Global fermionic mode optimization via swap gates

Abstract:An optimal choice of single-particle modes leads to an optimal tensor network-based compression of the many-body wave function for systems of indistinguishable particles, which compression can be essential for large, close-to-critical systems. The proposed mode optimization relies on the minimization of the block entropy area, a global quantity that measures entanglement of the wave function along the one-dimensional chain of modes. Extension of the two-site DMRG algorithm by nearest-neighbor mode optimizations is straightforward, but it performs poorly without systematic reordering of modes. Moreover, finding a stationary optimal point in the combination of the fixed-rank MPS manifold and the unitary group of mode rotations requires optimization for every generator, i.e., for every two-mode pair. Here, a systematic joint optimization protocol over the MPS manifold and the full unitary group is presented in which every two-mode pair is accessed by a carefully constructed sequence of two-qubit operations, including swap-gate controlled permutations. Large-scale DMRG simulations of strongly correlated two-dimensional fermionic lattice models and the multireference Fe$_4$S$_4$ transition metal cluster demonstrate rapid convergence towards the optimum, achieving low energy and low entanglement.

Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)

arXiv:2406.03449 [cond-mat.str-el]

(or arXiv:2406.03449v2 [cond-mat.str-el] for this version)

https://doi.org/10.48550/arXiv.2406.03449 Focus to learn more arXiv-issued DOI via DataCite

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