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Researchers connect quantum error-correcting codes to 2D conformal field theories (CFTs). This link simplifies modular invariance, enabling the construction of new CFT partition functions and distinct theories.

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Area of Science:

  • Theoretical Physics
  • Quantum Information Theory
  • String Theory

Background:

  • Modular invariance and unitarity are key constraints in 2D conformal field theories (CFTs), forming the basis of the numerical modular bootstrap program.
  • Quantum error-correcting codes offer a framework for understanding complex quantum systems and their properties.

Purpose of the Study:

  • To establish a novel correspondence between quantum error-correcting codes and a specific class of 2D CFTs, termed "code CFTs."
  • To leverage this connection to simplify the constraints imposed by modular invariance on CFT partition functions.
  • To explore new avenues for constructing and understanding CFTs and their associated partition functions.

Main Methods:

  • Establishing a mapping between a family of quantum error-correcting codes and a subset of Narain CFTs.
  • Translating the modular invariance condition of 2D CFT partition functions into algebraic relations for multivariate polynomials characterizing the codes.
  • Utilizing this correspondence to generate explicit examples of theoretical constructs.

Main Results:

  • Demonstrated that modular invariance for "code CFTs" reduces to simple algebraic conditions on code-defining polynomials.
  • Constructed numerous examples of physically distinct, isospectral 2D CFTs.
  • Generated novel examples of nonholomorphic functions satisfying 2D CFT partition function properties but lacking association with known CFTs.

Conclusions:

  • The established correspondence provides a powerful tool for studying CFTs via quantum error-correcting codes.
  • This approach expands the landscape of known CFTs and their partition functions.
  • The findings open new research directions at the intersection of quantum information and theoretical physics.