Modifying Method of Constructing Quantum Codes From Highly Entangled States

Raissi, Zahra

doi:10.1109/access.2020.3043401

Cited by 7 publications

(3 citation statements)

References 16 publications

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“…The stabilizer formalism is a useful tool in different branches of quantum information science like quantum error correcting codes [6,17,27], one-time or cluster states [28], and graph states [9]. We first recall the definition of the generalized Pauli operators acting on q-dimensional Hilbert space:…”

Section: Appendix B: Stabilizer Formalismmentioning

confidence: 99%

“…Graph states are multipartite stabilizer states in which each vertex of a given graph represents a qudit, and the graph adjacency matrix defines the stabilizer generators [9,10]. k-UNI states are highly entangled pure states that have the property that all of their k-qudit reduced density matrices are maximally mixed [15][16][17][18][19]. That is, the state |ψ is a k-UNI state if ρ S = Tr S c |ψ ψ| ∝ 1 ∀S ⊂ {1, .…”

Section: Introductionmentioning

confidence: 99%

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General stabilizer approach for constructing highly entangled graph states

Raissi¹,

Burchardt²,

Barnes³

2021

Preprint

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Highly entangled multipartite states such as k-uniform (k-UNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. However, there does not yet exist a complete classification of such states, and much remains unknown about their entanglement structure. Here, we substantially broaden the class of known k-UNI and AME states by introducing a method for explicitly constructing such states that combines classical error correcting codes and qudit graph states. This method in fact constitutes a general recipe for obtaining multipartitite entangled states from classical codes. Furthermore, we show that at least for a large subset of this new class of k-UNI states, the states are inequivalent under stochastic local operations and classical communication. This subset is defined by an iterative procedure for constructing a hierarchy of k-UNI graph states.

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Section: Appendix B: Stabilizer Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

General stabilizer approach for constructing highly entangled graph states

Raissi¹,

Burchardt²,

Barnes³

2021

Preprint

Self Cite

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“…Creating states with large m-uniformity is a key challenge in quantum information. Earlier studies discussed how to perform this task using orthogonal arrays [20,21,27,28], numerical methods [18,29], graph states [30][31][32] and other constructions [23,[33][34][35]. Special attention was drawn to n-qubit states that are n/2 -uniform, also known as absolutely maximal entangled (AME), which have important applications in quantum secret sharing and quantum teleportation [33,36].…”

Section: Introductionmentioning

confidence: 99%

Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

Sowrabh¹,

Azses²,

Torre³

et al. 2023

Preprint

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An entangled state is said to be m-uniform if the reduced density matrix of any m qubits is maximally mixed. This formal definition is known to be intimately linked to pure quantum error correction codes (QECCs), which allow not only to correct errors, but also to identify their precise nature and location. Here, we show how to create m-uniform states using local gates or interactions and elucidate several QECC applications. We first point out that D-dimensional cluster states, i.e. the ground states of frustration-free local cluster Hamiltonians, are m-uniform with m = 2D. We discuss finite size limitations of m-uniformity and how to achieve larger m values using quasi-D dimensional cluster states. We demonstrate experimentally on a superconducting quantum computer that the 1D cluster state allows to detect and identify 1-qubit errors, distinguishing, X, Y and Z errors. Finally, we show that m-uniformity allows to formulate pure QECCs with a finite logical space.

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Holographic codes from hyperinvariant tensor networks

Steinberg,

Feld,

Jahn

2023

Nat Commun

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Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code’s logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.

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Modifying Method of Constructing Quantum Codes From Highly Entangled States

Cited by 7 publications

References 16 publications

General stabilizer approach for constructing highly entangled graph states

General stabilizer approach for constructing highly entangled graph states

Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

Holographic codes from hyperinvariant tensor networks

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