Hybrid Ground-State Quantum Algorithms based on Neural Schrödinger Forging

Abstract

Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis states, or bitstrings, when performing the Schmidt decomposition of the whole system. To overcome this challenge, we propose a new method for entanglement forging employing generative neural networks to identify the most pertinent bitstrings, eliminating the need for the exponential sum. Through empirical demonstrations on systems of increasing complexity, we show that the proposed algorithm achieves comparable or superior performance compared to the existing standard implementation of entanglement forging. Moreover, by controlling the amount of required resources, this scheme can be applied to larger, as well as non permutation invariant systems, where the latter constraint is associated with the Heisenberg forging procedure. We substantiate our findings through numerical simulations conducted on spins models exhibiting one-dimensional ring, two-dimensional triangular lattice topologies, and nuclear shell model configurations.

arXiv comment12 pages, 9 figures, 5 pages supplemental material

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Cited by in corpus (5)

• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
• Advancing quantum simulations of nuclear shell model with noise-resilient protocols
• A Quantum Annealing Protocol to Solve the Nuclear Shell Model
• Toward scalable quantum computations of atomic nuclei
• Correcting and extending Trotterized quantum many-body dynamics