Artur Garcia-Saez, Valentin Murg, Tzu-Chieh Wei
Using exact diagonalization and tensor network techniques we compute the gap for the AKLT Hamiltonian in 1D and 2D spatial dimensions. Tensor Network methods are used to extract physical properties directly in the thermodynamic limit, and we support these results using finite-size scalings from exact diagonalization. Studying the AKLT Hamiltonian perturbed by an external field, we show how to obtain an accurate value of the gap of the original AKLT Hamiltonian from the field value at which the ground state verifies e_0<0, which is a quantum critical point. With the Tensor Network Renormalization Group methods we provide evidence of a finite gap in the thermodynamic limit for the AKLT models in the 1D chain and 2D hexagonal and square lattices. This method can be applied generally to Hamiltonians with rotational symmetry, and we also show results beyond the AKLT model.
Sergi Masot-Llima, Artur Garcia-Saez
Dec 23, 2024·quant-ph·PDF Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their flexibility and performance exploiting hardware acceleration. As ansätze, tensor networks can be used with flexible geometries, and it is known that for highly regular ones their dimensionality has a large impact in performance and representation power. For heterogeneous structures, however, these effects are not completely characterized. In this article, we train tensor networks with different geometries to encode a random quantum state, and see that densely connected structures achieve better infidelities than more sparse structures, with higher success rates and less time. Additionally, we give some general insight on how to improve memory requirements on these sparse structures and its impact on the trainings. Finally, as we use HPC resources for the calculations, we discuss the requirements for this approach and showcase performance improvements with GPU acceleration on a last-generation supercomputer.
Artur Garcia-Saez, J. Miguel Rubi
Mar 23, 2009·q-bio.BM·PDF We show the existence of a high interrelation between the different loops that may appear in a DNA segment. Conformational changes in a chain segment caused by the formation of a particular loop may either promote or prevent the appearance of another. The underlying loop selection mechanism is analyzed by means of a Hamiltonian model from which the looping free energy and the corresponding repression level can be computed. We show significant differences between the probability of single and multiple loop formation. The consequences that these collective effects might have on gene regulation processes are outlined.
Daniel Cavalcanti, Alessandro Ferraro, Artur Garcia-Saez, Antonio Acin
Dec 19, 2008·quant-ph·PDF We study the entanglement distillability properties of thermal states of many-body systems. Following the ideas presented in [D.Cavalcanti et al., arxiv:0705.3762], we first discuss the appearance of bound entanglement in those systems satisfying an entanglement area law. Then, we extend these results to other topologies, not necessarily satisfying an entanglement area law. We also study whether bound entanglement survives in the macroscopic limit of an infinite number of particles.
Artur Garcia-Saez, Jordi Riu
Nov 21, 2019·quant-ph·PDF We present a classical control mechanism for Quantum devices using Reinforcement Learning. Our strategy is applied to the Quantum Approximate Optimization Algorithm (QAOA) in order to optimize an objective function that encodes a solution to a hard combinatorial problem. This method provides optimal control of the Quantum device following a reformulation of QAOA as an environment where an autonomous classical agent interacts and performs actions to achieve higher rewards. This formulation allows a hybrid classical-Quantum device to train itself from previous executions using a continuous formulation of deep Q-learning to control the continuous degrees of freedom of QAOA. Our approach makes a selective use of Quantum measurements to complete the observations of the Quantum state available to the agent. We run tests of this approach on MAXCUT instances of size up to N = 21 obtaining optimal results. We show how this formulation can be used to transfer the knowledge from shorter training episodes to reach a regime of longer executions where QAOA delivers higher results.
Piotr Sierant, Jofre Vallès-Muns, Artur Garcia-Saez
Jan 12, 2026·quant-ph·PDF Non-stabilizerness, also known as ``magic,'' quantifies how far a quantum state departs from the stabilizer set. It is a central resource behind quantum advantage and a useful probe of the complexity of quantum many-body states. Yet standard magic quantifiers, such as the stabilizer Rényi entropy (SRE) for qubits and the mana for qutrits, are costly to evaluate numerically, with the computational complexity growing rapidly with the number $N$ of qudits. Here we introduce efficient, numerically exact algorithms that exploit the fast Hadamard transform to compute the SRE for qubits ($d=2$) and the mana for qutrits ($d=3$) for pure states given as state vectors. Our methods compute SRE and mana at cost $O(N d^{2N})$, providing an exponential improvement over the naive $O(d^{3N})$ scaling, with substantial parallelism and straightforward GPU acceleration. We further show how to combine the fast Hadamard transform with Monte Carlo sampling to estimate the SRE of state vectors, and we extend the approach to compute the mana of mixed states. All algorithms are implemented in the open-source Julia package HadaMAG ( https://github.com/bsc-quantic/HadaMAG.jl/ ), which provides a high-performance toolbox for computing SRE and mana with built-in support for multithreading, MPI-based distributed parallelism, and GPU acceleration. The package, together with the methods developed in this work, offers a practical route to large-scale numerical studies of magic in quantum many-body systems.
Ana Palacios, Artur Garcia-Saez, Bruno Julia-Diaz, Marta P. Estarellas
Apr 10, 2024·quant-ph·PDF Achieving densely connected hardware graphs is a challenge for most quantum computing platforms today, and a particularly crucial one for the case of quantum annealing applications. In this context, we present a scalable architecture for quantum annealers to realize effective Ising Hamiltonians of arbitrary connectivity. Our proposal consists on a resource-efficient configuration based on a hardware graph where physical qubits are connected to at most other 3 and containing exclusively 2-local interactions. We derive this configuration based on chains of qubits encoding logical variables by describing the problem graph in terms of triangles. We thus present a promising new route to scale up devices dedicated to classical optimization tasks within the quantum annealing paradigm.
Artur Garcia-Saez, Tzu-Chieh Wei
The distribution of Yang-Lee zeros in the ferromagnetic Ising model in both two and three dimensions is studied on the complex field plane directly in the thermodynamic limit via the tensor network methods. The partition function is represented as a contraction of a tensor network and is efficiently evaluated with an iterative tensor renormalization scheme. The free-energy density and the magnetization are computed on the complex field plane. Via the discontinuity of the magnetization, the density of the Yang-Lee zeros is obtained to lie on the unit circle, consistent with the Lee-Yang circle theorem. Distinct features are observed at different temperatures---below, above and at the critical temperature. Application of the tensor-network approach is also made to the $q$-state Potts models in both two and three dimensions and a previous debate on whether, in the thermodynamic limit, the Yang-Lee zeros lie on a unit circle for $q>2$ is resolved: they clearly do not lie on a unit circle except at the zero temperature. For the Potts models (q=3,4,5,6) investigated in two dimensions, as the temperature is lowered the radius of the zeros at a fixed angle from the real axis shrinks exponentially towards unity with the inverse temperature.
Alessandro Ferraro, Artur Garcia-Saez, Antonio Acin
We consider the ground-state entanglement in highly connected many-body systems, consisting of harmonic oscillators and spin-1/2 systems. Varying their degree of connectivity, we investigate the interplay between the enhancement of entanglement, due to connections, and its frustration, due to monogamy constraints. Remarkably, we see that in many situations the degree of entanglement in a highly connected system is essentially of the same order as in a low connected one. We also identify instances in which the entanglement decreases as the degree of connectivity increases.
Emanuele Costa, Axel Pérez-Obiol, Javier Menéndez, Arnau Rios, Artur García-Sáez, Bruno Juliá-Díaz
Quantum computing is emerging as a promising tool in nuclear physics. However, the cost of encoding fermionic operators hampers the application of algorithms in current noisy quantum devices. In this work, we analyze an encoding scheme based on pairing nucleon modes. This approach significantly reduces the complexity of the encoding, while maintaining a high accuracy for the ground states of semimagic nuclei across the $sd$ and $pf$ shells and for tin isotopes. In addition, we also explore the encoding ability to describe open-shell nuclei within the above configuration spaces. When this scheme is applied to a trotterized quantum adiabatic evolution, our results demonstrate a computational advantage of up to three orders of magnitude in CNOT gate count compared to the standard Jordan-Wigner encoding. Our approach paves the way for efficient quantum simulations of nuclear structure using quantum annealing, with applications to both digital and hybrid quantum computing platforms.
Roman Orus, Tzu-Chieh Wei, Oliver Buerschaper, Artur Garcia-Saez
Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement Rényi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on Projected Entangled Pair States to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation. When compared to tensor network methods for Rényi entropies, our approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster. The method can be adapted to deal with any topological state of the system, including minimally entangled ground states. It also allows to extract the critical exponent of the correlation length, and shows that there is no continuous entanglement-loss along renormalization group flows in topological phases.
Aashna Anil Zade, Kenji Sugisaki, Matthias Werner, Ana Palacios, Jordi Riu, Jan Nogue, Artur Garcia-Saez, Arnau Riera, V. S. Prasannaa
The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is arguably the most popular noisy intermediate-scale quantum (NISQ) era approach to quantum chemistry. We consider the underexplored quantum annealing eigensolver (QAE) algorithm as a worthy alternative. We use a combination of numerical calculations for a system where strong correlation effects dominate, and conclusions drawn from our preliminary scaling analysis for QAE and VQE to make the case for QAE as a NISQ era contender to VQE for quantum chemistry. For the former, we pick the representative example of computing avoided crossings in the H4 molecule in a rectangular geometry, and demonstrate that we obtain results to within about 1.2% of the full configuration interaction value on the D-Wave Advantage system 4.1 hardware. We carry out analyses on the effect of the number of shots, anneal time, and the choice of Lagrange multiplier on our obtained results. Following our numerical results, we carry out a detailed yet preliminary analysis of the scaling behaviours of both the QAE and the VQE algorithms. We analyze the non-recurring and recurring costs involved in both the algorithms and arrive at their net scaling behaviours.
Axel Pérez-Obiol, Sergi Masot-Llima, Antonio M. Romero, Javier Menéndez, Arnau Rios, Artur García-Sáez, Bruno Juliá-Díaz
Simulating physical systems with variational quantum algorithms is a well-studied approach, but it is challenging to implement in current devices due to demands in qubit number and circuit depth. We show how limited knowledge of the system, namely the entropy of its subsystems, its entanglement structure or certain symmetries, can be used to reduce the cost of these algorithms with entanglement forging. To do so, we simulate a Fermi-Hubbard one-dimensional chain with a parametrized hopping term, as well as atomic nuclei ${}^{28}$Ne and ${}^{60}$Ti with the nuclear shell model. Using an adaptive variational quantum eigensolver we find significant reductions in both the maximum number of qubits (up to one fourth) and the amount of two-qubit gates (over an order of magnitude) required in the quantum circuits. Our findings indicate that our method, entropy-driven entanglement forging, can be used to adjust quantum simulations to the limitations of noisy intermediate-scale quantum devices.
Matthias Werner, Artur García-Sáez, Marta P. Estarellas
Jun 10, 2024·quant-ph·PDF In recent years, analog quantum simulators have reached unprecedented quality, both in qubit numbers and coherence times. Most of these simulators natively implement Ising-type Hamiltonians, which limits the class of models that can be simulated efficiently. We propose a method to overcome this limitation and simulate the time-evolution of a large class of spinless fermionic systems in 1D using simple Ising-type Hamiltonians with local transverse fields. Our method is based on domain wall encoding, which is implemented via strong (anti-)ferromagnetic couplings $|J|$. We show that in the limit of strong $|J|$, the domain walls behave like spinless fermions in 1D. The Ising Hamiltonians are one-dimensional chains with nearest-neighbor and, optionally, next-nearest-neighbor interactions. As a proof-of-concept, we perform numerical simulations of various 1D-fermionic systems using domain wall evolution and accurately reproduce the systems' properties, such as topological edge states, Anderson localization, quantum chaotic time evolution and time-reversal symmetry breaking via Floquet-engineering. Our approach makes the simulation of a large class of fermionic many-body systems feasible on analogue quantum hardware that natively implements Ising-type Hamiltonians with transverse fields.
Jordi Riu, Jan Nogué, Gerard Vilaplana, Artur Garcia-Saez, Marta P. Estarellas
Dec 18, 2023·quant-ph·PDF We propose a novel Reinforcement Learning (RL) method for optimizing quantum circuits using graph-theoretic simplification rules of ZX-diagrams. The agent, trained using the Proximal Policy Optimization (PPO) algorithm, employs Graph Neural Networks to approximate the policy and value functions. We demonstrate the capacity of our approach by comparing it against the best performing ZX-Calculus-based algorithm for the problem in hand. After training on small Clifford+T circuits of 5-qubits and few tenths of gates, the agent consistently improves the state-of-the-art for this type of circuits, for at least up to 80-qubit and 2100 gates, whilst remaining competitive in terms of computational performance. Additionally, we illustrate the versatility of the agent by incorporating additional optimization routines on the workflow during training, improving the two-qubit gate count state-of-the-art on multiple structured quantum circuits for relevant applications of much larger dimension and different gate distributions than the circuits the agent trains on. This conveys the potential of tailoring the reward function to the specific characteristics of each application and hardware backend. Our approach is a valuable tool for the implementation of quantum algorithms in the near-term intermediate-scale range (NISQ).
Stavros Efthymiou, Sergi Ramos-Calderer, Carlos Bravo-Prieto, Adrián Pérez-Salinas, Diego García-Martín, Artur Garcia-Saez, José Ignacio Latorre, Stefano Carrazza
We present Qibo, a new open-source software for fast evaluation of quantum circuits and adiabatic evolution which takes full advantage of hardware accelerators. The growing interest in quantum computing and the recent developments of quantum hardware devices motivates the development of new advanced computational tools focused on performance and usage simplicity. In this work we introduce a new quantum simulation framework that enables developers to delegate all complicated aspects of hardware or platform implementation to the library so they can focus on the problem and quantum algorithms at hand. This software is designed from scratch with simulation performance, code simplicity and user friendly interface as target goals. It takes advantage of hardware acceleration such as multi-threading CPU, single GPU and multi-GPU devices.
Axel Pérez-Obiol, Adrián Pérez-Salinas, Sergio Sánchez-Ramírez, Bruna G. M. Araújo, Artur Garcia-Saez
We devise a quantum-circuit algorithm to solve the ground state and ground energy of artificial graphene. The algorithm implements a Trotterized adiabatic evolution from a purely tight-binding Hamiltonian to one including kinetic, spin-orbit and Coulomb terms. The initial state is obtained efficiently using Gaussian-state preparation, while the readout of the ground energy is organized into seventeen sets of measurements, irrespective of the size of the problem. The total depth of the corresponding quantum circuit scales polynomially with the size of the system. A full simulation of the algorithm is performed and ground energies are obtained for lattices with up to four hexagons. Our results are benchmarked with exact diagonalization for systems with one and two hexagons. For larger systems we use the exact statevector and approximate matrix product state simulation techniques. The latter allows to systematically trade off precision with memory and therefore to tackle larger systems. We analyze adiabatic and Trotterization errors, providing estimates for optimal periods and time discretizations given a finite accuracy. In the case of large systems we also study approximation errors.
Oliver Buerschaper, Artur Garcia-Saez, Roman Orus, Tzu-Chieh Wei
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in [R. Orus, T.-C. Wei, O. Buerschaper, A. Garcia-Saez, arXiv:1406.0585] for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
Eduard Alarcón, Sergi Abadal, Fabio Sebastiano, Masoud Babaie, Edoardo Charbon, Peter Haring Bolívar, Maurizio Palesi, Elena Blokhina, Dirk Leipold, Bogdan Staszewski, Artur Garcia-Sáez, Carmen G. Almudever
Mar 24, 2023·quant-ph·PDF The grand challenge of scaling up quantum computers requires a full-stack architectural standpoint. In this position paper, we will present the vision of a new generation of scalable quantum computing architectures featuring distributed quantum cores (Qcores) interconnected via quantum-coherent qubit state transfer links and orchestrated via an integrated wireless interconnect.
Ema Puljak, Sergio Sanchez-Ramirez, Sergi Masot-Llima, Jofre Vallès-Muns, Artur Garcia-Saez, Maurizio Pierini
Tensor Networks have emerged as a prominent alternative to neural networks for addressing Machine Learning challenges in foundational sciences, paving the way for their applications to real-life problems. This paper introduces tn4ml, a novel library designed to seamlessly integrate Tensor Networks into optimization pipelines for Machine Learning tasks. Inspired by existing Machine Learning frameworks, the library offers a user-friendly structure with modules for data embedding, objective function definition, and model training using diverse optimization strategies. We demonstrate its versatility through two examples: supervised learning on tabular data and unsupervised learning on an image dataset. Additionally, we analyze how customizing the parts of the Machine Learning pipeline for Tensor Networks influences performance metrics.