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Non-Abelian braiding of graph vertices in a superconducting processor
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Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing.
Forward citations
Cited by 3 Pith papers
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Bridging Microscopic Constructions and Continuum Topological Field Theory of Three-Dimensional Non-Abelian Topological Order
The D4 quantum double model realizes the BF+AAB field theory with (Z2)^3 gauge group at the level of its 22 excitations, fusion rules, and shrinking rules.
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Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
Color Heisenberg-Lie (super)algebras graded by Z3×Z3 provide a unified framework for mixed-bracket parabosons and parafermions, reproducing s=3,6 braided Majorana qubit truncations and a new two-particle density signature.
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Controlled Buildup of Half-Quantized Thermal Conductance in an Engineered Chiral Spin Liquid Platform
A finite engineered Kitaev spin liquid connected to two Ising reservoirs shows a quasi-steady thermal conductance that approaches half quantization when the tunnel coupling and temperature are tuned.
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