Detecting Topological Invariants in Nonunitary Discrete-Time Quantum Walks

Zhan, Xiang; Liu, Xiao; Bian, Zhihao; Wang, Kunkun; Qiu, Xingze; Sanders, Barry C.; Wu, Yi; Xue, Peng

doi:10.1103/physrevlett.119.130501

Cited by 197 publications

(127 citation statements)

References 42 publications

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“…The coin operator R is implemented by a set of HWPs. The shift operator S 1 (S 2 ) is implemented by a BD [12][13][14][15]. The mode-selective loss operator M E is implemented by a PPBS.…”

Section: Methodsmentioning

confidence: 99%

Non-Hermitian bulk–boundary correspondence in quantum dynamics

et al. 2020

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Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. Our work unequivocally establishes the non-Hermitian bulk-boundary correspondence as a general principle underlying non-Hermitian topological systems, and paves the way for a complete understanding of topological matter in open systems.

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“…The coin operator R is implemented by a set of HWPs. The shift operator S 1 (S 2 ) is implemented by a BD [12][13][14][15]. The mode-selective loss operator M E is implemented by a PPBS.…”

Section: Methodsmentioning

confidence: 99%

Non-Hermitian bulk–boundary correspondence in quantum dynamics

et al. 2020

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“…The dynamic coin operation implemented with a fast-switching electro-optic modulator (EOM) makes it suitable for a wide range of experiments, including the investigation of topological phenomena [22,58]. Previous photonic implementations allowed for accessing topological invariants associated with probability distributions or amplitudes within a certain step of the walk [9,22,[65][66][67][68][69]. However, topological properties can also manifest themselves in the emergence of eigenstates with associated eigenvalues that are revealed by the phase relation between the walker's wavefunctions for two consecutive steps.…”

Section: Experimental Implementation 31 Time-multiplexing Setupmentioning

confidence: 99%

Eigenvalue measurement of topologically protected edge states in split-step quantum walks

et al. 2019

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We study topological phenomena of quantum walks by implementing a novel protocol that extends the range of accessible properties to the eigenvalues of the walk operator. To this end, we experimentally realise for the first time a split-step quantum walk with decoupling, which allows for investigating the effect of a bulk-boundary while realising only a single bulk configuration. The experimental platform is implemented with the well-established time-multiplexing architecture based on fibre-loops and coherent input states. The symmetry protected edge states are approximated with high similarities and we read-out the phase relative to a reference for all modes. In this way we observe eigenvalues which are distinguished by the presence or absence of sign flips between steps. Furthermore, the results show that investigating a bulk-boundary with a single bulk is experimentally feasible when decoupling the walk beforehand.

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“…where the integer j represent sites of the walker in the 1D line. The implementations of DTQW have been achieved in several quantum systems, such as linear optics [22][23][24][32][33][34], ion traps [35,36], and neutral atom traps [37].…”

Section: Introductionmentioning

confidence: 99%

Protocol of a quantum walk in circuit QED

Zhou

Cai

et al. 2019

Phys. Rev. A

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Implementation of discrete-time quantum walk (DTQW) with superconducting qubits is difficult since on-chip superconducting qubits cannot hop between lattice sites. We propose an efficient protocol for the implementation of DTQW in circuit quantum electrodynamics (QED), in which only N +1 qutrits and N assistant cavities are needed for an N -step DTQW. The operation of each DTQW step is very quick because only resonant processes are adopted. The numerical simulations show that high-similarity DTQW with the number of step up to 20 is feasible with present-day circuit QED technique. This protocol can help to study properties and applications of large-step DTQW in experiments, which is important for the development of quantum computation and quantum simulation in circuit QED.

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Detecting Topological Invariants in Nonunitary Discrete-Time Quantum Walks

Cited by 197 publications

References 42 publications

Non-Hermitian bulk–boundary correspondence in quantum dynamics

Non-Hermitian bulk–boundary correspondence in quantum dynamics

Eigenvalue measurement of topologically protected edge states in split-step quantum walks

Protocol of a quantum walk in circuit QED

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