Quantifying Complexity in Quantum Phase Transitions via Mutual Information Complex Networks
Lincoln D. Carr
Dept. of Physics, Colorado School of Mines in collaboration with Marc Valdez, Daniel Jaschke, and David Vargas (CSM) Bhuvanesh Sundar and Kaden Hazzard (Rice) Complex networks occur between usual quantum physics regimes
Clustered Uniform = Random = Lattices, Hard Nuclear Condensed Dense Disparate Theory, Matter Physics, Quantum Quantum Chaos information theory Disparate Clustered Social Dense Food Web Metabolic Network Network Where do complex networks appear in quantum systems? Near-term quantum devices Digital quantum computer • Long-range entangling gates key factor in quantum volume for quantum advantage Quantum internet • Distributed entanglement on classical internet backbone? Present quantum devices Adiabatic quantum computer: D-Wave • Chimera map (degree 6) Analog quantum computer: Quantum simulators • At least 7 different platforms! Ø(see talk of Valentina Parigi) Complex networks in quantum simulators Whole Hamiltonian Quantum random walk on complex network Encode complex network directly into the links Part of Hamiltonian E.g. single particle terms vs. interactions Environment in open quantum systems Arising spontaneously in the state Quantum critical points in quantum phase transitions Quantum cellular automata No complex network required in Hamiltonian! Quantum Phase Transitions: Quantum Matter in a Crystal of Light Density image Optical Lattices Superfluid after expansion
Mott Insulator
DnDf ³1 But what are quantum phase transitions?
Non-analyticity in correlator in thermodynamic limit Driven by quantum not thermal fluctuations In practice: mesoscopic systems ok Huge field Condensed matter, AMO, Nuclear, QCD, String theory, Quantum information Adjacency matrix from quantum states (not operators, not “quantum networks” for a quantum internet) Density matrix � = |�⟩⟨�|
� = Tr � is a mixed state Describes quantum state of subsystem j Quantum entropy (von Neumann)
� = −Tr(� log� ) Quantifies entanglement, non-additive Quantum mutual information = adjacency matrix � = (� + � − � ) Two point quantum measure = nonlocality Bounded from below by all two-point correlators • Captures most essential feature of quantum phase transitions Quantum Mutual Information Complex Network
� forms an undirected, weighted adjacency matrix which does not permit self connection