Hybrid Ground-State Quantum Algorithms based on Neural Schrödinger Forging
This work addresses a computational bottleneck in quantum algorithms for physicists and researchers, representing an incremental improvement over existing entanglement forging techniques.
The paper tackles the exponential summation bottleneck in entanglement forging for ground-state quantum problems by using generative neural networks to select relevant bitstrings, achieving comparable or superior performance to standard methods in simulations on spin models and nuclear configurations.
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.