Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

TL;DR

This paper demonstrates a scalable method to prepare, manipulate, and measure Fibonacci anyons in a superconducting quantum processor, enabling fault-tolerant quantum computation and sampling classically-hard graph invariants.

Contribution

It introduces a dynamical string-net preparation approach suitable for near-term quantum devices, enabling the realization and braiding of Fibonacci anyons.

Findings

Successfully created and measured Fibonacci anyons with 94% accuracy.

Demonstrated braiding yields the golden ratio with 98% accuracy.

Sampled chromatic polynomial at a specific value for multiple graphs.

Abstract

The remarkable complexity of the vacuum state of a topologically-ordered many-body quantum system encodes the character and intricate braiding interactions of its emergent particles, the anyons.} Quintessential predictions exploiting this complexity use the Fibonacci string-net condensate (Fib-SNC) and its Fibonacci anyons to go beyond classical computing. Sampling the Fib-SNC wavefunction is expected to yield estimates of the chromatic polynomial of graph objects, a classical task that is provably hard. At the same time, exchanging anyons of Fib-SNC is expected to allow fault-tolerant universal quantum computation. Nevertheless, the physical realization of Fib-SNC and its anyons remains elusive. Here, we introduce a scalable dynamical string-net preparation (DSNP) approach, suitable even for near-term quantum processors, which dynamically prepares Fib-SNC and its anyons through reconfigurable graphs. Using a superconducting quantum processor, we couple the DSNP approach with composite error-mitigation on deep circuits to successfully create, measure, and braid anyons of Fib-SNC in a scalable manner. We certify the creation of anyons by measuring their `anyon charge', finding an average experimental accuracy of $94\%$. Furthermore, we validate that exchanging these anyons yields the { expected} golden ratio~$\phi$ with~$98\%$ average accuracy and~$8\%$ measurement uncertainty. Finally, we sample the Fib-SNC to estimate the chromatic polynomial at~$\phi+2$ for {several} graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and {for aiming at} a classically-hard problem.