Magnonic Gottesman-Kitaev-Preskill states

TL;DR

This paper introduces a novel protocol for preparing magnonic GKP states in a hybrid magnon-qubit system, enabling bosonic quantum error correction with potential applications in fault-tolerant quantum computing.

Contribution

First protocol for magnonic GKP state preparation using an anisotropic magnetic crystal coupled to a superconducting qubit via a microwave cavity.

Findings

Two rounds of conditional-displacement and measurement produce GKP-like states.

Single-qubit gates such as Pauli, Hadamard, and phase are realizable.

Establishes magnon-qubit systems as a platform for bosonic quantum error correction.

Abstract

Bosonic quantum error correction encodes a logical qubit in an oscillator, avoiding the hardware overhead of large qubit arrays. Among such encodings, Gottesman-Kitaev-Preskill (GKP) states are paticularly powerful because their phase-space grid structure protects against small displacement errors simultaneously in both conjugate quadratures. Here we provide the first protocol for preparing magnonic GKP states, which involves an ellipsoidal magnetic crystal effectively coupled to a superconducting qubit via a microwave cavity. The geometric anisotropy intrinsically squeezes the magnon mode, while the cavity-mediated qubit control realizes an effective conditional-displacement interaction. We show that two rounds of a conditional-displacement interaction and a qubit projective measurement yield three- and four-component magnonic GKP-like states. We also show how to realize single logical qubit gate operations, such as Pauli, Hadamard and phase gates, completing the logical Pauli basis of the approximate GKP code. Our results establish hybrid magnon-qubit systems as a promising platform for preparing bosonic code states, with applications in magnonic fault-tolerant quantum computation and quantum sensing.