Twisted multinomial coefficients factorize into a product of site-dependent q-binomials when inversion weights satisfy predecessor-uniformity, yielding exact MPS representations for pilot states in Hamiltonian Decoded Quantum Interferometry.
hub Canonical reference
The density-matrix renormalization group in the age of matrix product states
Canonical reference. 86% of citing Pith papers cite this work as background.
16
Pith papers citing it
Background
86% of classified citations
abstract
The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms.
hub tools
citation-role summary
background 6
method 1
citation-polarity summary
representative citing papers
A matrix product operator construction using link-enhanced MPOs enables infinite-lattice simulations of (1+1)D gauge theories with manifest translation invariance and symmetry.
A multimode-cavity picture is introduced for non-Markovian waveguide QED via spatial decomposition, approximating dynamics with a finite and growing number of cavity modes.
The claimed intrinsic dipole moment at FQH edges is protected only at filling factor 1/3 and absent in other representative edge systems.
Numerical DMRG study of the anisotropic J1-J2 spin-1 chain uncovers two non-magnetic incommensurate floating Luttinger liquid phases emerging from the trimerized background, separated from the Haldane phase by a composite c=2 critical line.
Peaked quantum circuits claimed to show quantum advantage can be classically simulated in one hour on a GPU via mirrored MPO contraction and unswapping.
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
Introduces a parallelizable hybrid tensor network algorithm for time-evolving matrix product states that combines classical BUG integration with quantum methods without synchronization barriers.
Uniform MPS simulations of dense 1+1D SU(2) gauge theory find Tomonaga-Luttinger liquid infrared behavior with central charge 1, density modulations at the predicted wavenumber, and a smooth crossover in the Luttinger parameter from K~1 to K~1/2 that realizes the quarkyonic picture with coexisting q
A variational quantum circuit trained solely on classical measurement outcomes reconstructs diverse quantum states including GHZ, spin-chain ground states, and random circuits with fidelities above 90% on simulators and real NISQ hardware.
Lower bounds on the best separable approximation distance for non-pure spin-squeezed states are obtained from the complete set of spin-squeezing inequalities, with symmetry-exploiting optimization for upper bounds, revealing finite-temperature entanglement in ordered phases of the XXZ model.
A variational quantum SVD framework with classical orthogonality correction enables high-precision extraction of Schmidt components from bipartite states using shallow circuits and classical tensor-network post-processing.
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.
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.
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
citing papers explorer
-
A Factorization Identity for Twisted Multinomial Coefficients with Application to Pilot States in Hamiltonian Decoded Quantum Interferometry
Twisted multinomial coefficients factorize into a product of site-dependent q-binomials when inversion weights satisfy predecessor-uniformity, yielding exact MPS representations for pilot states in Hamiltonian Decoded Quantum Interferometry.
-
Infinite matrix product states for $(1+1)$-dimensional gauge theories
A matrix product operator construction using link-enhanced MPOs enables infinite-lattice simulations of (1+1)D gauge theories with manifest translation invariance and symmetry.
-
Multimode-cavity picture of non-Markovian waveguide QED
A multimode-cavity picture is introduced for non-Markovian waveguide QED via spatial decomposition, approximating dynamics with a finite and growing number of cavity modes.
-
Does a Fractional Quantum Hall Edge Have a Protected Intrinsic Dipole Moment?
The claimed intrinsic dipole moment at FQH edges is protected only at filling factor 1/3 and absent in other representative edge systems.
-
Non-magnetic floating phases in frustrated Haldane chains with a single-ion anisotropy
Numerical DMRG study of the anisotropic J1-J2 spin-1 chain uncovers two non-magnetic incommensurate floating Luttinger liquid phases emerging from the trimerized background, separated from the Haldane phase by a composite c=2 critical line.
-
Efficient Classical Simulation of Heuristic Peaked Quantum Circuits
Peaked quantum circuits claimed to show quantum advantage can be classically simulated in one hour on a GPU via mirrored MPO contraction and unswapping.
-
Symmetry breaking phases and transitions in an Ising fusion category lattice model
The Ising fusion category lattice model features a symmetric critical phase equivalent to the Ising model, a categorical ferromagnetic phase with threefold degeneracy, and a critical categorical antiferromagnetic phase with fourfold degeneracy described by an Ising CFT.
-
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.
-
Dense $\mathrm{QC_2D_2}$ with uniform matrix product states
Uniform MPS simulations of dense 1+1D SU(2) gauge theory find Tomonaga-Luttinger liquid infrared behavior with central charge 1, density modulations at the predicted wavenumber, and a smooth crossover in the Luttinger parameter from K~1 to K~1/2 that realizes the quarkyonic picture with coexisting q
-
Quantum Machine Learning for State Tomography Using Classical Data
A variational quantum circuit trained solely on classical measurement outcomes reconstructs diverse quantum states including GHZ, spin-chain ground states, and random circuits with fidelities above 90% on simulators and real NISQ hardware.
-
Estimating the best separable approximation of non-pure spin-squeezed states
Lower bounds on the best separable approximation distance for non-pure spin-squeezed states are obtained from the complete set of spin-squeezing inequalities, with symmetry-exploiting optimization for upper bounds, revealing finite-temperature entanglement in ordered phases of the XXZ model.
-
High-Precision Variational Quantum SVD via Classical Orthogonality Correction
A variational quantum SVD framework with classical orthogonality correction enables high-precision extraction of Schmidt components from bipartite states using shallow circuits and classical tensor-network post-processing.
-
Preparing High-Fidelity Thermofield Double States
A gapped parent Hamiltonian built from two copies of a target Hamiltonian plus ultra-local inter-copy couplings allows adiabatic preparation of high-fidelity thermofield double states for ETH-obeying systems.
-
Conformal Data for the $O(2)$ Wilson-Fisher CFT in $(2+1)$-Dimensional Spacetime from Exact Diagonalization and Matrix Product States on the Fuzzy Sphere
Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.
-
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.
-
Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.