Majorana Zero Modes: Braiding, Robustness & Transport
Anchor paper: K. Agarwal, I. Martin, "Double braiding Majoranas for quantum computing and Hamiltonian engineering," PRX Quantum 1, 020324 (2020). [arXiv:2004.11385]
Background
In 1D topological superconductors (Kitaev chains), unpaired Majorana zero modes bind to the wire's ends and, when well separated, give the ground state a topologically protected degeneracy. Braiding Majoranas implements non-Abelian statistics as fault-tolerant gates — the basis of topological quantum computing. But in a single 1D wire the Majoranas sit at fixed endpoints, so physically transporting one around another requires geometrically awkward T/Y-shaped wire networks, and realistic Majoranas have finite overlap/hybridization that lifts the protected degeneracy. This motivated schemes reproducing braiding's topological effect — and suppressing hybridization — without literally moving Majoranas through space.
New results
The authors introduce "double braids" (draids): carrying one Majorana all the way around another and back, flipping the sign of both via a topologically robust π phase, without physical exchange or projective measurement. Draids can be implemented dynamically (e.g. by periodically modulating a quantum-dot–wire coupling), and rapid "polyfractal" sequences of draids can selectively cancel inter-Majorana couplings — "Majorana purification" — suppressing residual dynamics in the near-degenerate computational subspace. Beyond quantum-computing gates, the same toolkit engineers effective Hamiltonians and realizes nontrivial topological phases from otherwise imperfect, overlapping Majoranas, demonstrating over an order-of-magnitude suppression of hybridization with realistic parameters.
Fig. 1 — the double braid ("draid") operation, which flips the sign of a pair of Majoranas without physical exchange.
Related work in this direction
This anchors an active, ongoing research program: optimized transport/shuttling of Majoranas through disordered and noisy wires (Agarwal, Truong & Pereg-Barnea, 2023/2026), dynamical protocols to strengthen and identify genuine Majorana qubits vs. trivial bound states (Min, Fajardo, Pereg-Barnea & Agarwal, PRB 105, 155412, 2022), and foundational reformulations of braiding and edge-mode physics in number-conserving and undriven wires (Agarwal & Martin, PRB 113, 155149, 2026; Sajith, Agarwal & Martin, PRB 109, 184509, 2024; Thomas-Markarian, Agarwal & Martin, PRL 137, 086504, 2026). Together these push the original scheme toward experimentally realistic, noise-robust implementations of Majorana-based topological quantum computing.
Bath-Induced Dissipative Phase Transitions is nested here: it uses the SSH model — a simpler cousin of the Kitaev chain — as a testbed for the strong-coupling, non-Markovian bath effects relevant to assessing Majorana wire robustness against dissipation.