Optimizing two-dimensional isometric tensor networks with quantum computers
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917086433902592 |
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| author | Leontica, Sebastian Baiardi, Alberto Schuhmacher, Julian Tacchino, Francesco Tavernelli, Ivano |
| author_facet | Leontica, Sebastian Baiardi, Alberto Schuhmacher, Julian Tacchino, Francesco Tavernelli, Ivano |
| contents | We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix renormalization group, we optimize tensors sequentially by diagonalizing a series of effective Hamiltonians. These are constructed using a tomography-inspired method on a qubit subset whose size depends only on the bond dimension. Our approach leverages quantum computers to enable accurate solutions without relying on approximate contractions, circumventing the exponential complexity faced by classical techniques. We demonstrate our method on the two-dimensional (2D) transverse-field Ising model, achieving ground-state optimization on up to 25 qubits with modest quantum overhead -- significantly less than standard solutions based on variational quantum eigensolvers. Overall, our results offer a path towards scalable variational quantum algorithms in both noisy and fault-tolerant regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13827 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimizing two-dimensional isometric tensor networks with quantum computers Leontica, Sebastian Baiardi, Alberto Schuhmacher, Julian Tacchino, Francesco Tavernelli, Ivano Quantum Physics Strongly Correlated Electrons We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix renormalization group, we optimize tensors sequentially by diagonalizing a series of effective Hamiltonians. These are constructed using a tomography-inspired method on a qubit subset whose size depends only on the bond dimension. Our approach leverages quantum computers to enable accurate solutions without relying on approximate contractions, circumventing the exponential complexity faced by classical techniques. We demonstrate our method on the two-dimensional (2D) transverse-field Ising model, achieving ground-state optimization on up to 25 qubits with modest quantum overhead -- significantly less than standard solutions based on variational quantum eigensolvers. Overall, our results offer a path towards scalable variational quantum algorithms in both noisy and fault-tolerant regimes. |
| title | Optimizing two-dimensional isometric tensor networks with quantum computers |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2511.13827 |