Simulation of Bosonic Modes in a Discretized Zak Basis

Bosonic codes allow the storage of quantum information using the infinite Hilbert space of a quantum harmonic oscillator. A promising error correcting code in this category is the Gottesman-Kitaev-Preskill (GKP) code which can correct small quadrature shifts. GKP codewords are periodic and spread far into phase space making classical simulations of such states challenging in the conventional Fock basis. Indeed, large state vectors are needed to represent GKP states with high fidelity. In this talk, we explore the Zak basis from which we can simulate such states. This basis is ideal to represent periodic states and, when discretized, has the potential to reduce state vector sizes in classical simulation.