Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs
arXiv:2003.11190 · doi:10.1088/1751-8121/abc4b9
Abstract
In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer: the transmission of quantum states without dissipation. The essential goal is to develop the theoretical framework for understanding the interplay between perfect quantum state transfer, spectral properties, and the geometry of the underlying graph, in order to design novel protocols for applications in quantum information science. We present a new lifting and gluing construction, and use this to prove results concerning an inductive spectral structure, applicable to a wide variety of fractal-like graphs. We illustrate this construction with explicit examples for several classes of diamond graphs.
arXiv commentrevised version
References in corpus (30)
- Quantum Communication Through an Unmodulated Spin Chain
- Perfect state transfer in quantum spin networks
- Quantum Communication through Spin Chain Dynamics: an Introductory Overview
- A Review of Perfect State Transfer and its Application as a Constructive Tool
- Conclusive and arbitrarily perfect quantum state transfer using parallel spin chain channels
- Spin Chains as Perfect Quantum State Mirrors
- Perfect quantum state transfer with randomly coupled quantum chains
- Non-Perturbative Entangling Gates between Distant Qubits using Uniform Cold Atom Chains
- Optimal dynamics for quantum-state and entanglement transfer through homogeneous quantum wires
- How to construct spin chains with perfect state transfer
- Quantum Networks on Cubelike Graphs
- Perfect Quantum Routing in Regular Spin Networks
- Thermodynamics of photons on fractals
- On the Spectral Gap of a Quantum Graph
- Almost perfect state transfer in quantum spin chains
- High-dimensional quantum state transfer through a quantum spin chain
- Heat Kernels and Zeta Functions on Fractals
- Physical Consequences of Complex Dimensions of Fractals
- Analytic next-to-nearest neighbour XX models with perfect state transfer and fractional revival
- Spatial Log Periodic Oscillations of First-Passage Observables in Fractals
- Perfect State Transfer in Two and Three Dimensional Structures
- Explicit formulas for heat kernels on diamond fractals
- Perfect quantum state transfer on diamond fractal graphs
- Para-Krawtchouk polynomials on a bi-lattice and a quantum spin chain with perfect state transfer
- Perturbatively-perfect many-body transfer
- Simultaneous multiple-users quantum communication across a spin chain channel
- Many-qubit quantum state transfer via spin chains
- Energy and Laplacian on Hanoi-type fractal quantum graphs
- The quantum query complexity of certification
- Heat kernel analysis on diamond fractals
Cited by in corpus (9)
- Periodicity of quantum walks defined by mixed paths and mixed cycles
- Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line
- Renormalization-Group Theory of the Heisenberg Model in d Dimensions
- Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs
- Nematic Ordering in the Heisenberg Spin-Glass System in d=3 Dimensions
- Combinatorial necessary conditions for regular graphs to induce periodic quantum walks
- Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory
- XY-Ashkin-Teller Phase Diagram in d=3
- Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer