1,720,994 research outputs found
Quantum Benchmarking: entanglement measures in quantum computers
Get PDFMàster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2022-2023. Tutora : Alba Cervera-LiertaQuantum computation has emerged as a promising paradigm shift in the field of computing, and with the advent of new quantum computers, it has become crucial to assess and quantify their performance. Benchmarking, a wellestablished practice in the field, plays a vital role in this regard. One effective way to evaluate a quantum computer’s capabilities is by measuring the amount of entanglement it exhibits, as entanglement is a fundamental characteristic of quantum systems. In this thesis, we provide a comprehensive overview of the current landscape of quantum benchmarking and propose several protocols for estimating the Rényi entropy of quantum states, which offers valuable insights into the entanglement structure of these states. We present a protocol based on the renowned Swap test, specifically designed for future fault-tolerant devices, as well as another protocol based on randomized measurements to address the limitations of current NISQ devices. We have implemented these protocols on the quantum simulation framework of Qibo, ensuring an efficient and reliable execution on any quantum computer, in particular the one at the Barcelona
Supercomputing Center (BSC). Through this work, we aim to contribute to the advancement of quantum benchmarking and facilitate the assessment of entanglement in quantum computing systems
Quantum function fitting and classification beyond the single-qubit model
Get PDFMàster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2021-2022. Tutora: Alba Cervera-Lierta.Quantum Neural Networks (QNNs) have emerged as one promising Quantum
Machine Learning (QML) technique. While the models for single and
multi-qubit QNNs have been extensively studied, it remains unknown if using
higher-dimensional systems provide any advantage. In this work, we investigate
the theoretical foundation of the qubit model and we compare it with the
qutrit prototype. First, we show that a single qubit can reproduce a Fourier series,
while a qutrit can fit a more complicated type of function, with additional
degrees of freedom that the model can adjust. Second, we explore the benefits
of the third extra level of the qutrit for the classification task. In addition,
we examine the two-qubit classifier and see that using a local cost function
on the training improves the results, according to recent studies. Beyond the
theoretical discussion, we provide numerical benchmarks of the models studied
Application of Grover’s quantum algorithm for string matching
Get PDFTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2022, Tutors: Alba Cervera Lierta, Bruno Juliá DíazIn this work we present a quantum algorithm for exact string matching that relies on Grover’s algorithm. Grover’s algorithm, commonly used for unsorted data search, can be adapted to solve the problem and find a pattern’s location within a string. This work contains the demonstration of Grover’s algorithm for one and multiple target. It also presents the principles of quantum string matching, how to tackle this type of problem using Grover’s algorithm and the detailed steps to construct the query. The quantum string matching algorithm is then implemented in Qibo, an open-source full stack API for quantum simulation and quantum hardware control. We explicitly expose an example for a string of length N = 8 and a pattern of length M = 2
Simulation of XY model in a quantum computer
Get PDFTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2023, Tutors: Alba Cervera Lierta, Bruno Juliá DíazThe field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, with the aim of efficiently simulating and comprehending the complexities of quantum physics. In this paper, we address this need by utilizing a scheme proposed in previous works for the exact simulation of the 1-D XY model on a quantum computer. Using the Qibo software, we successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Among all possibilities this opens, we have computed the transverse magnetization’s expected value for the ground state which allows the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computer
Scaling of entanglement support for iTEBD algorithm
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: José Ignacio LatorreWe present the results obtained by using the iTEBD algorithm in the Ising and
Heisenberg models as well as in the AKLT model. By modifying the external eld parameter, in the
Ising case, and the anisotropy parameter, in the Heisenberg case, we can observe quantum phase
transitions in their ground states. In the AKLT model we study its generalization to nd its phase
transition. To study these transitions, we analyse the entanglement of the system near the critical point in order to nd scaling laws
Maximal Entanglement. Applications in Quantum Information and Particle Physics
Get PDFPrograma de Doctorat FísicaThe aim of this thesis is to study the quantum entanglement and, in particular, under which circumstances is maximum.
In the first place, Bell's inequalities are analyzed from an operational point of view. In particular, we focus on those involving qutrits. The states that maximally violate these inequalities are of the GHZ type, for inequalities involving qubits, and little deformations of GHZ state, for those involving qutrits. This result shows that, although maximum entanglement and non-locality are very close concepts, they are not equivalent.
In the second place, multipartite entanglement in spin chains is studied. We use as a figure of merit the hyperdeterminant and two polynomial invariants, S and T. These figures quantify a specific type of quadripartite entanglement, as demonstrated by an analysis of well-known quantum states such as the GHZ or W. In an Ising spin chain, we observe a pronounced peak near the quantum phase transition. Similar results are observed for the XXZ and Haldane- Shastry models for the case of the S and T invariants. For that reason, we conclude that these figures of merit are sensitive to quantum phase transitions.
The second part of the thesis focuses on the field of quantum computing. This field has experienced a significant expansion in recent years. Due to this growth, several companies have started to develop prototypes of quantum computers. For this reason, one line of research in quantum computing is to propose methods to benchmark these machines.
One of the methods presented in this thesis consists of the exact simulation of a XY spin chain. We propose a circuit that diagonalizes the XY Hamiltonian, which allows simulating time evolution and thermal states as well. Since this model is exactly solvable, the results obtained from a quantum computer can be compared with the theoretical solution. After running this circuit for four qubits on two IBM computers and one from Rigetti computing company, we obtain worse results than expected. With this, we conclude that there are error sources that, in general, are not being taken into account and that become relevant even in such small circuits.
Moreover, we propose another method to test quantum computers performance: the simulation of absolutely maximally entangled states. The implementation of these circuits is a hard but necessary test for a quantum computer since the advantage of quantum algorithms lies in the generation of entanglement.
Finally, we study the generation of entanglement at the most fundamental level: particle physics. We obtain that the QED interaction at tree-level is dictated by the imposition of maximal entanglement in outgoing particles. We apply the same philosophy in processes involving weak neutral currents obtaining that the weak mixing angle must be pi / 6, very close to the experimental value.La motivació d’aquesta tesi és estudiar l’entrellaçament en general i sota quines circumstàncies és màxim en particular.
Primerament, estudiem i deduïm noves desigualtats de Bell en termes d’operadors, focalitzant-nos en aquelles que involucren qutrits. Les desigualtats per qubits són violades màximament pels estats coneguts com a GHZ mentre que les de qutrits, per estats que són una deformació dels GHZ.
Seguidament, estudiem l’entrellaçament multipartit i la seva aplicació en la detecció de transicions de fase quàntiques. Com a figura de mèrit, utilitzem l’hiperdeterminant i els invariants S i T. Obtenim un pic pronunciat de l'hiperdeterminant al voltant de la transició de fase en el cas del model d’Ising. En el cas del model XXZ, el valor dels invariants canvia bruscament en els punts on hi ha transició de fase, resultat similar al obtingut en el model de Haldane-Shastry.
En una segona part de la tesi, ens centrem en el camp de la computació quàntica. Per una banda, proposem i testegem un mètode que consisteix en la simulació exacta del model d’Ising. Proposem un circuit quàntic que diagonalitza l’Hamiltonià d’Ising i que, per tant, fa possible la simulació en el temps i la preparació d’estats tèrmics. Testegem aquest circuit pel cas d’una cadena de quatre espins en tres ordinadors quàntics. Els resultats difereixen notablement del valor teòric esperat. Això fa pensar que encara hi ha moltes fonts d'error a tenir en compte en aquest tipus de dispositius.
Per altra banda, proposem la simulació d'estats absolutament màximament entrellaçats. També analitzem com l’entropia de cada bipartició majoritza i utilitzem aquesta propietat per trobar els circuits més òptims.
Finalment, estudiem quina ha de ser l’estructura de la interacció de QED per tal de poder generar estats màximament entrellaçats en termes de les helicitats de les partícules sortints. El resultat demostra que, a primer ordre, la interacció de QED es recupera imposant màxim entrellaçament. També estudiem quines implicacions té aquesta imposició en processos que involucrin corrents dèbils neutres. El resultat a primer ordre és que el valor de l’angle de Weinberg ha de ser de pi/6, molt proper al valor experimental
Scaling of entanglement support for iTEBD algorithm
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: José Ignacio LatorreWe present the results obtained by using the iTEBD algorithm in the Ising and
Heisenberg models as well as in the AKLT model. By modifying the external eld parameter, in the
Ising case, and the anisotropy parameter, in the Heisenberg case, we can observe quantum phase
transitions in their ground states. In the AKLT model we study its generalization to nd its phase
transition. To study these transitions, we analyse the entanglement of the system near the critical point in order to nd scaling laws
Multidimensional Fourier series with quantum circuits
Get PDFQuantum machine learning is the field that aims to integrate machine learning
with quantum computation. In recent years, the field has emerged as an active
research area with the potential to bring new insights to classical machine
learning problems. One of the challenges in the field is to explore the
expressibility of parametrized quantum circuits and their ability to be
universal function approximators, as classical neural networks are. Recent
works have shown that with a quantum supervised learning model, we can fit any
one-dimensional Fourier series, proving their universality. However, models for
multidimensional functions have not been explored in the same level of detail.
In this work, we study the expressibility of various types of circuit ansatzes
that generate multidimensional Fourier series. We found that, for some
ansatzes, the degrees of freedom required for fitting such functions grow
faster than the available degrees in the Hilbert space generated by the
circuits. For example, single-qudit models have limited power to represent
arbitrary multidimensional Fourier series. Despite this, we show that we can
enlarge the Hilbert space of the circuit by using more qudits or higher local
dimensions to meet the degrees of freedom requirements, thus ensuring the
universality of the models.Comment: 8 pages, 5 figures + appendice
Perspectives on Quantum Sensing and Computation for Particle Physics
No full textA universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this talk, I provide an overview of NISQ algorithms, their limitations and potential advantages
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