Quantum and quantum-inspired algorithms

Quantum algorithms take advantage of quantum phenomena such as entanglement and superposition to solve problems unreachable by classical computers, or to outperform them in the performance of similar tasks. While the applications of quantum computing are wide reaching, we are still in the NISQ era, where noise and small numbers of qubits dominate our quantum capabilities. Guided by these constraints, our group is dedicated to the research of novel quantum algorithms capable of working with short and medium term quantum computers, such as: partial differential equations (PDE’s) solvers, exploring quantum algorithms to solve hard optimization problems, and developing quantum-inspired algorithms that run in classical computers.

Quantum optimization

A wide range of optimization problems can be mapped into a QUBO problem or an Ising Hamiltonian, from finance and the more academic MaxCut problem to finding the ground state of spin glass Hamiltonians. Quantum variational optimization has emerged as a promising framework to solve these problems faster and at a larger scale than what classical methods allow. In this regard, we study the performance of state-of-art algorithms such as the Variational Quantum Eigensolver [1]. Furthermore, we explore practical applications in finance, where we have developed a hybrid quantum-classical algorithm to choose a series of assets that track a particular financial index [2].

Quantum PDE solvers

Quantum and quantum-inspired algorithms
Variational quantum PDE solver [3].

PDE’s have a wide range of applications, from physics and chemistry to finance, and hence its resolution is a particularly interesting problem. There is a great variety of classical numerical methods available for this task. However, their limited precision and memory and time requirements make it necessary to look for suitable alternatives. We propose the use of a variational hybrid quantum-classical algorithm to tackle this problem whose hybrid nature makes it suitable for current NISQ devices [3].

Tensor networks

Tensor networks are a mathematical description to represent quantum-many body states based on the entanglement structure. This formalism allows to reduce the number of parameters that represent a state, and hence is efficient for the simulation of many body systems. This can be applied to quantum computing, by using tensor networks to represent qubits, allowing for the use of a greater number of qubits than current quantum computers, both real and simulators. By using tensor networks we aim at developing quantum-inspired algorithms for a variety of problems, such as multivariate analysis [4].

Quantum and quantum-inspired algorithms
Matrix product state.

Group members working on this field


[1] Quantum variational optimization: the role of entanglement and problem hardness, Pablo Díez-Valle, Diego Porras, Juan José García-Ripoll, arXiv:2103.14479 (2021).

[2] Hybrid quantum-classical optimization for financial index tracking, Samuel Fernández-Lorenzo, Diego Porras, Juan José García-Ripoll, arXiv:2008.12050 (2020).

[3] Solving partial differential equations in quantum computers, Paula García-Molina, Javier Rodríguez-Mediavilla, Juan José García-Ripoll, arXiv:2104.02668 (2021).

[4] Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations, Juan José García-Ripoll, Quantum 5, 431 (2021).