Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials
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| Format: | Preprint |
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2024
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| _version_ | 1866915372632899584 |
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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 |
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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 |