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This research introduces Lindblad Multiproduct Formulas, a novel quantum error mitigation technique leveraging two-dimensional tensor networks and belief propagation to reduce computational costs for specific many-body systems. By integrating Clifford rescaling and GPU-accelerated classical workflows, the method successfully demonstrated a 5.6x speedup on a 65-qubit IBM quantum processor while providing estimated error bars for observables that are otherwise difficult to calculate.
Lindblad Multiproduct Formulas
arXiv:2609.05024v1 Announce Type: new Abstract: We introduce Lindblad Multiproduct Formulas: a quantum error mitigation technique that uses two-dimensional tensor networks contracted with loop-corrected belief propagation. The quantities required to implement the error mitigation scheme that are evaluated with tensor networks can be less computationally expensive to calculate than the expectation values themselves, thus allowing for the possibility of applying our method to certain systems for which tensor network methods may struggle to calculate the observable quantities of interest. The workflow incorporates Clifford rescaling techniques and outputs an estimated error bar. We apply our method to a model of two-dimensional discrete time crystals studied previously and implement it on $65$ qubits arranged in a $3\!\times\!3$ heavy-hexagonal topology on the quantum computer ibm_basquecountry. We show that a GPU implementation of the classical part of our workflow achieves a speedup of up to $5.6\times$.
Authors:Niall F. Robertson, Andrea D'Urbano, Anton Dekusar, Max Rossmannek, Eric D. Switzer, James R. Garrison, Nicolas Lorente, Igor Pasichnyk, Paolo D'Alberto, Muhammad Osama, Zachary Streeter, Yasuko Eckert, Constantinos Evangelinos, Sergiy Zhuk
Abstract:We introduce Lindblad Multiproduct Formulas: a quantum error mitigation technique that uses two-dimensional tensor networks contracted with loop-corrected belief propagation. The quantities required to implement the error mitigation scheme that are evaluated with tensor networks can be less computationally expensive to calculate than the expectation values themselves, thus allowing for the possibility of applying our method to certain systems for which tensor network methods may struggle to calculate the observable quantities of interest. The workflow incorporates Clifford rescaling techniques and outputs an estimated error bar. We apply our method to a model of two-dimensional discrete time crystals studied previously and implement it on $65$ qubits arranged in a $3\!\times\!3$ heavy-hexagonal topology on the quantum computer ibm_basquecountry. We show that a GPU implementation of the classical part of our workflow achieves a speedup of up to $5.6\times$.
arXiv:2609.05024 [quant-ph]
(or arXiv:2609.05024v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.05024 arXiv-issued DOI via DataCite (pending registration)
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