Stabilization of Gottesman-Kitaev-Preskill States

In the paper's words

Harmonic oscillators enable hardware-efficient quantum error correction through the redundancy of infinite-dimensional Hilbert spaces. Conventional stabilization relies on measurement-based feedback, which is limited by detection latency and recoil heating in trapped ion systems. We propose an autonomous stabilization protocol that replaces active control with engineered dissipative reservoir dynamics.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Dissipative Stabilization of Gottesman-Kitaev-Preskill States in Room-Temperature Ion Traps Author: Rowan Brad Quni-Gudzinas Contact: rowan.quni@outlook.com ORCID: 0009-0002-4317-5604 ISNI: 0000000526456062 URL: https://papers.qnfo.org/papers/stabilization-of-gottesman-kitaev-preskill-states/ Date: 2025-12-02 Version: 1.0 Abstract : Harmonic oscillators enable hardware-efficient quantum error correction through the redundancy of infinite-dimensional Hilbert spaces.

   from Autonomous

2. This approach utilizes a dissipative reservoir designed to autonomously pump entropy out of the system, relaxing the state into the target Gottesman-Kitaev-Preskill manifold (de Neeve et al., 2022).

   from 1.5 Autonomous

3. Theoretical models of sympathetic cooling demonstrate that a coolant ion can efficiently absorb energy from a logic ion via the Coulomb interaction (Wübbena et al., 2012).

   from 1.6 Entropy Export

4. Reiter and Sørensen’s formalism allows us to map the heat extracted from the system to the information entropy removed from the logical qubit (Reiter & Sørensen, 2012).

   from 3.4 Mapping

5. Reiter and Sørensen’s formalism ensures that the local reduction of entropy in the logic ion is compensated by a global increase in entropy in the radiation field (Reiter & Sørensen, 2012).

   from 3.13

6. Royer et al. derived the scaling of the logical error rate for dissipative GKP stabilization (Royer et al., 2020).

   from 4.3 Exponential

How it is done

1. We propose an autonomous stabilization protocol that replaces active control with engineered dissipative reservoir dynamics.

   from Autonomous

2. The bosonic approach circumvents this complexity by exploiting the large state space of a single oscillator to correct errors through hardware-efficient redundancy.

   from 1.1 Continuous Variable

3. This approach necessitates a complex control stack where the syndrome is extracted, processed by room-temperature electronics (FPGA), and converted into a corrective actuation signal.

   from 1.2 Active Error Correction

4. Heating Effects The process of projective measurement in ion traps is not a thermodynamically benign operation but introduces significant back-action heating into the system.

   from 1.4 Measurement-induced

What would falsify it

1. Turchette et al.‘s heating model predicts a rapid thermalization of the motional state (Turchette et al., 2000).

   from 4.7 Dynamics without

2. Lifetimes Exceeding Physical Limits We predict that the logical lifetime of the autonomously stabilized qubit will exceed the physical lifetime of the uncorrected state. de Neeve et al. demonstrated this extension experimentally (de Neeve et al., 2022).

   from 4.12 Logical

3. This prediction is the primary success metric for the proposed architecture.

   from 4.12 Logical

Where the claim stops

1. However, the infinite potential of the oscillator is constrained by specific continuous error channels, primarily photon loss and thermal heating.

   from 1.1 Continuous Variable

2. The assumption that the syndrome extraction is a non-invasive probe fails in the regime of high-sensitivity motional codes.

   from 1.4 Measurement-induced

3. The mechanism of recoil heating is fundamental to the light-matter interaction and cannot be eliminated by improved feedback algorithms.

   from 1.4 Measurement-induced

Where to read

1. 1.0 Introduction1,074 words · 5 min
2. 2.0 Literature Review1,027 words · 4 min
3. 3.0 Methodological Framework1,893 words · 8 min
4. 4.0 Analysis and Validation1,938 words · 8 min
5. Appendix A: Formal301 words · 1 min
6. Appendix B: Notation and106 words · 1 min
7. Appendix C: Algorithmic Logic153 words · 1 min