2024/06/18 by Minev, Zlatko K., Najafi, Khadijeh, Majumder, Swarnadeep +5 · 8 citations
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el) #Superconductivity (cond-mat.supr-con)
paper · doi:10.48550/arxiv.2406.12820
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~ϕ with~98% average accuracy and~8% measurement uncertainty. Finally, we sample the Fib-SNC to estimate the chromatic polynomial at~ϕ+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.