Æ codes

Diatomic molecular codes [1] are designed to encode quantum information in the orientation of a diatomic molecule, allowing for error correction from small torques and changes in angular momentum. Here, we directly study noise native to atomic and molecular platforms -- spontaneous emission, stray electromagnetic fields, and Raman scattering -- and show that diatomic molecular codes fail against this noise. We derive simple necessary and sufficient conditions for codes to protect against such noise. We develop new absorption-emission (Æ) codes [2] that are more practical than molecular codes, require lower average momentum, can directly protect against photonic processes up to arbitrary order, and are applicable to a broader set of atomic and molecular systems. We also identify existing bosonic [3] and spin codes [4,5] which can readily be adapted to Æ codes with their distances quantifying the protection against general transition errors in atomic and molecular systems. Finally, we propose potential hosts for implementation of the simplest examples of our codes in the near term.

References:

[1] V. V. Albert, J. P. Covey, and J. Preskill, Robust Encoding of a Qubit in a Molecule, Phys. Rev. X 10, 031050 (2020).

[2] S. P. Jain, E. R. Hudson, W. C. Campbell, and V. V. Albert, Æ codes, arXiv:2311.12324 (accepted in Physical Review Letters).

[3] M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, New Class of Quantum Error-Correcting Codes for a Bosonic Mode, Phys. Rev. X 6, 031006 (2016).

[4] J. A. Gross, Designing Codes around Interactions: The Case of a Spin, Physical Review Letters 127, 010504 (2021)

[5] S. Omanakuttan and J. A. Gross, Multispin Clifford codes for angular momentum errors in spin systems, arXiv:2304.08611 (2023).