary qubit per quantum device, which controls its dynamics, and a postselection strategy for a joint quantum measurement on such auxiliary qubits. In the multi-device case, the result of this measurement heralds the successful runs of the protocol. This allows us to demonstrate that our distributed algorithm reduces the energy variance faster compared to single-device implementations, thereby highlighting the potential of distributed algorithms for near-term and early fault-tolerant devices.

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arXiv2025

Quantum generative modeling for financial time series with temporal correlations

Quantum generative adversarial networks (QGANs) have been investigated as a method for generating synthetic data with the goal of augmenting training data sets for neural networks. This is especially relevant for financial time series, since we only ever observe one realization of the process, namely the historical evolution of the market, which is further limited by data availability and the age of the market. However, for classical generative adversarial networks it has been shown that generated data may (often) not exhibit desired properties (also called stylized facts), such as matching a certain distribution or showing specific temporal correlations. Here, we investigate whether quantum correlations in quantum inspired models of QGANs can help in the generation of financial time series. We train QGANs, composed of a quantum generator and a classical discriminator, and investigate two approaches for simulating the quantum generator: a full simulation of the quantum circuits, and an approximate simulation using tensor network methods. We tested how the choice of hyperparameters, such as the circuit depth and bond dimensions, influenced the quality of the generated time series. The QGAN that we trained generate synthetic financial time series that not only match the target distribution but also exhibit the desired temporal correlations, with the quality of each property depending on the hyperparameters and simulation method.

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arXiv2025

Symmetric quantum states: a review of recent progress

Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique physical properties: they exhibit genuine multipartite entanglement and notable robustness against noise and perturbations. These features make such states particularly well-suited for a wide range of quantum information tasks. Here, we provide a pedagogic analysis of the mathematical structure and relevant physical properties of this class of states. Beyond the theoretical framework, robust tools for certifying and verifying the properties of symmetric states in experimental settings are essential. In this regard, we explore how standard techniques -- such as quantum state tomography, Bell tests, and entanglement witnesses -- can be specifically adapted for symmetric systems. Next, we provide an up-to-date overview of the most relevant applications in which these states outperform other classes of states in specific tasks. Specifically, we address their central role in quantum metrology, highlight their use in quantum error correction codes, and examine their contribution in computation and communication tasks. Finally, we present the current state-of-the-art in their experimental generation, ranging from systems of cold atoms to implementations via quantum algorithms. We also review the most significant results obtained in the different experimental realizations. Despite the notable progress made in recent years with regard to the characterisation and application of symmetric quantum states, several intriguing questions remain unsolved. We conclude this review by discussing some of these open problems and outlining promising directions for future research.

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arXiv2025

Mitigating shot noise in local overlapping quantum tomography with semidefinite programming

Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum states. In the context of near-term quantum computing, RDMs provide sufficient information to effectively design variational quantum algorithms. However, their experimental estimation is challenging, as it involves preparing and measuring quantum states in multiple bases--a resource-intensive process susceptible to producing non-physical RDMs due to shot noise from limited measurements. To address this, we propose a method to mitigate shot noise by re-enforcing certain physicality constraints on RDMs. While verifying RDM compatibility with a global state is quantum Merlin-Arthur complete, we relax this condition by enforcing compatibility constraints up to a certain level using a polynomial-size semidefinite program to reconstruct overlapping RDMs from simulated data. Our approach yields, on average, tighter bounds for the same number of measurements compared to tomography without compatibility constraints. We demonstrate the versatility and efficacy of our method by integrating it into an algorithmic cooling procedure to prepare low-energy states of local Hamiltonians. Simulations on frustrated Hamiltonians reveal notable improvements in accuracy and resource efficiency, highlighting the potential of our approach for practical applications in near-term quantum computing.

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arXiv2025

Approximation and Generalization Capacities of Parametrized Quantum Circuits for Functions in Sobolev Spaces

Parametrized quantum circuits (PQC) are quantum circuits which consist of both fixed and parametrized gates. In recent approaches to quantum machine learning (QML), PQCs are essentially ubiquitous and play the role analogous to classical neural networks. They are used to learn various types of data, with an underlying expectation that if the PQC is made sufficiently deep, and the data plentiful, the generalization error will vanish, and the model will capture the essential features of the distribution. While there exist results proving the approximability of square-integrable functions by PQCs under the $L^2$ distance, the approximation for other function spaces and under other distances has been less explored. In this work we show that PQCs can approximate the space of continuous functions, $p$-integrable functions and the $H^k$ Sobolev spaces under specific distances. Moreover, we develop generalization bounds that connect different function spaces and distances. These results provide a theoretical basis for different applications of PQCs, for example for solving differential equations. Furthermore, they provide us with new insight on the role of the data normalization in PQCs and of loss functions which better suit the specific needs of the users.

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arXiv2025

Multiple-basis representation of quantum states

Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing limited quantum computers can contribute to this enhancement. In this work, we explore a new hybrid, efficient quantum-classical representation of quantum states, the multiple-basis representation. This representation consists of a linear combination of states that are sparse in some given and different bases, specified by quantum circuits. Such representation is particularly appealing when considering depth-limited quantum circuits within reach of current hardware. We analyze the expressivity of multiple-basis representation states depending on the classical simulability of their quantum circuits. In particular, we show that multiple-basis representation states include, but are not restricted to, both matrix-product states and stabilizer states. Furthermore, we find cases in which this representation can be used, namely approximation of ground states, simulation of deeper computations by specifying bases with shallow circuits, and a tomographical protocol to describe states as multiple-basis representations. We envision this work to open the path of simultaneous use of several hardware-friendly bases, a natural description of hybrid computational methods accessible for near-term hardware.

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arXiv2024

Optimising entanglement distribution policies under classical communication constraints assisted by reinforcement learning

Quantum repeaters play a crucial role in the effective distribution of entanglement over long distances. The nearest-future type of quantum repeater requires two operations: entanglement generation across neighbouring repeaters and entanglement swapping to promote short-range entanglement to long-range. For many hardware setups, these actions are probabilistic, leading to longer distribution times and incurred errors. Significant efforts have been vested in finding the optimal entanglement-distribution policy, i.e. the protocol specifying when a network node needs to generate or swap entanglement, such that the expected time to distribute long-distance entanglement is minimal. This problem is even more intricate in more realistic scenarios, especially when classical communication delays are taken into account. In this work, we formulate our problem as a Markov decision problem and use reinforcement learning (RL) to optimise over centralised strategies, where one designated node instructs other nodes which actions to perform. Contrary to most RL models, ours can be readily interpreted. Additionally, we introduce and evaluate a fixed local policy, the `predictive swap-asap' policy, where nodes only coordinate with nearest neighbours. Compared to the straightforward generalization of the common swap-asap policy to the scenario with classical communication effects, the `wait-for-broadcast swap-asap' policy, both of the aforementioned entanglement-delivery policies are faster at high success probabilities. Our work showcases the merit of considering policies acting with incomplete information in the realistic case when classical communication effects are significant.

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arXiv2024

Spectral Gap Optimization for Enhanced Adiabatic State Preparation

The preparation of non-trivial states is crucial to the study of quantum many-body physics. Such states can be prepared with adiabatic quantum algorithms, which are restricted by the minimum spectral gap along the path. In this letter, we propose an efficient method to adiabatically prepare tensor networks states (TNSs). We maximize the spectral gap leveraging degrees of freedom in the parent Hamiltonian construction. We demonstrate this efficient adiabatic algorithm for preparing TNS, through examples of random TNS in one dimension, AKLT, and GHZ states. The Hamiltonian optimization applies to both injective and non-injective tensors, in the latter case by exploiting symmetries present in the tensors.

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arXiv2024

Necessary and Sufficient Condition for Randomness Certification from Incompatibility

Quantum randomness can be certified from probabilistic behaviors demonstrating Bell nonlocality or Einstein-Podolsky-Rosen steering, leveraging outcomes from uncharacterized devices. However, such nonlocal correlations are not always sufficient for this task, necessitating the identification of required minimum quantum resources. In this work, we provide the necessary and sufficient condition for nonzero certifiable randomness in terms of measurement incompatibility and develop approaches to detect them. Firstly, we show that the steering-based randomness can be certified if and only if the correlations arise from a measurement compatibility structure that is not isomorphic to a hypergraph containing a star subgraph. In such a structure, the central measurement is individually compatible with the measurements at branch sites, precluding certifiable randomness in the central measurement outcomes. Subsequently, we generalize this result to the Bell scenario, proving that the violation of any chain inequality involving $m$ inputs and $d$ outputs rules out such a compatibility structure, thereby validating all chain inequalities as credible witnesses for randomness certification. Our results point out the role of incompatibility structure in generating random numbers, offering a way to identify minimum quantum resources for the task.

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arXiv2024

Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario

Device-independent randomness certification based on Bell nonlocality does not require any assumptions about the devices and therefore provides adequate security. Great effort has been made to demonstrate that nonlocality is necessary for generating quantum randomness, but the minimal resource required for random number generation has not been clarified. Here we first prove and experimentally demonstrate that violating any two-input Bell inequality is both necessary and sufficient for certifying randomness, however, for the multi-input cases, this sufficiency ceases to apply, leading to certain states exhibiting Bell nonlocality without the capability to certify randomness. We examine two typical classes of Bell inequalities with multi-input and multi-output, the facet inequalities and Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio Bell inequalities, in the high-dimensional photonic system, and observe the violation of the latter one can always certify randomness which is not true for the former. The private randomness with a generation rate of 1.867\pm0.018 bits per photon pair is obtained in the scenario of Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio Bell inequalities with 3-input and 4-output. Our work unravels the internal connection between randomness and nonlocality, and effectively enhances the performance of tasks such as device-independent random number generation.

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arXiv2024

Virtual mitigation of coherent non-adiabatic transitions by echo verification

Transitions out of the ground space limit the performance of quantum adiabatic algorithms, while hardware imperfections impose stringent limitations on the circuit depth. We propose an adiabatic echo verification protocol which mitigates both coherent and incoherent errors, arising from non-adiabatic transitions and hardware noise, respectively. Quasi-adiabatically evolving forward and backwards allows for an echo-verified measurement of any observable. In addition to mitigating hardware noise, our method uses positive-time dynamics only. Crucially, the estimator bias of the observable is reduced when compared to standard adiabatic preparation, achieving up to a quadratic improvement.

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arXiv2024

Learning Density Functionals from Noisy Quantum Data

The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy. A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models. In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi-Hubbard model. We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms. The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point. Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data. The trained models can be applied to solving new problem instances in a Kohn-Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances. Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.

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arXiv2024

Tropical contraction of tensor networks as a Bell inequality optimization toolset

We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is replaced by the arithmetic addition. We illustrate our method with paradigmatic examples both in the multipartite scenario and the bipartite scenario with multiple outcomes. We showcase how the method extends into the thermodynamic limit for some translationally invariant systems and establish a connection between the notions of tropical eigenvalue and the classical bound per particle as a fixed point of a tropical renormalization procedure.

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arXiv2024

Improved Nonlocality Certification via Bouncing between Bell Operators and Inequalities

Bell nonlocality is an intrinsic feature of quantum mechanics, which can be certified via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here, we present an optimization scheme to improve nonlocality certification by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds than the original one, enabling a more robust detection of nonlocality. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical demonstration, we apply this method to an XXZ-like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, as well as combining the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient nonlocality certification techniques and enable broader experimental explorations.

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arXiv2024

Unextendible product operator basis

Quantum nonlocality is associated with the local indistinguishability of orthogonal states. Unextendible product basis (UPB), a widely used tool in quantum information, exhibits nonlocality which is the powerful resource for quantum information processing. In this work we extend the definitions of nonlocality and genuine nonlocality from states to operators. We also extend UPB to the notions of unextendible product operator basis, unextendible product unitary operator basis (UPUOB) and strongly UPUOB. We construct their examples, and show the nonlocality of some strongly UPUOBs under local operations and classical communications. We study the phenomenon of these operators acting on quantum states. As an application, we distinguish the two-dimensional strongly UPUOB which only consumes three ebits of entanglement. Our results imply that such UPUOBs exhibit nonlocality as UPBs and the distinguishability of them requires entanglement resources.

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