Quantum max-flow in the bridge graph

Abstract

The quantum max-flow is a linear algebraic version of the classical max-flow of a graph, used in quantum many-body physics to quantify the maximal possible entanglement between two regions of a tensor network state. In this work, we calculate the quantum max-flow exactly in the case of the bridge graph. The result is achieved by drawing connections to the theory of prehomogenous tensor spaces and the representation theory of quivers. Further, we highlight relations to invariant theory and to algebraic statistics.

27 pages, final version

References in corpus (27)

• Area laws for the entanglement entropy - a review
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• An Area Law for One Dimensional Quantum Systems
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Tensor networks for complex quantum systems
• Holographic duality from random tensor networks
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• What limits the simulation of quantum computers?
• An Efficient Matrix Product Operator Representation of the Quantum-Chemical Hamiltonian
• cMERA as Surface/State Correspondence in AdS/CFT
• Solving the sampling problem of the Sycamore quantum circuits
• Low communication high performance ab initio density matrix renormalization group algorithms
• Supervised Learning with Projected Entangled Pair States
• Hyper-invariant tensor networks and holography
• qTorch: The Quantum Tensor Contraction Handler
• Entanglement-guided architectures of machine learning by quantum tensor network
• Quantum Max-flow/Min-cut
• Invariant theory and scaling algorithms for maximum likelihood estimation
• Optimization at the boundary of the tensor network variety
• Towards a Geometric Approach to Strassen's Asymptotic Rank Conjecture
• Maximum likelihood estimation for tensor normal models via castling transforms
• The Asymptotics of Quantum Max-Flow Min-Cut
• Matrix product states and the quantum max-flow/min-cut conjectures
• The Linear Span of Uniform Matrix Product States