A Review of Perfect State Transfer and its Application as a Constructive Tool

Abstract

We review the subject of perfect state transfer; how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.

18 pages, 6 figures. Although mainly a review, this does contain some minor new results. v2: minor improvements. v3: journal version (to appear in Int. J. Quant. Inform.)

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• Control-limited perfect state transfer, quantum stochastic resonance and many-body entangling gate in imperfect qubit registers
• Computation on Spin Chains with Limited Access
• The Non-Equilibrium Reliability of Quantum Memories
• The Computational Power of Symmetric Hamiltonians
• Interfacing with Hamiltonian Dynamics
• Heisenberg chains cannot mirror a state
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• Limitations of Passive Protection of Quantum Information

Cited by in corpus (205)

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• 99%-fidelity ballistic quantum-state transfer through long uniform channels
• Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• A Faithful Communication Hamiltonian in Photonic Lattices
• Robustness of spin-coupling distributions for perfect quantum state transfer
• Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs
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• Discrete Time Quantum Walk Approach to State Transfer
• Spin chains for robust state transfer: Modified boundary couplings vs. completely engineered chains
• Fast and robust quantum state transfer via a topological chain
• Coherent state transfer via highly mixed quantum spin chains
• Almost perfect state transfer in quantum spin chains
• Landau-Zener topological quantum state transfer
• Universal quantum computation by discontinuous quantum walk
• Propagation of non-classical correlations across a quantum spin chain
• Transfer of arbitrary two qubit states via a spin chain
• Speed Limits for Macroscopic Transitions
• Quantum spin chains with fractional revival
• Optimized dynamical control of state transfer through noisy spin chains
• Topologically protected localised states in spin chains
• Robust Quantum Entanglement Generation and Generation-plus-Storage Protocols with Spin Chains
• Experimental characterization of coherent magnetization transport in a one-dimensional spin system
• Eigenvalues of Cayley graphs
• Pretty Good State Transfer in Qubit Chains - The Heisenberg Hamiltonian
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• Arbitrary entangled state transfer via a topological qubit chain
• Robust state transfer with high fidelity in spin-1/2 chains by Lyapunov control
• Perfect wave-packet splitting and reconstruction in a one-dimensional lattice
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• Supersymmetric Quantum Mechanics with Reflections
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• High-fidelity state transfer through long-range correlated disordered quantum channels
• Supervised learning of time-independent Hamiltonians for gate design
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• Interplay between speed and fidelity in off-resonant quantum-state transfer protocols
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• The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors
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• Ballistic quantum state transfer in spin chains: general theory for quasi-free models and arbitrary initial states
• Limitations of nearest-neighbour quantum networks
• NOON States via Quantum Walk of Bound Particles
• Uncertainty and symmetry bounds for the quantum total detection probability
• Initialization and Readout of Spin Chains for Quantum Information Transport
• Quantum walk transport properties on graphene structures
• Mixed-state quantum transport in correlated spin networks
• An Exactly Solvable Spin Chain Related to Hahn Polynomials
• Feedback-assisted quantum search by continuous-time quantum walks
• Optimal Quench for Distance-Independent Entanglement and Maximal Block Entropy
• Evolutionary computation for adaptive quantum device design
• Quantum efficiencies in finite disordered networks connected by many-body interactions
• Pretty good quantum state transfer on isotropic and anisotropic Heisenberg spin chains with tailored site dependent exchange couplings
• Generating Quantum States through Spin Chain Dynamics
• Quantum Control Theory for State Transformations: Dark States and their Enlightenment
• Dual -1 Hahn polynomials and perfect state transfer
• Inhomogeneous XX spin chains and quasi-exactly solvable models
• Coherent transfer by adiabatic passage in two-dimensional lattices
• Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
• Quantum transfer of interacting qubits
• Controlling and reversing the transition from classical diffusive to quantum ballistic transport in a quantum walk by driving the coin
• Combatting the Effects of Disorder in Quantum State Transfer
• Birth and death processes and quantum spin chains
• Analysis and minimization of bending losses in discrete quantum networks
• Perfect transfer of multiple excitations in quantum networks
• Reconfigurable Network for Quantum Transport Simulation
• A novel analytic spin chain model with fractional revival
• Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering
• Knitting distributed cluster state ladders with spin chains
• Non-Hermitian and Zeno limit of quantum systems under rapid measurements
• Photon-assisted quantum state transfer and entanglement generation in spin chains
• Robustness of spin-chain state-transfer schemes
• Statistics of a quantum-state-transfer Hamiltonian in the presence of disorder
• A Toolbox for Linear Optics in a 1D Lattice via Minimal Control
• Robust optimization for quantum reinforcement learning control using partial observations
• Exact Fractional Revival in Spin Chains
• Hamiltonian quantum computing with superconducting qubits
• Time-crystalline behavior in an engineered spin chain
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• Understanding the propagation of excitations in quantum spin chains with different kind of interactions
• Breaking the Speed Limit for Perfect Quantum State Transfer
• The impact of nuclear spin dynamics on electron transport through donors
• An infinite family of superintegrable Hamiltonians with reflection in the plane
• Voltage-controlled Hubbard spin transistor
• Adiabatic quantum state transfer in tight-binding chains using periodic driving fields
• Robustness of optimal transport in disordered interacting many-body networks
• Tailoring Spin Chain Dynamics for Fractional Revivals
• Quantum state transfer between twins in weighted graphs
• Bound state and Localization of excitation in many-body open systems
• Pretty good state transfer via adaptive quantum error correction
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• Multi-fractal Geometry of Finite Networks of Spins
• Perfect Coding for Dephased Quantum State Transfer
• A New Method for Multi-Bit and Qudit Transfer Based on Commensurate Waveguide Arrays
• Continuous dynamical decoupling of spin chains: modulating the spin-environment and spin-spin interactions
• Emulating quantum state transfer through a spin-1 chain on a 1D lattice of superconducting qutrits
• Selective dynamical decoupling for quantum state transfer
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• Perfect state transfer on hypercubes and its implementation using superconducting qubits
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• Strongly cospectral vertices in normal Cayley graphs
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• Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks
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• Phase transition in complex-time Loschmidt echo of short and long range spin chain
• Perfect Function Transfer in two- and three- dimensions without initialization
• Noise to lubricate qubit transfer in a spin network
• Quantum simulation of the Riemann-Hurwitz zeta function
• A framework for optimal quantum spatial search using alternating phase-walks
• Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing
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• Perfect State Transfer on Weighted Graphs of the Johnson Scheme
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• Quantum Walks on Graphs of the Ordered Hamming Scheme and Spin Networks
• How to Suppress Dark States in Quantum Networks and Bio-Engineered Structures
• Multiple-scale integro-differential perturbation method for generic non-Markovian environments
• Integrated information storage and transfer with a coherent magnetic device
• Quasi-Perfect State Transfer in Spin Chains via Parametrization of On-Site Energies
• Tunable refraction in a two dimensional quantum metamaterial
• Breakdown of local convertibility through Majorana modes in a quantum quench
• Transfer of optical signals around bends in two-dimensional linear photonic networks
• Generation and Robustness of Quantum Entanglement in Spin Graphs
• Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices
• Adiabatic freezing of entanglement with insertion of defects in a one-dimensional Hubbard model
• State Transfer in Latent-Symmetric Networks
• Scalable Structure For Chiral Quantum Routing
• Noise reducing encoding strategies for spin chains
• Tunable non-Markovian dynamics in a collision model: an application to coherent transport
• Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians
• Comparison of entangling protocols in ABC-type spin chains
• Designing spin channel geometries for entanglement distribution
• Mass-Assisted Local Deconfinement in a Confined ${\mathbb{Z}}_2$ Lattice Gauge Theory
• Scalable Quantum Spin Networks from Unitary Construction
• Perfect transfer of arbitrary continuous variable states across optical waveguide lattices
• Temporal witnesses of non-classicality in a macroscopic biological system
• Optimal quantum transport on a ring via locally monitored chiral quantum walks
• Dissipation-assisted quantum correlations in coupled qubits
• Quantum correlations between distant qubits conveyed by large-$S$ spin chains
• Quantum Fractional Revival on Graphs
• Analytic "Newton's cradles" with perfect transfer and fractional revival
• Information Transfer Fidelity in Spin Networks and Ring-based Quantum Routers
• Perfect Wave Transfer in Continuous Quantum Systems
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• Expediting quantum state transfer through the long-range extended XY model
• The Entanglement Level and the Detection of Quantum Data Transfer Correctness in Short Qutrit Spin Chains
• Transfer of quantum-enhanced information through a many-body system
• Comparative analysis of robust entanglement generation in engineered XX spin chains
• Remote entanglement generation via enhanced quantum state transfer
• State transfer analysis for linear spin chains with non-uniform on-site energies
• Spectral analysis of three-state quantum walks with general coin matrices
• Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer
• A Note on Eigenvalues of Cayley Graphs
• State Transfer in Complex Quantum Walks
• Incorporating Encoding into Quantum System Design
• Effective non-local parity-dependent couplings in qubit chains
• Efficient Classical Simulation of the DQC1 Circuit with Zero Discord