Observing and braiding topological Majorana modes on programmable quantum simulators

This work advances the quantum simulation of topological matter. Our work enables the detailed study of the emergent topological Majorana modes localized at the boundaries. We propose a method to verify the topological nature of the modes and then propose an efficient technique for braiding them.
Observing and braiding topological Majorana modes on programmable quantum simulators

Majorana fermions, first proposed by the Italian theoretical physicist Ettore Majorana in 1937, are a unique example of particles that are their own antiparticles. Originally proposed as possible candidates for neutrinos, these fermions have also been considered as part of the solution to the mysteries of dark matter and baryon asymmetry. The pioneering work of Alexei Kitaev in 2001 [1] showed that Majorana fermions can exist as "half-electron" states, also known as Majorana modes, in certain quantum materials. This discovery has sparked extensive research into the use of these exotic particles to encode quantum information with applications in quantum computing.

Despite the ingenuity, implementation of Kitaev's idea has proven to be a challenging journey [2]. Issues such as the destructive role of disorder and electron interactions make Majorana modes difficult to observe. This is exacerbated by the difficulty of distinguishing topological Majorana modes from other trivial ones lacking any interesting properties.

Detection of Majorana modes. (a) The Fourier transform of the signal from the device as a function of a system parameter. A single peak corresponds to a Majorana zero mode (MZM), two peaks correspond to a Majorana π mode (MPM). (b) Detected wavefunctions of the Majorana zero modes. The dots represent the experimental data, the solid lines are the theoretical calculations. Each curve corresponds to an odd or even component of one of the Majorana modes.

In recent years, near-term quantum computation has gained momentum with various physical platforms being used to simulate quantum phenomena in the laboratory. This development has led to new ideas on how to observe Majorana fermions using cold atoms, superconducting qubits, and systems of interacting photons. However, many of these experiments face a common problem: their dynamics only reveal the presence of "Majorana-like" states, without providing conclusive evidence that these particles are indeed Majorana modes.

The best test to confirm the existence of Majorana fermions is their exchange, or braiding. However, performing this braiding process extremely slowly, as required by existing methods, is currently impractical for near-term quantum processors. This is due to the high risk of causing "spillage" -- the decay of the Majorana modes into other excitations -- if the process is not executed slow enough. An apt analogy is the case of a full cup of coffee. Just as any sudden or inaccurate movement can cause the coffee to spill, moving Majorana fermions too hastily can cause them to decay.

In light of these challenges, the goal of our work is to provide definitive evidence for the existence of Majorana modes. Using IBM's superconducting qubit processors to simulate Kitaev's original idea, we succeed in detecting and quantifying a pair of Majorana modes, which were localized at the opposite boundaries of a long chain of qubits. We also observe how the Majorana modes changed their shape by changing the system's parameters and turning the many-body interactions on and off.

One of the main achievements of our work is a new method to mimic the brading of Majorana modes – Fast Approximate Swap. Unlike the standard approach of slow particle exchange, we use many very fast but "imperfect" exchanges. The average of a sequence of these braiding operations looks like the ideal braiding of two Majorana modes.

Our work can be used in the future to braid multiple particles in search of more exotic non-Abelian statistics. It also allows the study of more complex topological systems and real-world materials in search of the one that could lay the foundation for fault-tolerant quantum computing.

  1. Kitaev, A.Y., 2001. Unpaired Majorana fermions in quantum wires. Physics-uspekhi, 44(10S), p.131. Doi: 10.1070/1063-7869/44/10S/S29
  2. Castelvecchi, D., 2021. Evidence of elusive Majorana particle dies with retraction - but computing hope lives on. Nature, 591(7850), pp.354-355. https://www.nature.com/articles/d41586-021-00612-z

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