Twirling and Hamiltonian Engineering via Dynamical Decoupling for GKP Quantum Computing

TL;DR

This paper presents a method for energy-constrained twirling and dynamical decoupling to improve GKP quantum error correction and enable protected quantum computing without explicit stabilizer measurements.

Contribution

It introduces a novel energy-constrained twirling operation and a dynamical decoupling sequence for GKP codes, facilitating passive stabilization and Hamiltonian engineering.

Findings

Effective diagonalization of logical channels in GKP codes.

Construction of a dynamical decoupling sequence with fast displacements.

Potential for protected GKP quantum computing without explicit stabilizer measurements.

Abstract

I introduce an energy constrained approximate twirling operation that can be used to diagonalize effective logical channels in GKP quantum error correction, project states into the GKP code space and construct a dynamical decoupling sequence with fast displacements pulses to distill the GKP stabilizer Hamiltonians from a suitable substrate-Hamiltonian. The latter is given by an LC-oscillator comprising a superinductance in parallel to a Josephson Junction. This platform in principle allows for protected GKP quantum computing without explicit stabilizer measurements or state-reset by dynamically generating a `passively' stabilized GKP qubit.