MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
An area law for one-dimensional quantum systems.Journal of Statistical Mechanics: Theory and Experiment, 2007(08):P08024, aug 2007
6 Pith papers cite this work, alongside 1,065 external citations. Polarity classification is still indexing.
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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.
Tensor network model achieves 77.98% accuracy in modeling order-dependent emotional memory in children.
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
Pure-state BNMR is an intrinsic function of the nonzero Schmidt spectrum via dimension reduction, yielding quadratic perturbation response, Haar-random profiles localized at symmetric cuts, and closed forms for rank-2 states.
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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Absence of poor local minima in matrix product states
MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogonality center moves.
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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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Modelling Emotional Memory in Children with Tensor Networks
Tensor network model achieves 77.98% accuracy in modeling order-dependent emotional memory in children.
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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
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Intrinsic spectral structure of bipartite nonlocal magic resource
Pure-state BNMR is an intrinsic function of the nonzero Schmidt spectrum via dimension reduction, yielding quadratic perturbation response, Haar-random profiles localized at symmetric cuts, and closed forms for rank-2 states.
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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.