Structure and Classification of Matrix Product Quantum Channels

arXiv:2603.19866 · quant-ph, cond-mat.str-el, math-ph, math.MP · Submitted 2026-03-20 · Read on arXiv

quant-ph, cond-mat.str-el, math-ph, math.MP

Submitted: 2026-03-20

Updated: 2026-09-16

Terminology

• Entanglement — 29× in this paper · explained in 3 episodes
• Local Purification — 19× in this paper
• Homogeneity — 16× in this paper · explained in 2 episodes
• Trace — 16× in this paper · explained in 2 episodes
• Quantum Circuits — 10× in this paper · explained in 2 episodes
• Matrix Product Quantum Channels — 9× in this paper
• Generalization — 4× in this paper · explained in 13 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• Entanglement Entropy — 3× in this paper · explained in 2 episodes
• Topological Order — 3× in this paper · explained in 2 episodes
• Post-Selection — 2× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Gibbs State — 1× in this paper · explained in 2 episodes
• Locality Preserving Quantum Channel — 1× in this paper
• Matrix Product States (MPS) — 1× in this paper · explained in 2 episodes
• Multipartite Entanglement — 1× in this paper · explained in 2 episodes
• Process tomography — 1× in this paper · explained in 2 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes

Sources

• An Area Law for One Dimensional Quantum Systems
• An area law and sub-exponential algorithm for 1D systems
• Anomalous matrix product operator symmetries and 1D mixed-state phases
• Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries
• Quantum process tomography with unsupervised learning and tensor networks
• Matrix product channel: Variationally optimized quantum tensor network to mitigate noise and reduce errors for the variational quantum eigensolver
• Efficiently Learning Global Quantum Channels with Local Tomography
• Symmetry defects and gauging for quantum states with matrix product unitary symmetries
• Causal Decompositions of 1D Quantum Cellular Automata
• Reversible quantum cellular automata
• Preparing matrix product states via fusion: constraints and extensions
• Matrix Product State Representations
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories

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