Circuit Complexity through phase transitions: consequences in quantum state preparation

In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.Comment: 25 pages, 12 figure

Simulación de materiales magnéticos en un ordenador cuántico.

Introducción de algoritmos en ordenadores cuánticos y análisis de sistemas magnéticos con estos algoritmos.<br /

Waveguide QED at the onset of spin-spin correlations

We experimentally explore the competition between light-mediated and direct matter-matter interactions in waveguide quantum electrodynamics. For this, we couple a superconducting line to a model magnetic material, made of organic free radical DPPH molecules with a spin $S=1/2$ and a $g_{S}$ factor very close to that of a free electron. The microwave transmission has been measured in a wide range of temperatures ($0.013$ K $\leq T \leq 2$ K), magnetic fields ($0\leq B \leq 0.5$ T) and frequencies ($0 \leq \omega/2 \pi \leq 14$ GHz). We find that molecules belonging to the crystal sublattice B form one-dimensional spin chains. Temperature then controls intrinsic spin correlations along the chain in a continuous and monotonic way. In the paramagnetic region ($T > 0.7$ K), the microwave transmission shows evidences for the collective coupling of quasi-identical spins to the propagating photons, with coupling strengths that reach values close to the dissipation rates. As $T$ decreases, the growth of intrinsic spin correlations, combined with the anisotropy in the spin-spin exchange constants, break down the collective spin-photon coupling. In this regime, the temperature dependence of the spin resonance visibility reflects the change in the nature of the dominant spin excitations, from single spin flips to bosonic magnons, which is brought about by the magnetic correlation growth

Qudit machine learning

We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST datasets. We explore various learning models in the metric learning framework, along with different encoding strategies. In particular, we employ data re-uploading techniques and maximally orthogonal states to accommodate input data within low-dimensional systems. Our findings reveal optimal strategies, indicating that when the dimension of input feature data and the number of classes are not significantly larger than the qudit’s dimension, our results show favorable comparisons against the best classical models. This trend holds true even for small quantum systems, with dimensions d<5 and utilizing algorithms with a few layers (L =1,2). However, for high-dimensional data such as MNIST, we adopt a hybrid approach involving dimensional reduction through a convolutional neural network. In this context, we observe that small quantum systems often act as bottlenecks, resulting in lower accuracy compared to their classical counterparts

Control eléctrico de qubits de espín

The modulation of matter through electromagnetic fields is usually associated with magnetic fields to control spins and electric fields to displace charges. But is there a way to control spins with electric fields? In this master's thesis we explore how to couple spins of magnetic molecules to electric fields in order to control qubits coherently in an efficient way. In the first section we present the theoretical basis on which the modulation of molecules by electric fields is based; in the second section we propose a candidate material that can exhibit magnetoelectric coupling and, finally, in the third section we discuss light-matter coupling theory and propose circuit designs on which to experimentally measure these effects.<br /

Teorema adiabático y computación cuántica

Obtención del estado fundamental del modelo ZZXZ mediante el teorema adiabático y el uso de la computación cuántica para la construcción de circuitos cuánticos, los cuales simulan un sistema cuántico real. También está el aprendizaje de diversos métodos para llegar a la solución más allá del convencional, como los llamados "atajos hacia la adiabaticidad", y comparar el funcionamiento de ambas formas de resolución del problema inicial.<br /

Generación de estados de espín "squeezed" en materiales híbridos

We explore the interaction between light and matter inside cavities. Specifically, we start in Section 1 with the electromagnetic field quantization and presenting the essential parameters that we will use to describe this interaction. In Section 2 we study non-linear interactions in which one photon can generate two excitations in a spin ensemble to finally, in Section 3, determine whether it is feasible to observe this effect experimentally or not.<br /