Superconducting quantum dynamics with the time-dependent Pfaffian method
Dan Crawford
School of Physics, University of Melbourne, Parkville, VIC 3010, Australia
Superconducting heterostructures generate many interesting physical phenomena, such as topological superconductivity, tailored spin textures, or the superconducting diode effect. Thus, they are key elements of quantum technologies, with applications for example in spintronics and quantum computing. It is essential to simulate the superconducting many-body quantum dynamics of realistic microscopic systems.
Existing methods for studying many-body superconducting dynamics are restricted to tiny system sizes, give approximate results, or are unable to compute arbitrary overlaps. Because of anomalous terms superconducting many-body states cannot be constructed with a Slater determinant. Here I introduce a new method --- the time-dependent Pfaffian --- for constructing and time evolving many-body superconducting states out of single-particle states. I show how to calculate arbitrary many-body overlaps, as well as expectation values and correlators.
I use this method to simulate the braiding of Majorana zero-modes, which constitute the primary path toward topologically protected quantum computing. By calculating the fidelity, transition probabilities, and joint parities of Majorana pairs, I demonstrate the single-qubit gates and the two-qubit CNOT gate, via dynamical braiding. These results open the path to test and analyze the many theoretical implementations of Majorana qubits, as well as demonstrating the potential for applying this method to other superconducting problems.
