For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
Vidal, Efficient classical simulation of slightly entan- gled quantum computations, Phys
9 Pith papers cite this work. Polarity classification is still indexing.
9
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
roles
background 1polarities
background 1representative citing papers
Low-energy states of local Hamiltonians have half-system entanglement entropies upper-bounded by the thermal entropies of two fictitious systems whose combined energies match the state's energy.
The reduced transition matrix in chaotic dual-unitary quantum circuits has low-rank structure with entropy growing at most logarithmically in time, enabling efficient approximation for local expectation values.
The frame potential of a disordered Tomonaga-Luttinger liquid decays as a power law at early times and saturates to a late-time plateau controlled by a single coupling parameter.
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
Develops an optimization-free disentangling algorithm and algebraic criterion for efficient CAMPS representations of Clifford circuits doped with αI+βP gates, enabling polynomial classical simulation for more circuits including typical N-T-gate random instances.
Analytical Pauli-string coefficients plus multistage state refinement let tensor networks find low eigenstates of million-dimensional Laplacians with high fidelity on 20 qubits.
Matrix-product-state calculations on a correlated two-band model show a doping-induced in-gap branch tied to excitonic correlations.
MPO encodings of the Magnus expansion and Dyson series for accurate time evolution of time-dependent 1D quantum Hamiltonians on finite or infinite lattices with long-range interactions.
citing papers explorer
-
Algorithmic Locality via Provable Convergence in Quantum Tensor Networks
For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
-
Quantum matter is weakly entangled at low energies
Low-energy states of local Hamiltonians have half-system entanglement entropies upper-bounded by the thermal entropies of two fictitious systems whose combined energies match the state's energy.
-
Low Rank Structure of the Reduced Transition Matrix
The reduced transition matrix in chaotic dual-unitary quantum circuits has low-rank structure with entropy growing at most logarithmically in time, enabling efficient approximation for local expectation values.
-
Solvable Random Unitary Dynamics in a Disordered Tomonaga-Luttinger Liquid
The frame potential of a disordered Tomonaga-Luttinger liquid decays as a power law at early times and saturates to a late-time plateau controlled by a single coupling parameter.
-
Taming Trotter Errors with Quantum Resources
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
-
Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
Develops an optimization-free disentangling algorithm and algebraic criterion for efficient CAMPS representations of Clifford circuits doped with αI+βP gates, enabling polynomial classical simulation for more circuits including typical N-T-gate random instances.
-
Efficient Pauli-decomposition and multistage state-refinement for tensor network based differential equation solver
Analytical Pauli-string coefficients plus multistage state refinement let tensor networks find low eigenstates of million-dimensional Laplacians with high fidelity on 20 qubits.
-
Correlation-driven branch in doped excitonic insulators
Matrix-product-state calculations on a correlated two-band model show a doping-induced in-gap branch tied to excitonic correlations.
-
Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series
MPO encodings of the Magnus expansion and Dyson series for accurate time evolution of time-dependent 1D quantum Hamiltonians on finite or infinite lattices with long-range interactions.