Baker's map, introducción al caos cuántico

Los sistemas dinámicos se pueden cuantizar para encontrar equivalentes dentro de la mecánica cuántica. En este trabajo, se ha estudiado como ejemplode sistema caótico el mapa del panadero (Bakers map). En primer lugar, se ha realizado un estudio desde un punto de vista clásico que posteriormentese generaliza a un mapa cuántico caótico. Además, se proponen nuevos métodos para analizar los mapas unitarios que se ejecutan en ordenadorescuánticos reales, con experimentos que intentan encontrar indicios de caos a partir de estadísticas de medidas cuánticas. Aplicando estos métodos conun circuito de prueba, se propone usar los resultados para medir la calidad de los computadores cuánticos en los que se ejecutan.Grado en Matemática

All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks

Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.Comment: 36+14 page

Estudio de QSVM, algoritmo de Machine Learning Cuántico

El Machine Learning es una rama que se está viendo potenciada con la aparición de la computación cuántica. Uno de los algoritmos tradicionales en este campo es el Suport Vector Machine(SVM). En este trabajo, desarrollado con IBM, se estudiará su versión cuántica y su aplicación en tareas de clasificación complejas. Además se llevará a cabo una experimentación sobre los resultados en computadores cuánticos reales para estudiar su comportamiento con la tecnología actual.Grado en Ingeniería Informática de Servicios y Aplicacione

GPS: A New TSP Formulation for Its Generalizations Type QUBO

We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. After, we will present a detailed study of the constraints subject to the new TSP model and benchmark it with MTZ and native formulations. Finally, we will test whether the correctness of the formulation by entering it into a QUBO problem solver. The solver chosen is a D-Wave_2000Q6 quantum computer simulator due to the connection between Quantum Annealing and QUBO formulations

GPS: A New TSP Formulation for Its Generalizations Type QUBO

We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of necessary variables. After, we will present a detailed study of the constraints subject to the new TSP model and benchmark it with MTZ and native formulations. Finally, we will test whether the correctness of the formulation by entering it into a QUBO problem solver. The solver chosen is a D-Wave_2000Q6 quantum computer simulator due to the connection between Quantum Annealing and QUBO formulations

qRobot: A Quantum Computing Approach in Mobile Robot Order Picking and Batching Problem Solver Optimization

This article aims to bring quantum computing to robotics. A quantum algorithm is developed to minimize the distance traveled in warehouses and distribution centers where order picking is applied. For this, a proof of concept is proposed through a Raspberry Pi 4, generating a quantum combinatorial optimization algorithm that saves the distance travelled and the batch of orders to be made. In case of computational need, the robot will be able to parallelize part of the operations in hybrid computing (quantum + classical), accessing CPUs and QPUs distributed in a public or private cloud. We developed a stable environment (ARM64) inside the robot (Raspberry) to run gradient operations and other quantum algorithms on IBMQ, Amazon Braket (D-Wave), and Pennylane locally or remotely. The proof of concept, when run in the above stated quantum environments, showed the execution time of our algorithm with different public access simulators on the market, computational results of our picking and batching algorithm, and analyze the quantum real-time execution. Our findings are that the behavior of the Amazon Braket D-Wave is better than Gate-based Quantum Computing over 20 qubits, and that AWS-Braket has better time performance than Qiskit or Pennylane