Topologically protected localised states in spin chains

Estarellas, Marta P.; D’Amico, Irene; Spiller, Timothy P.

doi:10.1038/srep42904

Cited by 46 publications

(55 citation statements)

References 41 publications

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“…Let us first briefly review the QST protocols based on Rabi flopping of left ( L ) and right ( R ) topological edge states, recently introduced in refs. []. In such protocols, one assumes

δ = 0

(no local magnetic fields) and the nontrivial topological phase

r \equiv t_{2} / t_{1} < 1

of the SSH chain, which ensures the existence of topological edge states.…”

Section: Quantum State Transfer In a Dimerized Spin Chainmentioning

confidence: 99%

“…This is basically the transfer method considered in refs. []. The main limitation of this transfer scheme is that, in order to achieve transfer from

scriptA

scriptB

with high fidelity, the ratio

r = t_{2} / t_{1}

should be chosen as much as small possible, corresponding to an extremely long transit time T according to Equations and .…”

Section: Quantum State Transfer In a Dimerized Spin Chainmentioning

confidence: 99%

“…The main advantage of the LZ topological QST method, over Rabi‐flopping schemes, is to be robust against disorder and structural imperfections of the chain, thus fully harnessing the topological protection feature of edge states. In addition, since the LZ transition is rather insensitive to the precise value of energy splitting of the edge states, the robustness of the LZ QST protocol persists even for disorder that breaks the chiral symmetry of the SSH lattice.…”

Section: Effect Of Disorder On Quantum State Transfer: Comparison Betmentioning

confidence: 99%

“…For an SSH chain with an even number of sites, that is, with an integer number of dimers, in the nontrivial topological phase

r < 1

there are two edge modes. For finite chains, the two edge modes hybridize and undergo Rabi‐like oscillations, which can be exploited to realize QST between the two edge sites of the chain . For static chains, the time required to achieve QST with a high fidelity turns out to be extremely long, which is undesirable owing to decoherence effects.…”

Section: Introductionmentioning

confidence: 99%

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Landau–Zener Topological Quantum State Transfer

2019

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Fast and robust quantum state transfer (QST) is a major requirement in quantum control and in scalable quantum information processing. Topological protection has emerged as a promising route for the realization of QST robust against sizable imperfections in the network. Here, a scheme is presented for robust QST of topologically protected edge states in a dimeric Su-Schrieffer-Heeger spin chain assisted by Landau-Zener tunneling. As compared to topological QST protocols based on Rabi flopping proposed in recent works, the method is more advantageous in terms of robustness against both diagonal and off-diagonal disorder in the chain, without a substantial increase of the interaction time.

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“…Let us first briefly review the QST protocols based on Rabi flopping of left ( L ) and right ( R ) topological edge states, recently introduced in refs. []. In such protocols, one assumes

δ = 0

(no local magnetic fields) and the nontrivial topological phase

r \equiv t_{2} / t_{1} < 1

of the SSH chain, which ensures the existence of topological edge states.…”

Section: Quantum State Transfer In a Dimerized Spin Chainmentioning

confidence: 99%

“…This is basically the transfer method considered in refs. []. The main limitation of this transfer scheme is that, in order to achieve transfer from

scriptA

scriptB

with high fidelity, the ratio

r = t_{2} / t_{1}

should be chosen as much as small possible, corresponding to an extremely long transit time T according to Equations and .…”

Section: Quantum State Transfer In a Dimerized Spin Chainmentioning

confidence: 99%

Section: Effect Of Disorder On Quantum State Transfer: Comparison Betmentioning

confidence: 99%

“…For an SSH chain with an even number of sites, that is, with an integer number of dimers, in the nontrivial topological phase

r < 1

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Landau–Zener Topological Quantum State Transfer

2019

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show abstract

“…This separates the system into two independent but equivalent chains, whose single-excitation spectra each contain a topologically protected, strongly localised eigenstate at site X (see the lower panel of Fig.5). The presence of this state can be explained by considering site X as a defect between two topologically distinct configurations, giving rise to a spatially localised state at zero energy within an energy gap [29]. The occupation probability distributions of the five single-excitation eigenstates for the new separated chain are presented in Fig.5.…”

Section: Entanglement Generation-plus-storage Protocolmentioning

confidence: 99%

Robust quantum entanglement generation and generation-plus-storage protocols with spin chains

2017

Self Cite

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Reliable quantum communication/processing links between modules are a necessary building block for various quantum processing architectures. Here we consider a spin chain system with alternating strength couplings and containing three defects, that impose three domain walls between topologically distinct regions of the chain. We show that -in addition to its useful, high fidelity, quantum state transfer properties -an entangling protocol can be implemented in this system, with optional localisation and storage of the entangled states. We demonstrate both numerically and analytically that, given a suitable initial product-state injection, the natural dynamics of the system produces a maximally entangled state at a given time. We present detailed investigations of the effects of fabrication errors, analyzing random static disorder both in the diagonal and off-diagonal terms of the system Hamiltonian. Our results show that the entangled state formation is very robust against perturbations of up to ∼ 10% the weaker chain coupling, and also robust against timing injection errors. We propose a further protocol which manipulates the chain in order to localise and store each of the entangled qubits. The engineering of a system with such characteristics would thus provide a useful device for quantum information processing tasks involving the creation and storage of entangled resources.

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Topological Phase Transition with Larger Winding Number in the Non‐Hermitian Dimerized Lattice

Han

Wang

et al. 2023

Annalen der Physik

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The topological phase transitions among normal insulator phase, two kinds of topological insulator phases, and topological semimetal phase are shown based on the non‐Hermitian dimerized Su–Schrieffer–Heeger (SSH) model with the nonreciprocal intercell and long‐range hopping. In contrast to the previous work, it is found that the topological insulator phase in the present SSH model can hold the larger non‐Bloch winding number accompanied by exceptional winding of the generalized Brillouin zone around the gap‐closing points. Compared with the usual topological insulator phase in non‐Hermitian SSH model, the topological insulator with the larger winding number owns two pairs of zero energy modes with a distinct form of edge localization in the gap. The physical mechanism of the distinct edge localization for zero energy modes via a equivalent Hermitian version of the non‐Hermitian SSH model is revealed. Additionally, the process of the phase transition is visualized among normal insulator phase, topological insulator phases, and topological semimetal phase in detail via the evolution of the gap‐closing points on the plane of generalized Brillouin zone. This work further verifies the non‐Bloch theory and enrich the investigation about the topologically nontrivial phase with the larger topological invariant in the non‐Hermitian SSH model.

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Topologically protected localised states in spin chains

Cited by 46 publications

References 41 publications

Landau–Zener Topological Quantum State Transfer

Landau–Zener Topological Quantum State Transfer

Robust quantum entanglement generation and generation-plus-storage protocols with spin chains

Topological Phase Transition with Larger Winding Number in the Non‐Hermitian Dimerized Lattice

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