Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.
Canonical reference
Density matrix formulation for quantum renormalization groups,
Canonical reference. 80% of citing Pith papers cite this work as background.
33
Pith papers citing it
7,815
external citations · OpenAlex
Background
80% of classified citations
citation-role summary
background 4
method 1
citation-polarity summary
representative citing papers
Presents an incremental TT compression algorithm operating directly on streaming TT-formatted data via core-wise operations, with error bounds and application to ROM construction from low-rank snapshots.
Introduces an efficient SSE QMC algorithm with global updates and parallel tempering for mixed-dimensional models and applies it to map angle-dependent correlated insulators and Wigner-Mott states in M-point twisted AA-stacked SnSe2.
Equilibrium quantum many-body methods are encoders from admissible states to represented variables, with exact decoders existing precisely when tasks are constant on encoder fibers.
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.
Tensor networks enable tunable, objective compression of 1D fluid data with lossless reconstruction at high bond dimension and efficient in-compressed-space operations like periodic convolution.
AI coding agents evolve simple ground-state protocols into improved versions for VQE, DMRG, and AFQMC on spin models and molecules by using executable energy scores under fixed compute budgets.
Imaginary-time evolution in coupled-cluster theory reaches standard amplitude solutions when they exist but supplies additional regularization information via minima of a newly defined energy variance.
Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
An adaptive patching method exploits block-sparse QTT structures to reduce computational costs for tensor contractions and enables efficient evaluation of bubble diagrams and Bethe-Salpeter equations.
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
Tensor network scans reveal that the stationary spin entanglement entropy ridge follows population phase boundaries at small s but lacks the two-branch structure at large s in the sub-Ohmic spin-boson model.
A solver-independent constrained orbital optimization framework on the Stiefel manifold using RDMs, shown to lower energies and improve convergence for MP2, CASCI, and DMRG on LiF, H2O, and pyrazine.
Clifford disentanglers classified by Schmidt spectrum action reduce energy errors at fixed bond dimension in MPS simulations of molecules and improve shallow-circuit VQE calculations.
Canonical mapping of quantum-dot-superconductor clusters enables neural quantum-state calculations that reveal trivial singlet, Heisenberg-like, and critical regimes with 1D gaplessness and 2D triplet states.
DMFT on the 2D Hubbard-Holstein model produces two Fermi-resonance peaks in electronic friction missed by MFT, with EF-LD simulations revealing substantial differences in electron population dynamics.
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
A structure-preserving low-rank factorization of 2RDMs achieves linear rank scaling with system size and ~99% compression while retaining chemical accuracy for correlated states.
New techniques for error-independent unified path variation, non-degenerate batched sampling, and flexible contraction accelerate tensor network quantum trajectory simulations by more than 10^8 times.
Spectral bounds relate graph Laplacian eigenvalues to the congestion of binary-tree embeddings, with an efficient spectral-ordering algorithm and applications to tensor-network contraction complexity.
Develops a translationally invariant tensor network algorithm to calculate disorder-averaged quantities in infinite random spin chains without sampling, benchmarked on the random transverse-field Ising model at its infinite-randomness critical point.
A modified boost-operator method yields new integrable anyonic chains (including su(2)_k spin-3/2, TY(Z_n), Fib×Fib, Fib×Ising) and a criterion for when Temperley-Lieb algebras appear.
Numerical study demonstrates controlled transport of Z4 parafermion edge states in a ladder model and quantifies the adiabatic speed limit under realistic conditions.
citing papers explorer
-
Renormalization flows for 1D mixed states and a quantum Goursat lemma
Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.
-
Incremental Tensor-Train Compression from Streaming TT-Formatted Data: Applications to Reduced-Order Modeling
Presents an incremental TT compression algorithm operating directly on streaming TT-formatted data via core-wise operations, with error bounds and application to ROM construction from low-rank snapshots.
-
Mixed-dimensional quantum Monte Carlo studies of M-point moir\'e materials
Introduces an efficient SSE QMC algorithm with global updates and parallel tempering for mixed-dimensional models and applies it to map angle-dependent correlated insulators and Wigner-Mott states in M-point twisted AA-stacked SnSe2.
-
Full-State and Reduced-Moment Encodings: A Representation-Level View of Equilibrium Quantum Many-Body Theory
Equilibrium quantum many-body methods are encoders from admissible states to represented variables, with exact decoders existing precisely when tasks are constant on encoder fibers.
-
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.
-
Tensor network compression using fluid dynamics as a testbed: Analytical foundations in one dimension
Tensor networks enable tunable, objective compression of 1D fluid data with lossless reconstruction at high bond dimension and efficient in-compressed-space operations like periodic convolution.
-
Optimizing ground state preparation protocols with autoresearch
AI coding agents evolve simple ground-state protocols into improved versions for VQE, DMRG, and AFQMC on spin models and molecules by using executable energy scores under fixed compute budgets.
-
Coupled-Cluster Imaginary-Time Evolution and the Coupled-Cluster Energy Variance
Imaginary-time evolution in coupled-cluster theory reaches standard amplitude solutions when they exist but supplies additional regularization information via minima of a newly defined energy variance.
-
Fast elementwise operations on tensor trains with alternating cross interpolation
Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
-
Adaptive Patching for Tensor Train Computations
An adaptive patching method exploits block-sparse QTT structures to reduce computational costs for tensor contractions and enables efficient evaluation of bubble diagrams and Bethe-Salpeter equations.
-
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.
-
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.
-
Entanglement structure of the dynamical phases in the sub-Ohmic spin-boson model
Tensor network scans reveal that the stationary spin entanglement entropy ridge follows population phase boundaries at small s but lacks the two-branch structure at large s in the sub-Ohmic spin-boson model.
-
Constrained Optimization Algorithms for Orbital Optimization in Quantum Chemistry
A solver-independent constrained orbital optimization framework on the Stiefel manifold using RDMs, shown to lower energies and improve convergence for MP2, CASCI, and DMRG on LiF, H2O, and pyrazine.
-
Clifford disentanglers for entanglement reduction in molecular electronic structure simulations
Clifford disentanglers classified by Schmidt spectrum action reduce energy errors at fixed bond dimension in MPS simulations of molecules and improve shallow-circuit VQE calculations.
-
Correlated States in Quantum Dot Clusters Coupled to a Common Superconductor
Canonical mapping of quantum-dot-superconductor clusters enables neural quantum-state calculations that reveal trivial singlet, Heisenberg-like, and critical regimes with 1D gaplessness and 2D triplet states.
-
A DMFT approach to evaluate electronic frictional effects near solid surfaces of strongly correlated systems
DMFT on the 2D Hubbard-Holstein model produces two Fermi-resonance peaks in electronic friction missed by MFT, with EF-LD simulations revealing substantial differences in electron population dynamics.
-
Absorbing Many-Body Correlations into Core-Optimized Orbitals
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
-
Low-rank compression of two-electron reduced density matrices
A structure-preserving low-rank factorization of 2RDMs achieves linear rank scaling with system size and ~99% compression while retaining chemical accuracy for correlated states.
-
Accelerating Quantum Tensor Network Simulations with Unified Path Variations and Non-Degenerate Batched Sampling
New techniques for error-independent unified path variation, non-degenerate batched sampling, and flexible contraction accelerate tensor network quantum trajectory simulations by more than 10^8 times.
-
Congestion bounds via Laplacian eigenvalues and their application to tensor networks with arbitrary geometry
Spectral bounds relate graph Laplacian eigenvalues to the congestion of binary-tree embeddings, with an efficient spectral-ordering algorithm and applications to tensor-network contraction complexity.
-
Extracting average properties of disordered spin chains with translationally invariant tensor networks
Develops a translationally invariant tensor network algorithm to calculate disorder-averaged quantities in infinite random spin chains without sampling, benchmarked on the random transverse-field Ising model at its infinite-randomness critical point.
-
Constrained integrability and anyonic chains
A modified boost-operator method yields new integrable anyonic chains (including su(2)_k spin-3/2, TY(Z_n), Fib×Fib, Fib×Ising) and a criterion for when Temperley-Lieb algebras appear.
-
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.
-
Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
-
Comparison of MPS based real time evolution algorithms for Anderson Impurity Models
Adapted TEBD in star geometry is the most efficient MPS method for real-time evolution of Anderson impurity models among the tested combinations.
-
Quantum-Inspired Hamiltonian Optimization, Stochastic Tensor Networks and Adaptive Congestion Routing for Large-Scale QKD Networks
A quantum-inspired framework using effective Hamiltonians, Metropolis annealing and stochastic tensor-network compression is proposed for adaptive multi-demand routing in large-scale QKD networks.
-
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.
-
Entanglement is Half the Story: Post-Selection vs. Partial Traces
A hybrid tensor network framework interpolates between classical and quantum models via controllable post-selection, with a trainable hyperparameter that complements bond dimension to enhance quantum machine learning.
-
A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
TNRKit.jl implements symmetry-aware TRG/HOTRG/LoopTNR coarse-graining and fixed-point conformal-data extraction for classical statistical models and Euclidean lattice field theories.
-
Accurate, full-dimensional computations of thousands of complex vibrational eigenstates with tree tensor network states
Perspective reviewing TTNS-DMRG methods for computing thousands of vibrational eigenstates in molecules up to 33 dimensions, with emphasis on connections to ML-MCTDH and practical challenges.
-
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.
-
Introduction to matrix-product states and tensor networks
Introductory lecture notes on tensor networks with emphasis on matrix-product states, their algorithms, higher-dimensional generalizations, and applications to mixed states and open quantum systems, accompanied by Julia code.