A unique normal form for tensor trains over arbitrary fields is defined using a novel LDPU matrix decomposition, with a polynomial-time reduction algorithm and direct construction from full tensors.
1088/1751-8121/aa6dc3
11 Pith papers cite this work, alongside 407 external citations. Polarity classification is still indexing.
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representative citing papers
Introduces forward-assisted purification via a new spatiotemporal framework that outperforms conventional static purification by up to 50x in copy efficiency and circumvents no-purification theorems for Bell states.
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
Local tensor-train surrogates approximate quantum machine learning models via Taylor polynomials and tensor networks, delivering polynomial parameter scaling and explicit generalization bounds controlled by patch radius.
Relativistic continuous matrix product states yield competitive variational approximations to ground state energies and observables in the phi^4, Sine-Gordon, and Sinh-Gordon models, including strongly coupled regimes.
All embedding quantum kernels can be understood as entangled tensor kernels, yielding new insights into their inductive bias and potential dequantization.
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
Reshetikhin-Turaev knot polynomials are fixed-parameter tractable in the treewidth of the input diagram via tensor network contraction, yielding e^{O(sqrt n)} time.
Numerical study demonstrates controlled transport of Z4 parafermion edge states in a ladder model and quantifies the adiabatic speed limit under realistic conditions.
PEPSKit.jl is a Julia package that supplies high-level algorithms for ground-state, time-evolution and finite-temperature iPEPS simulations with symmetry support on various lattices.
Tensor networks developed for quantum states are reviewed as tools for machine learning models, with assessment of their potential computational, explanatory, and privacy advantages alongside remaining challenges.
citing papers explorer
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A Unique Normal Form for Tensor Trains over Arbitrary Fields
A unique normal form for tensor trains over arbitrary fields is defined using a novel LDPU matrix decomposition, with a polynomial-time reduction algorithm and direct construction from full tensors.
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Forward-Assisted Purification: A Spatiotemporal Framework Beyond Conventional Limits
Introduces forward-assisted purification via a new spatiotemporal framework that outperforms conventional static purification by up to 50x in copy efficiency and circumvents no-purification theorems for Bell states.
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Algebras of order parameters in one-dimensional spin systems
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
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Local tensor-train surrogates for quantum learning models
Local tensor-train surrogates approximate quantum machine learning models via Taylor polynomials and tensor networks, delivering polynomial parameter scaling and explicit generalization bounds controlled by patch radius.
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Some progress on the use of the variational method in quantum field theory
Relativistic continuous matrix product states yield competitive variational approximations to ground state energies and observables in the phi^4, Sine-Gordon, and Sinh-Gordon models, including strongly coupled regimes.
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New perspectives on quantum kernels through the lens of entangled tensor kernels
All embedding quantum kernels can be understood as entangled tensor kernels, yielding new insights into their inductive bias and potential dequantization.
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Time Evolution on Hybrid Tensor Networks -- A Novel and Parallelizable Algorithm
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
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Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networks
Reshetikhin-Turaev knot polynomials are fixed-parameter tractable in the treewidth of the input diagram via tensor network contraction, yielding e^{O(sqrt n)} time.
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Shuttling of $\mathbb{Z}_4$ parafermions in an electronic ladder model
Numerical study demonstrates controlled transport of Z4 parafermion edge states in a ladder model and quantifies the adiabatic speed limit under realistic conditions.
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PEPSKit.jl: A Julia package for projected entangled-pair state simulations
PEPSKit.jl is a Julia package that supplies high-level algorithms for ground-state, time-evolution and finite-temperature iPEPS simulations with symmetry support on various lattices.
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Quantum-inspired tensor networks in machine learning models
Tensor networks developed for quantum states are reviewed as tools for machine learning models, with assessment of their potential computational, explanatory, and privacy advantages alongside remaining challenges.