Pretty good quantum state transfer on isotropic and anisotropic Heisenberg spin chains with tailored site dependent exchange couplings

Serra, Pablo; Ferrón, Alejandro; Osenda, Omar

doi:10.48550/arxiv.2101.03194

Cited by 3 publications

(5 citation statements)

References 35 publications

(44 reference statements)

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“…For example, for the second chain, one should set J max,B = πN B /4t m,A , if N B , is even; or J max,B = π Having set the mirroring time of both chains to be equal, we can now generate a bipartite maximally entangled state between the ends of the SN, following the protocol given in Fig. (4) or the second entanglement protocol given in section III B 2. If we use the second entanglement protocol then the entangled state will be given by…”

Section: Entanglement Generationmentioning

confidence: 99%

“…Spin chain systems are linear Spin Networks (SN) that have been shown to be useful for realising various tasks in quantum information processing (QIP). For example, such systems can be used to efficiently transfer quantum information from site to site, a process known as quantum state transfer [2][3][4]. Transferring information with unit fidelity can occur in certain SN, in a process known as Perfect State Transfer (PST) [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

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Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing

D’Amico

Estarellas³

et al. 2022

Adv Quantum Tech

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Spin chains can be used to describe a wide range of platforms for quantum computation and quantum information. They enable the understanding, demonstration, and modeling of numerous useful phenomena, such as high fidelity transfer of quantum states, creation and distribution of entanglement, and creation of resources for measurement-based quantum processing. In this paper, a more complex spin system, a 2D spin network (SN) engineered by applying suitable unitaries to two uncoupled spin chains, is studied. Considering only the single-excitation subspace of the SN, it is demonstrated that the system can be operated as a router, directing information through the SN. It is also shown that it can serve to generate maximally entangled states between two sites. Furthermore, it is illustrated that this SN system can be used as a sensor device able to determine an unknown phase applied to a system spin. A detailed modeling investigation of the effects of static disorder in the system shows that this system is robust against different types of disorder.

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Section: Entanglement Generationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing

D’Amico

Estarellas³

et al. 2022

Adv Quantum Tech

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show abstract

“…Obtaining analytical expressions in a completely general scenario would be impossible. We start asking for centrosymmetric spin chains as in most of our previous works [34,40,41]…”

Section: Exact Solution For Spin Chains With Staggered Exchange Coupl...mentioning

confidence: 99%

“…Heisenberg spin chains with nearest-neighbor time-independent staggered, or alternating, exchange coefficients are easier to implement than chains with all their spin coupling interactions tuned to precise values, at least in principle. Despite that the tailoring of all couplings can be, in principle, achieved in some implementations and result in nearperfect QST at known times [40,41], in this paper we aim to study the simpler staggered case, when the exchange couplings can take only two alternating values, J 1 and J 2 . The typical chain has an exchange coupling (EC) equal to J 1 between the first and second spin, J 2 between the second and third spin, and so on.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Serra,

Ferrón,

Osenda

2022

Preprint

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We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two different values. We work out the exact solutions in the one-excitation subspace. Regarding the problem of quantum state transfer, we use the solution and some theorems concerning the approximation of irrational numbers, to show the appearance of conclusive pretty good transmission for chains with particular lengths. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two. The set of spin chains that shows pretty good transmission is a subset of the family with an exact solution. Using perturbation theory, we thoroughly analyze the case when one of the exchange coupling strengths is orders of magnitude larger than the other. This strong coupling limit allows us to study, in a simple way, the appearance of pretty good transmission. The use of analytical closed expressions for the eigenvalues, eigenvectors, and transmission probabilities allows us to obtain the precise asymptotic behavior of the time where the pretty good transmission is observed. Moreover, we show that this time scales as a power law whose exponent is an increasing function of the chain length. We also discuss the crossover behavior obtained for the pretty good transmission time between the regimes of strong coupling limit and the one observed when the exchange couplings are of the same order of magnitude.

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“…For example, such systems can be used to efficiently transfer quantum information from site to site, a process known as quantum state transfer. [1][2][3] Transferring information with unit fidelity can occur in certain SNs, in a process known as perfect state transfer (PST). [4][5][6] SNs have interesting entanglement properties [7] and can also be used to generate and/or distribute entanglement.…”

Section: Introductionmentioning

confidence: 99%

Scalable Quantum Spin Networks from Unitary Construction

Alsulami,

D'Amico,

Estarellas

et al. 2023

Adv Quantum Tech

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Spin network (SN) systems can be used to achieve quantum state transfer with high fidelity and to generate entanglement. A new approach to design spin‐chain‐based spin network systems, for short‐range quantum information processing and phase‐sensing, has been proposed recently in Advanced Quantum Technologies. In this paper, the scalability of such systems is investigated, by designing larger SN systems that can be used for longer‐range quantum information tasks, such as connecting together quantum processors. Furthermore, more complex SN designs, which can produce different types of entangled states, are presented. Simulations of disorder effects show that even such larger SN systems are robust against realistic levels of disorder.

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Pretty good quantum state transfer on isotropic and anisotropic Heisenberg spin chains with tailored site dependent exchange couplings

Cited by 3 publications

References 35 publications

Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing

Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

Scalable Quantum Spin Networks from Unitary Construction

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