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.
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Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
11 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We use this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions.
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2026 11roles
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Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
A zero-mode gauge fixing technique truncates bonds in loopy tensor networks by exploiting linear dependencies in the metric tensor of cut-bond states, applied to iPEPS representations of the finite-temperature 2D Z2 lattice gauge theory.
Trotter error cancellation for energy gaps in nanographene simulations yields an order-of-magnitude reduction in quantum circuit depth, enabling chemical-accuracy estimates with fewer than 3.2×10^7 Toffoli gates for large 2D systems in the PPP model.
SCALE and ACE are new convolutional backflow architectures for Neural Quantum States that deliver O(N^3) scaling with high accuracy and over 40x speedup on Hubbard and t-J models up to 32x32 lattices.
A gauge-covariant PEPS ansatz with virtual flux tensors ensures translation-invariant physical expectation values for 2D interacting systems in a magnetic field, allowing gauge-independent simulations without enlarged magnetic unit cells.
A Grassmann CTMRG tensor network method is introduced for 1D fermionic models and tested on the Hubbard model with magnetic field to capture phase diagram features.
The thesis introduces a topology-aware tensor-network heuristic called SpinGlassPEPS.jl and thermodynamic metrics to benchmark quantum annealers on Ising problems while accounting for dissipation and effective temperature.
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
citing papers explorer
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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.
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Coherent-State Propagation: A Computational Framework for Simulating Bosonic Quantum Systems
Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
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Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
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Truncating loopy tensor networks by zero-mode gauge fixing: the $Z_2$ lattice gauge theory at finite temperature
A zero-mode gauge fixing technique truncates bonds in loopy tensor networks by exploiting linear dependencies in the metric tensor of cut-bond states, applied to iPEPS representations of the finite-temperature 2D Z2 lattice gauge theory.
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Quantum simulation of nanographenes and Trotter error cancellation
Trotter error cancellation for energy gaps in nanographene simulations yields an order-of-magnitude reduction in quantum circuit depth, enabling chemical-accuracy estimates with fewer than 3.2×10^7 Toffoli gates for large 2D systems in the PPP model.
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Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions
SCALE and ACE are new convolutional backflow architectures for Neural Quantum States that deliver O(N^3) scaling with high accuracy and over 40x speedup on Hubbard and t-J models up to 32x32 lattices.
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Gauge-covariant projected entangled paired states for interacting systems in a magnetic field
A gauge-covariant PEPS ansatz with virtual flux tensors ensures translation-invariant physical expectation values for 2D interacting systems in a magnetic field, allowing gauge-independent simulations without enlarged magnetic unit cells.
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Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models
A Grassmann CTMRG tensor network method is introduced for 1D fermionic models and tested on the Hubbard model with magnetic field to capture phase diagram features.
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Neural and Tensor Networks in the Study of Quantum Annealing Processors
The thesis introduces a topology-aware tensor-network heuristic called SpinGlassPEPS.jl and thermodynamic metrics to benchmark quantum annealers on Ising problems while accounting for dissipation and effective temperature.
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Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.