Quantum Codes, CFTs, and Defects

Buican, Matthew; Dymarsky, Anatoly; Radhakrishnan, Rajath

doi:10.48550/arxiv.2112.12162

Cited by 3 publications

(7 citation statements)

References 35 publications

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“…The physical interpretation of the construction of Narain CFTs with quantum codes is also to be given. Recently this has been studied by [21,22]. Finally, it is a future subject to extend the correspondence between Narain CFTs and quantum stabilizer codes.…”

Section: Discussionmentioning

confidence: 94%

Relation between spectra of Narain CFTs and properties of associated boolean functions

Furuta

2022

J. High Energ. Phys.

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Recently, the construction of Narain CFT from a certain class of quantum error correcting codes has been discovered. In particular, the spectral gap of Narain CFT corresponds to the binary distance of the code, not the genuine Hamming distance. In this paper, we show that the binary distance is identical to the so-called EPC distance of the boolean function uniquely associated with the quantum code. Therefore, seeking Narain CFT with large spectral gap can be addressed by getting a boolean function with high EPC distance. Furthermore, this problem can be undertaken by finding lower Peak-to-Average Power ratio (PAR) with respect to the binary truth table of the boolean function. Though this is neither sufficient nor necessary condition for high EPC distance, we construct some examples of relatively high EPC distances referring to the constructions for lower PAR. We also see that codes with high distance are related to induced graphs with low independence numbers.

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Section: Discussionmentioning

confidence: 94%

Relation between spectra of Narain CFTs and properties of associated boolean functions

Furuta

2022

J. High Energ. Phys.

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“…Speaking of the latter, one can straightforwardly generalize our construction by starting with a glue lattice Λ ⊂ R 3,3 or in fact Λ ⊂ R r,r for any r ≥ 2. Another important direction would be to connect the bottom-up approach of this paper with the top-down approach of [13] where quantum codes were given an interpretation in terms of CFT Hilbert space extended by defect operators. Finally, given our conjecture that optimal theories are code theories, it would be interesting to develop our approach into a practical way of constructing optimal theories with c > 8, thus complementing conventional modular bootstrap.…”

Section: Discussionmentioning

confidence: 99%

“…This emphasizes the bottom-up nature of our approach. While codes are expected to reflect some algebraic properties of the underlying CFTs in the top-down constructions [13], in our construction certain non-rational CFTs without obvious algebraic properties which would make them "finite" also can be obtained from codes.…”

Section: =mentioning

confidence: 99%

“…In this way constraints of modular invariance reduce to two algebraic constrains at the level of enumerator polynomial. The relation to quantum codes was recently extended and interpreted in terms of CFT Hilbert space in [13]. There are also "bottom-up" generalizations when the connection with codes is perceived as a tool to solve modular bootstrap constraints and construct interesting CFTs [14,15], also see [16,17] for the subsequent developments.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Narain CFTs from codes

Nikolaos

Chakraborty

Dymarsky

2022

J. High Energ. Phys.

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Recently established connection between additive codes and Narain CFTs provides a new tool to construct theories with special properties and solve modular bootstrap constraints by reducing them to algebraic identities. We generalize previous constructions to include many new theories, in particular we show that all known optimal Narain theories, i.e. those maximizing the value of spectral gap, can be constructed from codes. For asymptotically large central charge c we show there are code theories with the spectral gap growing linearly with c, with the coefficient saturating the conjectural upper bound. We therefore conjecture that optimal Narain theories for any value of c can be obtained from codes.

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“…In addition, we can construct an error-correcting code from A, which can reproduce the partition function with use of the weight enumerator polynomial. This might be the inverse of Construction A, and partially the extension of the work of Buican et al [BDR21]. Before describing this, we will continue to illustrate how to regard a Narain CFT as a simple current orbifold model for non-homogeneous cases.…”

Section: Always In the Image Of ϕ If And Only If ( ⃗ L −⃗ A) Is One O...mentioning

confidence: 99%

On the rationality and the code structure of a Narain CFT, and the simple current orbifold

Furuta

2024

J. Phys. A: Math. Theor.

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In this paper, we discuss the simple current orbifold of a rational Narain CFT (Narain RCFT). This is a method of constructing other rational CFTs from a given rational CFT, by “orbifolding” the global symmetry formed by a particular primary fields (called the simple current). Our main result is that a Narain RCFT satisfying certain conditions can be described in the form of a simple current orbifold of another Narain RCFT, and we have shown how the discrete torsion in taking that orbifold is obtained. Additionally, the partition function can be considered a simple current orbifold with discrete torsion, which is determined by the lattice and the B-field. We establish that the partition function can be expressed as a polynomial, with the variables substituted by certain q-series. In a specific scenario, this polynomial corresponds to the weight enumerator polynomial of an error-correcting code. Using this correspondence to the code theory, we can relate the B-field, the discrete torsion, and the B-form to each other.

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Quantum Codes, CFTs, and Defects

Cited by 3 publications

References 35 publications

Relation between spectra of Narain CFTs and properties of associated boolean functions

Relation between spectra of Narain CFTs and properties of associated boolean functions

Optimal Narain CFTs from codes

On the rationality and the code structure of a Narain CFT, and the simple current orbifold

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