Scientific Results

General phase spaces: from discrete variables to rotor and continuum limits

Year: 2017

Authors: Albert VV., Pascazio S., Devoret MH.

Autors Affiliation: [Albert, Victor V.] Yale Univ, Yale Quantum Inst, New Haven, CT 06520 USA.
[Pascazio, Saverio] Univ Bari, Dipartimento Fis, I-70126 Bari, Italy and Univ Bari, MECENAS, I-70126 Bari, Italy and CNR, INO, I-50125 Florence, Italy and INFN, Sez Bari, I-70126 Bari, Italy.
[Devoret, Michel H.] Yale Univ, Dept Appl Phys, New Haven, CT 06520 USA.

Abstract: We provide a basic introduction to discrete-variable, rotor, and continuous-variable quantum phase spaces, explaining how the latter two can be understood as limiting cases of the first. We extend the limit-taking procedures used to travel between phase spaces to a general class of Hamiltonians (including many local stabilizer codes) and provide six examples: the Harper equation, the Baxter parafermionic spin chain, the Rabi model, the Kitaev toric code, the Haah cubic code (which we generalize to qudits), and the Kitaev honeycomb model. We obtain continuous-variable generalizations of all models, some of which are novel. The Baxter model is mapped to a chain of coupled oscillators and the Rabi model to the optomechanical radiation pressure Hamiltonian. The procedures also yield rotor versions of all models, five of which are novel many-body extensions of the almost Mathieu equation. The toric and cubic codes are mapped to lattice models of rotors, with the toric code case related to U(1) lattice gauge theory.

Journal/Review: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Volume: 50 (50)      Pages from: 504002  to: 504002

KeyWords: Rabi model; Harper equation; Baxter model; toric code; Haah code
DOI: 10.1088/1751-8121/aa9314

English