aiqbench analysis
This research delivers a practical end-to-end pipeline for approximating the Jones polynomial on noisy hardware, specifically demonstrating near-term quantum advantage using Quantinuum's H2-2 processor. By benchmarking both DQC1-complete Markov-closed braids and BQP-complete Plat-closed braids alongside classical tensor-network methods, the study establishes a rigorous framework for characterizing noise effects in real-world knot theory applications. The work provides essential tools for resource estimation to identify viable problem sizes where quantum computers outperform classical simulations without requiring full fault tolerance.
End-to-End Quantum Algorithms for the Jones Polynomial
arXiv:2503.05625v2 Announce Type: replace Abstract: We present an end-to-end algorithmic pipeline where a noisy digital quantum computer is used to approximate the value of the Jones polynomial at the fifth root of unity for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we develop and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The reconfigurable tools provided in this work allow for precise resource estimation to identify minimum link sizes for near-term quantum advantage in practice for a meaningful quantum-native problem in knot theory, if a candidate set of links are provided.
Abstract:We present an end-to-end algorithmic pipeline where a noisy digital quantum computer is used to approximate the value of the Jones polynomial at the fifth root of unity for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we develop and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The reconfigurable tools provided in this work allow for precise resource estimation to identify minimum link sizes for near-term quantum advantage in practice for a meaningful quantum-native problem in knot theory, if a candidate set of links are provided.
arXiv:2503.05625 [quant-ph]
(or arXiv:2503.05625v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2503.05625 Focus to learn more arXiv-issued DOI via DataCite
PRX Quantum 7 (2) p.020355 (2026)
https://doi.org/10.1103/jgv8-l3j1 Focus to learn more DOI(s) linking to related resources
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