A first introduction to Matrix Product State algorithms for the integration of Lindblad equation

arXiv:2609.18841 · cond-mat.stat-mech, quant-ph · Submitted 2026-09-16 · Read on arXiv

cond-mat.stat-mech, quant-ph

Submitted: 2026-09-16

Updated: 2026-09-16

Terminology

• Accuracy — 6× in this paper · explained in 1 episode
• Entanglement — 6× in this paper · explained in 4 episodes
• Quantum Trajectories — 6× in this paper · explained in 2 episodes
• Effective Hamiltonian — 5× in this paper · explained in 2 episodes
• Hilbert Space — 5× in this paper · explained in 2 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Matrix Product States — 3× in this paper
• Benchmark — 2× in this paper · explained in 2 episodes
• Entanglement Entropy — 2× in this paper · explained in 2 episodes
• Matrix Product Density Operator — 2× in this paper
• Matrix Product States (MPS) — 2× in this paper · explained in 2 episodes
• Time-Evolving Block Decimation — 2× in this paper
• Unitary Dynamics — 2× in this paper · explained in 2 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Matrix Product Operator — 1× in this paper

Sources

• Introduction to matrix-product states and tensor networks
• An introduction to graphical tensor notation for mechanistic interpretability

Related papers

• Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt
• Measurement-induced phase transitions in disordered fermions
• Quantum Thermalization beyond Non-Integrability and Quantum Scars in a Multispecies Bose-Josephson Junction
• Quantum many-body operator cascade as a route to chaos
• Proof of the absence of local conserved quantities in the Holstein model
• Work fluctuation speed limit in boundary conformal field theories