Photonic implementation of Majorana-based Berry phases

Abstract

Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies, alike. Intriguingly, the exotic statistics of anyons realised in physical systems can be interpreted as a topological version of geometric phases. However, non-Abelian statistics has not yet been demonstrated in the laboratory. Here we employ an all optical quantum system that simulates the statistical evolution of Majorana fermions. As a result we experimentally realise non-Abelian Berry phases with the topological characteristic that they are invariant under continues deformations of their control parameters. We implement a universal set of Majorana inspired gates by performing topological and non-topological evolutions and investigate their resilience against perturbative errors. Our photonic experiment, while it is not scalable, it suggests the intriguing possibility of experimentally simulating Majorana statistics with scalable technologies.

8 pages, 4 figures

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana Zero Modes and Topological Quantum Computation
• An Open-System Quantum Simulator with Trapped Ions
• Quantum trajectories and open many-body quantum systems
• Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor
• Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure

Cited by in corpus (9)

• Non-Abelian braiding on photonic chips
• Majorana nanowires for topological quantum computation
• Noise-resilient Edge Modes on a Chain of Superconducting Qubits
• Emulating quantum teleportation of a Majorana zero mode qubit
• Digital Simulation of Topological Matter on Programmable Quantum Processors
• Observing and braiding topological Majorana modes on programmable quantum simulators
• Topological contextuality and anyonic statistics of photonic-encoded parafermions
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Twenty years of quantum contextuality at USTC