Multiplicative Majorana zero-modes

Abstract

Topological qubits composed of unpaired Majorana zero-modes are under intense experimental and theoretical scrutiny in efforts to realize practical quantum computation schemes. In this work, we show the minimum four \textit{unpaired} Majorana zero-modes required for a topological qubit according to braiding schemes and control of entanglement for gate operations are inherent to multiplicative topological phases, which realize symmetry-protected tensor products -- and maximally-entangled Bell states -- of unpaired Majorana zero-modes known as multiplicative Majorana zero-modes. We introduce multiplicative Majorana zero-modes as topologically-protected boundary states of both one and two-dimensional multiplicative topological phases, using methods reliant on multiplicative topology to construct relevant Hamiltonians from the Kitaev chain model. We furthermore characterize topology in the bulk and on the boundary with established methods while also introducing techniques to overcome challenges in characterizing multiplicative topology. In the process, we explore the potential of these multiplicative topological phases for an alternative to braiding-based topological quantum computation schemes, in which gate operations are performed through topological phase transitions.

24 pages, 23 figures, and 2 tables in main text, 11 pages in supplementary materials

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana box qubits
• Parity qubits and poor man's Majorana bound states in double quantum dots
• Observation of a Majorana zero mode in a topologically protected edge channel
• Multiplicative topological phases
• Finite-size Topology

Cited by in corpus (8)

• Quantum skyrmion Hall effect
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Finite-size topological phases from semimetals
• Multiplicative topological semimetals
• Topological quantum criticality from multiplicative topological phases
• Topological states constructed by two different trivial quantum wires
• Observable-enriched entanglement
• Multiplicative Chern insulator