Quantum simulation of minimal Kitaev chains

This master thesis presents a computational framework to simulate the time evolution of the minimal Kitaev chain. A minimal Kitaev chain is a system of spinless fermions with two-sites and p-wave superconductivity that hosts self-conjugate quasiparticles known as poor man's Majorana modes, like regular Majorana zero modes but without topological protection. The minimal Kitaev chains have properties akin to their regular counterparts, such as being useful for non-local information encoding and indicating an emerging state of matter. Despite recent experimental efforts, its realization remains challenging. This master thesis aims to provide an alternative approach to realizing minimal Kitaev chains using existing noisy quantum processors. These systems are challenging to implement experimentally, making quantum simulation a compelling and practical alternative to study them. The focus is on simulating various configurations of minimal Kitaev chains, demonstrating how their behavior can be explored through quantum computation when direct physical realization is not feasible. The framework integrates theoretical modeling of the Kitaev chain's Hamiltonian with quantum computing techniques; the core of this work involves translating the system's Hamiltonian and its time-evolution into the language of quantum computers. The study is structured as follows: Chapter 1 introduces the work, while Chapter 2 lays down the basic concepts from condensed matter and quantum physics. Chapter 3 goes through the required quantum computing theory. Subsequently, Chapter 4 presents the methodology for quantum simulation used in this work. Building upon these principles, Chapter 5 investigates the specifics of two- and three-site Kitaev chains. The work then finishes with Chapter 6 by analyzing a Josephson junction comprised oftwo coupled minimal Kitaev chains, where phase-dependent energy spectra and zero-energy modes are studied. The results demonstrate that minimal Kitaev chains can be effectively simulated, and physically relevant quantities can be extracted through measurements of targeted observables. The findings of this work show that, by operating within specific parameter regimes, circuit depth can be minimized, thereby reducing the risk of decoherence. Challenges in quantum simulation, such as Trotterization errors and circuit complexity are examined, as these are important to address to for enable simulation on noisy quantum processors. Overall, this research offers a feasible strategy for studying poor man's Majorana modes on currently available quantum processors