skip to main content

Quantum Matter Seminar

Monday, May 15, 2023
4:00pm to 5:00pm
Add to Cal
East Bridge 114
Realizing non-Abelian statistics using graph gauge theory on a quantum processor
Eun-Ah Kim, Professor, Department of Physics, Cornell University,

The indistinguishability of particles is a fundamental principle of quantum mechanics. For all (quasi)particles observed to date - including fermions, bosons, and Abelian anyons this principle guarantees that the double-exchange of identical particles leaves the system unchanged. However, an intriguing possibility exists in two spatial dimensions: double-braiding of non-Abelian anyons transforms the multi-anyon state. Such anyons can non-locally encode quantum information, which can be processed through pair-wise exchanges. Despite numerous theoretical proposals, experimental realization of non-Abelian anyon exchange, i.e., braiding of their space-time trajectories, has remained elusive. We propose[1] a simple and systematic prescription to construct unitary protocols for braiding, manipulating, and readout of non-Abelian anyons and preparing their entangled states on a digital quantum processor. We define the plaquette surface code as a stabilizer code on a generic planar graph of qubits with vertices of degrees 2, 3, and 4.

By mapping each qubit to four Majoranas and recognizing that each degree-3 vertex (D3V) carries a new discrete Z2 flux of "Kasteleyn" field, we prove non-Abelian statistics of D3V's. In our approach, all the experimentally relevant operators are unambiguously fixed by locality, unitarity, and gauge invariance. Our specific prescriptions for experiments on a near-term digital quantum processor have been carried out to create and braid D3Vs on a superconducting quantum processor[2]. Further, we created an entangled state of three logical qubits by braiding D3Vs. I will discuss the prospect of employing these anyons for quantum computation.

[1] Y. Lensky, K. Kechedzhi, I. Aleiner, EAK, Annals of Physics, 452, 159286 (2023)

[2] T. Anderson, Y. Lensky, EAK et al, arXiv: 2210.10255, to appear in Nature (2023)