Generalized Conditional Displacement

Shiran Even-Haim; Asaf A. Diringer; Ron Ruimy; Gefen Baranes; Alexey Gorlach; Shay Hacohen-Gourgy; Ido Kaminer

doi:10.22331/q-2025-12-10-1934

Generalized Conditional Displacement

Shiran Even-Haim¹, Asaf A. Diringer², Ron Ruimy³, Gefen Baranes³, Alexey Gorlach⁴, Shay Hacohen-Gourgy², and Ido Kaminer¹

¹Faculty of Electrical & Computer Engineering, Technion - Israel Institute of Technology, Israel
²Faculty of Physics, Technion-Israel Institute of Technology, Israel
³Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁴Solid State Institute, Technion-Israel Institute of Technology, Haifa 32000, Israel

Published:	2025-12-10, volume 9, page 1934
Editor:	Ulysse Chabaud
Eprint:	arXiv:2405.09977v3
Doi:	https://doi.org/10.22331/q-2025-12-10-1934
Citation:	Quantum 9, 1934 (2025).

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Abstract

Conditional displacement with a qubit ancilla is a critical component in continuous-variable error correction protocols. We present the generalized conditional displacement operator, conditioned on a qudit ancilla, and explore potential implementations. We show how this operator can be used to enhance error correction with Gottesman-Kitaev-Preskill (GKP) codes.

Featured image: Wigner representations after the generalized conditional displacement (CD) operator and d-level qudit measurement in the Xd basis.

Popular summary

Our research focuses on hybrid continuous-variable discrete-variable quantum error correction and its applications for creating and stabilizing the Gottesman-Kitaev-Preskill (GKP) code. We generalize the conventional conditional displacement (CD) gate from qubits to multi-level qudits. By exploiting the extra levels of a qudit, the generalized CD can act on both quadratures of a quantum oscillator simultaneously, doubling stabilization speed and improving resilience to noise. We investigate the fundamental interactions of the GKP with various systems, including another harmonic oscillator, a quantum planar rotor, and an atom ensemble, that can create this gate, thereby connecting to leading experimental platforms.

► BibTeX data

@article{EvenHaim2025generalized,
  doi = {10.22331/q-2025-12-10-1934},
  url = {https://doi.org/10.22331/q-2025-12-10-1934},
  title = {Generalized {C}onditional {D}isplacement},
  author = {Even-Haim, Shiran and Diringer, Asaf A. and Ruimy, Ron and Baranes, Gefen and Gorlach, Alexey and Hacohen-Gourgy, Shay and Kaminer, Ido},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1934},
  month = dec,
  year = {2025}
}

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