Measuring the winding number in a large-scale chiral quantum walk

Abstract

We report the experimental measurement of the winding number in an unitary chiral quantum walk. Fundamentally, the spin-orbit coupling in discrete time quantum walks is implemented via birefringent crystal collinearly cut based on time-multiplexing scheme. Our protocol is compact and avoids extra loss, making it suitable for realizing genuine single-photon quantum walks at a large-scale. By adopting heralded single-photon as the walker and with a high time resolution technology in single-photon detection, we carry out a 50-step Hadamard discrete-time quantum walk with high fidelity up to 0.948$\pm$0.007. Particularly, we can reconstruct the complete wave-function of the walker that starts the walk in a single lattice site through local tomography of each site. Through a Fourier transform, the wave-function in quasi-momentum space can be obtained. With this ability, we propose and report a method to reconstruct the eigenvectors of the system Hamiltonian in quasi-momentum space and directly read out the winding numbers in different topological phases (trivial and non-trivial) in the presence of chiral symmetry. By introducing nonequivalent time-frames, we show that the whole topological phases in periodically driven system can also be characterized by two different winding numbers. Our method can also be extended to the high winding number situation.

arXiv comment26 pages, 8 figures

References in corpus (40)

• Classification of topological insulators and superconductors in three spatial dimensions
• Experimental realisation of the topological Haldane model
• On the Measurement of Qubits
• Periodic table for topological insulators and superconductors
• Quantum state tomography via compressed sensing
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Observation of topologically protected bound states in a one dimensional photonic system
• Photons Walking the Line: A quantum walk with adjustable coin operations
• Exploring Topological Phases With Quantum Walks
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Topological Transition in a Non-Hermitian Quantum Walk
• A 2D Quantum Walk Simulation of Two-Particle Dynamics
• Decoherence and disorder in quantum walks: From ballistic spread to localization
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Quantum walks and wavepacket dynamics on a lattice with twisted photons
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Photonic quantum walk in a single beam with twisted light
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Dynamical moments reveal a topological quantum transition in a photonic quantum walk
• Tomography of band insulators from quench dynamics
• Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms
• Topological phases and delocalization of quantum walks in random environments
• Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
• Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks
• Dynamical Buildup of a Quantized Hall Response from Non-Topological States
• Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
• Measuring Topological Invariants in Disordered Discrete Time Quantum Walks
• Experimental realisation of a delayed-choice quantum walk
• Scattering theory of topological phases in discrete-time quantum walks
• Robustness of topologically protected edge states in quantum walk experiments with neutral atoms
• Detecting topological invariants in chiral symmetric insulators via losses
• Bulk-edge correspondence of one-dimensional quantum walks
• Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments
• Determination of any pure spatial qudits from a minimum number of measurements by phase stepping interferometry

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• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• Digital Simulation of Topological Matter on Programmable Quantum Processors
• Topological Anderson insulators induced by random binary disorders
• Eigenvalue Measurement of Topologically Protected Edge states in Split-Step Quantum Walks
• Topological quantum walks: theory and experiments
• Probing the topological Anderson transition with quantum walks
• Simulating topological materials with photonic synthetic dimensions in cavities
• Spectrally uncorrelated biphotons generated from `the family of BBO crystal'
• Probing Bulk Band Topology from Time Boundary Effect in Synthetic Dimension
• Maximal coin-walker entanglement in a ballistic quantum walk
• Robust measurement of wave function topology on NISQ quantum computers
• Efficient learning of mixed-state tomography for photonic quantum walk
• Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics
• Global calibration of large-scale photonic integrated circuits
• Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands
• Quantum computing topological invariants of two-dimensional quantum matter
• Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman lattice
• Wannier center spectroscopy to identify boundary-obstructed topological insulators
• Relative homotopy approach to topological phases in quantum walks
• Second-order topological insulator in a coinless discrete-time quantum walk
• Nonlinear three-state quantum walks
• History states of one-dimensional quantum walks
• Many topological regions on the Bloch sphere of the spin-1/2 double kicked top
• Investigating the quench dynamics of the bound states in a spin-orbital coupling system using a trapped ion
• Experimental measurement of quantum first-passage-time distributions
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Proximity-induced flat bands and topological properties in a decorated diamond chain