A hardware-native time-frequency GKP logical qubit toward fault-tolerant photonic operation

TL;DR

This paper demonstrates a hardware-native time-frequency GKP logical qubit in single photons, enabling fault-tolerant photonic quantum computing through continuous phase space encoding, deterministic state generation, and accessible logical operations.

Contribution

It introduces a novel photonic implementation of the GKP logical qubit using time--frequency encoding with deterministic state generation and hardware-level stabilizers.

Findings

Deterministic generation of finite-energy grid states in single photons.

Implementation of stabilizer enforcement directly at hardware level.

Pathway toward active syndrome extraction and fault-tolerant operations.

Abstract

We realize a hardware-native time--frequency Gottesman--Kitaev--Preskill (GKP) logical qubit encoded in the continuous phase space of single photons, establishing a propagating photonic implementation of bosonic grid encoding. Finite-energy grid states are generated deterministically using coherently driven entangled nonlinear biphoton sources that produce single-photon frequency-comb supermodes. An optical-frequency-comb reference anchors the time--frequency phase space and enforces commuting displacement stabilizers directly at the hardware level, continuously defining the logical subspace. Timing jitter, spectral drift, and phase noise map naturally onto Gaussian displacement errors within this lattice, yielding intrinsic correctability inside a stabilizer cell. Logical operations correspond to experimentally accessible phase and delay controls, enabling deterministic state preparation and manipulation. Building on the modal time--frequency GKP framework, we identify a concrete pathway toward active syndrome extraction and deterministic displacement recovery using ancillary grid states and interferometric time--frequency measurements. These primitives establish a hardware-compatible route for integrating the time--frequency GKP logical layer into erasure-aware and fusion-based fault-tolerant photonic architectures.