RQC Seminar

279th RQC Seminar

• Speaker

  Ms. Victoria Wadewitz
  ( Forschungszentrum Jülich )

• Date

  16:00-17:00, (4:00 p.m.-5:00 p.m.) Monday, June 8, 2026

• Venue

  Hybrid( Zoom,
  345-347 Seminar Room, 3F, Main Research Building, Wako Campus / 和光地区 研究本館3階 セミナー室 (345-347) (C01))

• Title

  Harnessing Zak Transform and Modular Variables for Gottesman–Kitaev–Preskill Code Applications

• Inquiries

  norilab_rqc_assist[at]ml.riken.jp

Abstract
Encoding a qubit in the continuous degrees of freedom of an oscillator is a promising route toward fault-tolerant quantum computation. The Gottesman–Kitaev–Preskill (GKP) code achieves this by embedding a qubit in a bosonic mode using periodic wavefunctions. This inherent periodicity makes the Zak transform a natural tool, as it provides a compact and structured representation of such states. Within this framework, the modular-variable bosonic subsystem decomposition (SSD) factorizes the Hilbert space into a virtual logical qubit and a gauge mode. Tracing out the gauge stabilizer subsystem is equivalent to an ideal decoding of the logical state.

In the first part of the talk, we analyze an error mitigation method known as probabilistic error cancellation (PEC) for GKP codes. We compare Steane-type and teleportation-based error correction schemes and evaluate their sampling overheads for both square and hexagonal GKP lattices. The corresponding sampling distributions are derived using the stabilizer subsystem decomposition formulated in the Zak basis.

In the second part, we explore how the modular-variable SSD can be leveraged for more efficient simulation of hybrid discrete-continuous-variable algorithms acting on GKP-like states formed by superpositions of squeezed position eigenstates. By representing bosonic modes in bases derived from modular subsystem codes and discrete truncated Zak representations, we identify potential advantages over conventional truncated Fock-space simulations.