Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography

arXiv:2609.04165 · quant-ph, cs.DS, cs.LG · Submitted 2026-09-03 · Read on arXiv

quant-ph, cs.DS, cs.LG

Submitted: 2026-09-03

Updated: 2026-09-03

Comments: 74 + 12 pages; 6 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 36× in this paper · explained in 2 episodes
• Entanglement — 23× in this paper · explained in 3 episodes
• Accuracy — 20× in this paper · explained in 1 episode
• Sample Complexity — 11× in this paper · explained in 15 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Quantum Circuits — 7× in this paper · explained in 2 episodes
• Stabilizer States — 7× in this paper · explained in 2 episodes
• Fidelity — 4× in this paper · explained in 2 episodes
• Projected Entangled Pair State — 4× in this paper
• AGN — 3× in this paper · explained in 1 episode
• Agnostic Learning — 3× in this paper · explained in 1 episode
• BQP — 2× in this paper · explained in 2 episodes
• Benchmarking — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Hamiltonian Learning — 2× in this paper · explained in 2 episodes
• Symposium on Foundations of Computer Science — 2× in this paper
• Trace Distance — 2× in this paper · explained in 3 episodes
• ACM-SIAM Symposium on Discrete Algorithms — 1× in this paper
• Adam — 1× in this paper · explained in 2 episodes
• Adaptivity — 1× in this paper · explained in 1 episode
• BQP-complete — 1× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Tucker Decomposition — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Adversarially robust quantum state learning and testing
• Hamiltonian Property Testing
• Tolerant testing of stabilizer states with a polynomial gap via a generalized uncertainty relation
• Certifying and learning quantum Ising Hamiltonians
• Breaking the Treewidth Barrier in Quantum Circuit Simulation with Decision Diagrams
• Testing classical properties from quantum data
• Gaussian decomposition of magic states for matchgate computations
• Efficient Contraction of Large Tensor Networks for Weighted Model Counting through Graph Decompositions
• Efficient learning of bosonic Gaussian unitaries
• Quantum Hamiltonian Certification
• Is it Gaussian? Testing bosonic quantum states
• The Heisenberg Representation of Quantum Computers
• Adaptive Learning of Tensor Network Structures
• Tolerant Testing of Stabilizer States with Mixed State Inputs
• Mildly-Interacting Fermionic Unitaries are Efficiently Learnable
• Carving-width and contraction trees for tensor networks
• An Improved Parameterized Algorithm for Treewidth
• Efficient Matrix Product State Learning in Logarithmic Depth
• Nearly tight bounds for testing tree tensor network states
• Efficient Direct Tomography for Matrix Product States

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity