Characterization and simulation of multipartite open quantum systems

Cattaneo, Marco (Supervisors: Zambrini, Roberta; Maniscalco, Sabrina; Rossi, Matteo A.C. and Giorgi, Gian Luca)
PhD Thesis (2023)

Having a quick look at contemporary quantum mechanics, we immediately see that the study of open quantum systems is of great relevance both for fundamental reasons and for the development of quantum technologies that will be able to display quantum advantage. An open quantum system is defined in a very general way as a non-isolated quantum system that is interacting with one or more external environments. This picture can give us a valuable insight, for instance, into how a single superconducting qubit of a quantum computer that is subject to thermal fluctuations loses its coherences, or into the thermodynamics of an atom immersed in the electromagnetic field. Hence, improving our understanding of the dynamics and characterization of open quantum systems is a crucial challenge in the second quantum revolution, as well as a fascinating step forward in the study of the deepest concepts in Physics, such as the quantum to classical transition.

Motivated by renewed studies on dissipative collective effects, by new discoveries about the features of noise in quantum computers, and by recent experiments focused on many-qubit systems, the interest in multipartite open quantum systems has recently risen. A dissipative collective effect may be defined as the coherent interference of the emissions (and/or absorptions) of many quantum particles interacting with external environments. Multipartite open quantum systems are open systems made of multiple subsystems, which can interact with each other and at the same time may be coupled to local and/or collective environments. This type of open quantum systems plays a crucial role, for instance, in the study of ``crosstalk errors'' in quantum information processors, in the thermodynamic analysis of spin or harmonic oscillator chains, as well as in the description of collective phenomena such as superradiance and quantum synchronization. The characterization and simulation of the dynamics of multipartite open quantum systems is the topic of this doctoral dissertation.

This thesis consists of six original research articles and an introduction to their methodology, scope, and significance. The first two publications explore the validity and features of the so-called global and local master equations (i.e., the equations of motion for open quantum systems), which are widely employed in quantum thermodynamics. In particular, these papers are focused on a particular type of master equation based on the ``partial secular approximation'', which is shown to be accurate in all regimes of validity of the standard Markovian master equation. Moreover, the symmetry properties of these master equations are discussed. The third scientific article shows how the most common examples of multipartite open quantum systems can be simulated through a platform of superconducting qubits coupled to a resistor emitting thermal noise. The fourth publication studies how different collective effects, such as quantum synchronization, subradiance and entanglement generation, can emerge in a model of two detuned qubits coupled to a common bath. The fifth research paper introduces a quantum algorithm based on a collision model that is able to simulate the most general Markovian multipartite quantum dynamics, and proves that this algorithm can be efficiently simulated on a quantum computer. Finally, the sixth publication presents the experimental implementation of this algorithm on a near-term quantum computer, and assesses both theoretically and experimentally the features of noise on the algorithm.

In conclusion, this thesis brings some relevant contributions to the field of multipartite open quantum systems, not only regarding methodological questions, but also phenomenological predictions and experimental implementations on a quantum computer. These contributions include the description and characterization of a general master equation for Markovian multipartite open quantum systems, and some new procedures for the analog and digital quantum simulation thereof.

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