4 research outputs found
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 /
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 /
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 /