Demonstration of Topological Robustness of Anyonic Braiding Statistics with a Superconducting Quantum Circuit

Abstract

Anyons are quasiparticles occurring in two dimensions, whose topological properties are believed to be robust against local perturbations and may hold promise for fault tolerant quantum computing. Here we present an experiment of demonstrating the path independent nature of anyonic braiding statistics with a superconducting quantum circuit, which represents a 7-qubit version of the toric code model. We dynamically create the ground state of the model, achieving a state fidelity of 0.688±0.015 as verified by quantum state tomography. Anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations. The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct, but topologically equivalent paths: Both reveal the nontrivial π-phase shift, the hallmark of Abelian 1/2 anyons, with a phase accuracy of ∼99% in the Ramsey-type interference measurement.

Observation of Bloch oscillations and Wannier-Stark localization on a superconducting quantum processor

“…Superconducting circuits can be fabricated into different lattice structures, such as 1D chain, ladder, fully connected graphs, and 2D square lattice. It is a versatile platform for performing various kinds of quantum-simulation experiments, e.g., quantum many-body dynamics [21][22][23][24][25][26][27][28][29][30][31][32][33][34] , quantum chemistry 35,36 , and implementing quantum algorithms [37][38][39][40][41][42] . Our quantum processor with 1D array of superconducting qubits is well suited for studying essential transport properties of spin and energy in BOs and WSL.…”

Realizing topologically ordered states on a quantum processor

“…Given both its inherent richness and quantum computing applications, experimentally realizing Z 2 topological order has sparked extensive interest, resulting in several experimental studies with comparatively small-scale synthetic quantum systems [9][10][11][12][13][14][15][16][17][18][19]. Despite these efforts, the experimental realization of topologically ordered states remains a major challenge, requiring the generation of long-range entanglement.…”

Observation of Emergent $\mathbb{Z}_2$ Gauge Invariance in a Superconducting Circuit

“…Due to the good scalability, long decoherence time, and high-precision full control, the superconducting circuit [15,16] becomes one of the most competitive candidates for achieving the universal quantum computation [31], and it is also a much suitable platform for per-forming quantum simulations [1,[17][18][19][20][21][22][23][24][25][26][27][28][29]. Thus, it is natural to ask whether we can benefit advantages of superconducting circuits to simulate and further study LGTs.…”