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Unified structured factorization framework for quantum state tomography using Burer-Monteiro-type factorization parametrizing density matrix as FF†, guaranteeing physical validity while incorporating structural priors.
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| name | quantum-structured-factorization-tomography |
| description | Unified structured factorization framework for quantum state tomography using Burer-Monteiro-type factorization parametrizing density matrix as FF†, guaranteeing physical validity while incorporating structural priors. |
| category | quantum |
| created | 2026-07-06T00:00:00.000Z |
| source | arXiv:2607.01608 |
arXiv:2607.01608 - "Structured Factorization Approaches for Quantum State Tomography" by Zhen Qin, Joseph M. Lukens, Brian T. Kirby, Zhihui Zhu (2026-07-02)
Since quantum state tomography (QST) complexity scales exponentially with system size, exploiting priors such as low-rankness, tensor-network structures, and neural-network representations is essential for scalable QST.
Burer-Monteory Factorization: Parametrize the density matrix as FF† where factor F is constrained to belong to a structured model class.
Physical Validity by Construction: This factorization guarantees physical validity by construction while allowing broad range of structural priors.
Structured Model Classes: Range from generic Cholesky decomposition to low-rank matrices, matrix product states, tensor train formats, and neural network representations.
Unified Framework: Provides single framework encompassing multiple approaches to scalable QST.
quantum state tomography, structured factorization, Burer-Monteiro, density matrix, low-rank, tensor network, neural network representation, sample complexity
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