Contributor info: Mr Sebastian Miles

A. Mert Bozkurt, Sebastian Miles, Sebastiaan L. D. ten Haaf, Chun-Xiao Liu, Fabian Hassler, Michael Wimmer

SciPost Phys. 18, 206 (2025) · published 25 June 2025 | Toggle abstract · pdf

We theoretically explore the emergence of strong zero modes in a two-site chain consisting of two quantum dots coupled due to a central dot that mediates electron hopping and singlet superconducting pairing. In the presence of time-reversal symmetry, the on-site Coulomb interaction leads to a three-fold ground-state degeneracy when tuning the system to a sweet spot as a function of the inter-dot couplings. This degeneracy is protected against changes of the dot energies in the same way as "poor man's" Majorana bound states in short Kitaev chains. In the limit of strong interactions, this protection is maximal and the entire spectrum becomes triply degenerate, indicating the emergence of a "poor man's" version of a strong zero mode. We explain the degeneracy and protection by constructing corresponding Majorana Kramers-pair operators and $\mathbb{Z}_3$-parafermion operators. The strong zero modes share many properties of Majorana bound states in short Kitaev chains, including the stability of zero-bias peaks in the conductance and the behavior upon coupling to an additional quantum dot. However, they can be distinguished through finite-bias spectroscopy and the exhibit a different behavior when scaling to longer chains.

Isidora Araya Day, Sebastian Miles, Hugo K. Kerstens, Daniel Varjas, Anton R. Akhmerov

SciPost Phys. Codebases 50 (2025) · published 12 February 2025 | Toggle abstract · pdf

A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer-Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.

Isidora Araya Day, Sebastian Miles, Hugo K. Kerstens, Daniel Varjas, Anton R. Akhmerov

SciPost Phys. Codebases 50-r2.1 (2025) · published 12 February 2025 | Toggle abstract · src

A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer-Wolff transformation achieves this and constructs an effective Hamiltonian, its scaling is suboptimal, it is limited to two subspaces, and implementing it efficiently is both challenging and error-prone. We introduce an algorithm for constructing an equivalent effective Hamiltonian as well as a Python package, Pymablock, that implements it. Our algorithm combines an optimal asymptotic scaling and the ability to handle any number of subspaces with a range of other improvements. The package supports numerical and analytical calculations of any order and it is designed to be interoperable with any other packages for specifying the Hamiltonian. We demonstrate how the package handles constructing a k.p model, analyses a superconducting qubit, and computes the low-energy spectrum of a large tight-binding model. We also compare its performance with reference calculations and demonstrate its efficiency.

Kostas Vilkelis, Antonio Manesco, Juan Daniel Torres Luna, Sebastian Miles, Michael Wimmer, Anton Akhmerov

SciPost Phys. 16, 135 (2024) · published 27 May 2024 | Toggle abstract · pdf

We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device consists of quantum dots tunnel-coupled by a hybrid superconducting island and a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions implements the universal set of quantum gates defined by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002)]. Due to the similarity with charge qubits, we expect charge noise to be the main source of decoherence. For this reason, we also consider an alternative design where the quantum dots have tunable coupling to the superconductor. In this second device design, we show that there is a sweet spot for which the local fermionic modes are charge neutral, making the device insensitive to charge noise effects. Finally, we compare both designs and their experimental limitations and suggest future efforts to overcome them.