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Quantum operations for Kramers-Wannier duality by Khan, Maaz; Khan, Syed Anausha Bin Zakir; Mohd, Arif is a scholarly article available to read on EtoBox.

What is Quantum operations for Kramers-Wannier duality about?

We study the Kramers-Wannier duality for the transverse-field Ising lattice on a ring. A careful consideration of the ring boundary conditions shows that the duality has to be implemented with a proper treatment of different charge sectors of both the twisted and untwisted Ising and the dual-Ising Hilbert spaces. We construct a superoperator that explicitly maps the Ising operators to the dual-Ising operators. The superoperator naturally acts on the tensor product of the Ising and the dual-Ising Hilbert space. We then show that the relation between our superoperator and the Kramers-Wannier duality operator that maps the Ising Hilbert space to the dual-Ising Hilbert space is naturally provided by quantum operations and the duality can be understood as a quantum operation that we construct. We provide the operator-sum representation for the Kramers-Wannier quantum operations and reproduce the well-known fusion rules. In addition to providing the quantum information perspective on the Kramers-Wannier duality, our explicit protocol will also be useful in implementing the Kramers-Wannier duality on a quantum computer.

Author

Khan, Maaz; Khan, Syed Anausha Bin Zakir; Mohd, Arif

Published

2024

Language

EN