How to construct spin chains with perfect state transfer

Abstract

It is shown how to systematically construct the $XX$ quantum spin chains with nearest-neighbor interactions that allow perfect state transfer (PST). Sets of orthogonal polynomials (OPs) are in correspondence with such systems. The key observation is that for any admissible one-excitation energy spectrum, the weight function of the associated OPs is uniquely prescribed. This entails the complete characterization of these PST models with the mirror symmetry property arising as a corollary. A simple and efficient algorithm to obtain the corresponding Hamiltonians is presented. A new model connected to a special case of the symmetric $q$-Racah polynomials is offered. It is also explained how additional models with PST can be derived from a parent system by removing energy levels from the one-excitation spectrum of the latter. This is achieved through Christoffel transformations and is also completely constructive in regards to the Hamiltonians.

7 pages

References in corpus (7)

• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Mirror Inversion of Quantum States in Linear Registers
• Spin Chains as Perfect Quantum State Mirrors
• All Possible Coupling Schemes in XY Spin Chains for Perfect State Transfer
• An Exactly Solvable Spin Chain Related to Hahn Polynomials
• Dual -1 Hahn polynomials and perfect state transfer
• Quantum state transfer in spin chains with q-deformed interaction terms

Cited by in corpus (59)

• Quantum-state transfer via resonant tunnelling through local field induced barriers
• Automatic spin-chain learning to explore the quantum speed limit
• Almost perfect state transfer in quantum spin chains
• Quantum spin chains with fractional revival
• Free-Fermion entanglement and orthogonal polynomials
• No Laplacian Perfect State Transfer in Trees
• Analytic next-to-nearest neighbour XX models with perfect state transfer and fractional revival
• Pretty good state transfer of entangled states through quantum spin chains
• Perfect quantum state transfer on diamond fractal graphs
• A graph with fractional revival
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Coherent ground-state transport of neutral atoms
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs
• Asymptotically perfect efficient quantum state transfer across uniform chains with two impurities
• Atoms versus photons as carriers of quantum states
• Evolutionary computation for adaptive quantum device design
• Dual -1 Hahn polynomials and perfect state transfer
• Ising analogues of quantum spin chains with multispin interactions
• Inhomogeneous XX spin chains and quasi-exactly solvable models
• Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
• Birth and death processes and quantum spin chains
• A novel analytic spin chain model with fractional revival
• High-dimensional quantum state transfer in a noisy network environment
• Exact Fractional Revival in Spin Chains
• Transfer arbitrary photon state along a cavity array without initialization
• Parity-dependent state transfer for direct entanglement generation
• Spin lattices, state transfer and bivariate Krawtchouk polynomials
• Ergotopy transport in a one dimensional spin chain
• Phase transition in complex-time Loschmidt echo of short and long range spin chain
• Perfect routing of quantum information in regular cavity QED networks
• The multivariate Hahn polynomials and the singular oscillator
• A classical model for perfect transfer and fractional revival based on $q$-Racah polynomials
• Perfect State Transfer in a Spin Chain without Mirror Symmetry
• Quasi-Perfect State Transfer in Spin Chains via Parametrization of On-Site Energies
• Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials
• Perfect quantum state transfer of hard-core bosons on weighted path graphs
• Perfect State Transfer on Weighted Graphs of the Johnson Scheme
• Enhancing quantum state transfer efficiency in binary-tree spin networks by partially collapsing measurements
• State Transfer in Latent-Symmetric Networks
• Pretty Good State Transfer and Minimal Polynomials
• Fast and efficient long-distance quantum state transfer in long-range spin-$\frac{1}{2}$ models
• Scalable Quantum Spin Networks from Unitary Construction
• The para-Racah polynomials
• Analytic "Newton's cradles" with perfect transfer and fractional revival
• Time-dependent density functional theory for open spin chains
• Open and closed spin chains as multiprocessor wires: optimal engineering and reachability
• A $q$-version of the relation between the hypercube, the Krawtchouk chain and Dicke states
• Laurent skew orthogonal polynomials and related symplectic matrices
• High-Field NMR Characterization and Indirect $J$-Spectroscopy of a Nuclear Spin Chain [U-${}^{13}$C,${}^{15}$N]-butyronitrile
• A New Perspective on the Average Mixing Matrix
• The Entanglement Level and the Detection of Quantum Data Transfer Correctness in Short Qutrit Spin Chains
• Memory effects in repeated uses of quantum channels
• Perfect quantum state transfer in weighted paths with potentials (loops) using orthogonal polynomials
• Perfect state transfer in two dimensions and the bivariate dual-Hahn polynomials
• Emergent mirror symmetry in the optimization of the central-spin quantum battery
• A Theorem of Joseph-Alfred Serret and its Relation to Perfect Quantum State Transfer
• Effective non-local parity-dependent couplings in qubit chains
• State transfer analysis for linear spin chains with non-uniform on-site energies
• Transfer of quantum-enhanced information through a many-body system