Entanglement in Shor's Factoring Algorithm

Tan, Jianing; Liu, Zhihao; Chen, Hanwu

doi:10.5121/csit.2020.100307

Cited by 1 publication

(2 citation statements)

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“…These are all properties fulfilled by spin-network states belonging to the Hilbert space of TQFT and realizing a holonomic quantum computing system. [42,43] Focusing on a quantum Turing machine 𝔐, satisfying specific axioms [44] and resulting as an instantiation of a quantum simulator, it is possible to identify the computational space of 𝔐 with spin-network states, and hence code information in terms of irreducible representations of SU (2). Suppose for instance to recover as building blocks of 𝔐 an ordered collection of n + 1 mutually commuting angular momentum operators, which we denote as {J l }, with l = 1, … , n + 1.…”

Section: Marzuoli-rasetti Coding and Tqft As Quantum Simulatormentioning

confidence: 99%

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Communication Protocols and QECC From the Perspective of TQFT, Part II: QECCs as Spacetimes

Fields,

Glazebrook,

Marcianò

2024

Fortschritte der Physik

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Topological quantum field theories (TQFTs) provide a general, minimal‐assumption language for describing quantum‐state preparation and measurement. They therefore provide a general language in which to express multi‐agent communication protocols, e.g., local operations, classical communication (LOCC) protocols. In the accompanying Part I, we construct LOCC protocols using TQFT, and show that LOCC protocols induce quantum error‐correcting codes (QECCs) on the agent‐environment boundary. Such QECCs can be regarded as implementing or inducing the emergence of spacetimes on such boundaries. Here connection between inter‐agent communication and spacetime is investigated, by exploiting different realizations of TQFT. The authors delved into TQFTs that support on their boundaries spin‐networks as computational systems: these are known as topological quantum neural networks (TQNNs). TQNNs, which have a natural representation as tensor networks, implement QECC. The HaPPY code is recognized to be a paradigmatic example. How generic QECCs, as bulk‐boundary codes, induce effective spacetimes is then shown. The effective spatial and temporal separations that take place in QECC enables LOCC protocols between spatially separated observers. The implementation of QECCs in BF and Chern‐Simons theories are then considered, and QECC‐induced spacetimes are shown to provide the classical redundancy required for LOCC. Finally, the topological M‐theory is considered as an implementation of QECC in higher spacetime dimensions.

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Section: Marzuoli-rasetti Coding and Tqft As Quantum Simulatormentioning

confidence: 99%

“…They provide, as elements of the transfer matrices connecting any pair of states, the analog of the transition function of the quantum Turing Machine. [44] They also represent perfect tensor-networks, in the sense of ref. [17].…”

Section: Marzuoli-rasetti Coding and Tqft As Quantum Simulatormentioning

confidence: 99%