Observing and braiding topological Majorana modes on programmable quantum simulators

Abstract

Electrons are indivisible elementary particles, yet paradoxically a collection of them can act as a fraction of a single electron, exhibiting exotic and useful properties. One such collective excitation, known as a topological Majorana mode, is naturally stable against perturbations, such as unwanted local noise, and can thereby robustly store quantum information. As such, Majorana modes serve as the basic primitive of topological quantum computing, providing resilience to errors. However, their demonstration on quantum hardware has remained elusive. Here, we demonstrate a verifiable identification and braiding of topological Majorana modes using a superconducting quantum processor as a quantum simulator. By simulating fermions on a one-dimensional lattice subject to a periodic drive, we confirm the existence of Majorana modes localized at the edges, and distinguish them from other trivial modes. To simulate a basic logical operation of topological quantum computing known as braiding, we propose a non-adiabatic technique, whose implementation reveals correct braiding statistics in our experiments. This work could further be used to study topological models of matter using circuit-based simulations, and shows that long-sought quantum phenomena can be realized by anyone in cloud-run quantum simulations, whereby accelerating fundamental discoveries in quantum science and technology.

6 pages (main text)+ 9 pages (supplementary); 6 figures

References in corpus (5)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Constructing local integrals of motion in the many-body localized phase
• Stability of zero modes in parafermion chains
• Spin-polarized Yu-Shiba-Rusinov states in an iron based superconductor
• Emulating anyonic fractional statistical behavior in a superconducting quantum circuit

Cited by in corpus (10)

• Noise-resilient Edge Modes on a Chain of Superconducting Qubits
• Slowly decaying zero mode in a weakly non-integrable boundary impurity model
• Simulating Majorana zero modes on a noisy quantum processor
• Simulation of Kitaev model using one-dimensional chain of superconducting qubits and environmental effect on topological states
• Tensor Network enhanced Dynamic Multiproduct Formulas
• Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions
• Isolated zero mode in a quantum computer from a duality twist
• Braiding fractional quantum Hall quasiholes on a superconducting quantum processor
• Non-Abelian anyon statistics through AC conductance of a Majorana interferometer
• Realizing non-trivial doublon formation using a quantum computer