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 $5.6\times$.
Tensor networks have attracted much attention as a powerful tool for modeling quantum many-body systems. Their contraction is a significant challenge, however, especially in highly connected networks, as memory requirements become prohibitive and the optimal contraction order is increasingly hard to find. The belief pr...
A quantum circuit synthesis method for preparing a class of tensor network states tractable with belief propagation (BP), a tensor network gauging scheme which recently allowed for classical simulations at large scales.
A protocol for approximating the measurement distributions of quantum states, extending beyond standard observable estimation is introduced, and tightened gate complexity bounds for practically relevant systems, including those with k-local interactions, long-tailed matrix ensembles, and conserved quantities are provid...
Arul Rhik Mazumder, James D. Watson, Samson Wang· 0 citations
SCENT (Spectral Clustering for Entanglement miNimizing Trees) is a protocol that utilizes efficiently-computable pairwise entanglement metrics to determine a suitable tree tensor network (TTN) structure, which is efficiently approximated using tensor cross-interpolation (TCI) and substantially outperforms MPS methods a...
Matthew L. Sims-Goh, L. Cincio, Annina Z. Lieberherr et al.· 2 citations
A scalable noise-learning framework for Lindblad dissipation rates that combines a stochastic simulation method, the Tensor Jump Method (TJM), with gradient-free optimization of a least-squares cost-function defined on time series of local-observable expectation values is proposed.
A. R. Ramos Ramos, Maximilian Fröhlich, Aaron Sander et al.· 0 citations
The results show that the factorization underlying a quantum block encoding can itself provide sufficient classical structure even when sampling-and-query access to the composite matrix is unavailable, suggesting a classical sampler with prescribed accuracy and polynomially related runtime.
Natsuto Isogai, M. Murao, Hayata Yamasaki· 0 citations
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