Hybrid Tree Tensor Networks for quantum simulation
arxiv(2024)
摘要
Hybrid Tensor Networks (hTN) offer a promising solution for encoding
variational quantum states beyond the capabilities of efficient classical
methods or noisy quantum computers alone. However, their practical usefulness
and many operational aspects of hTN-based algorithms, like the optimization of
hTNs, the generalization of standard contraction rules to an hybrid setting,
and the design of application-oriented architectures have not been thoroughly
investigated yet. In this work, we introduce a novel algorithm to perform
ground state optimizations with hybrid Tree Tensor Networks (hTTNs), discussing
its advantages and roadblocks, and identifying a set of promising applications.
We benchmark our approach on two paradigmatic models, namely the Ising model at
the critical point and the Toric code Hamiltonian. In both cases, we
successfully demonstrate that hTTNs can improve upon classical equivalents with
equal bond dimension in the classical part.
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