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

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Main Authors: Minev, Zlatko K., Najafi, Khadijeh, Majumder, Swarnadeep, Wang, Juven, Stern, Ady, Kim, Eun-Ah, Jian, Chao-Ming, Zhu, Guanyu
Format: Preprint
Published: 2024
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author Minev, Zlatko K.
Najafi, Khadijeh
Majumder, Swarnadeep
Wang, Juven
Stern, Ady
Kim, Eun-Ah
Jian, Chao-Ming
Zhu, Guanyu
author_facet Minev, Zlatko K.
Najafi, Khadijeh
Majumder, Swarnadeep
Wang, Juven
Stern, Ady
Kim, Eun-Ah
Jian, Chao-Ming
Zhu, Guanyu
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_12820
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
Minev, Zlatko K.
Najafi, Khadijeh
Majumder, Swarnadeep
Wang, Juven
Stern, Ady
Kim, Eun-Ah
Jian, Chao-Ming
Zhu, Guanyu
Quantum Physics
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Superconductivity
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.
title Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
topic Quantum Physics
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
Superconductivity
url https://arxiv.org/abs/2406.12820