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arXiv:2311.12324 · Physical Review Letters

Absorption-Emission Codes for Atomic and Molecular Quantum Information Platforms

Shubham P. Jain, Eric R. Hudson, Wesley C. Campbell, Victor V. Albert

Published Dec 23, 2024• 16 citations
arXivHTMLPDF

Abstract

Diatomic molecular codes [V. V. Albert, J. P. Covey, and J. Preskill, Robust encoding of a qubit in a molecule, Phys. Rev. X 10, 031050 (2020).PRXHAE2160-330810.1103/PhysRevX.10.031050] are designed to encode quantum information in the orientation of a diatomic molecule, allowing 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 conditions that are sufficient for codes to protect against such noise. We also identify existing and develop new absorption-emission (Æ) codes 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.

DOI
10.1103/physrevlett.133.260601

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Diatomic molecular codes [V. V. Albert, J. P. Covey, and J. Preskill, Robust encoding of a qubit in a molecule, Phys. Rev. X 10, 031050 (2020).PRXHAE2160-330810.1103/PhysRevX.10.031050] are designed to encode quantum information in the orientation of a diatomic molecule, allowing 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 conditions that are sufficient for codes to protect against such noise. We also identify existing and develop new absorption-emission (Æ) codes 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.
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a single molecule have been developed. These codes are currently an abstract concept, as no implementation strategy is yet known. Here, we present a step towards experimental implementation of one family of such codes, namely absorption-emission codes. We first construct architecture-agnostic check and correction operators. These operators are then decomposed into elements of the quantum logic spectroscopy toolbox that is available for molecular ions. We then describe and analyze a measurement-based sequential as well as an autonomous implementation strategy in the presence of thermal background radiation, a major noise source for rotation in polar molecules. The presented strategies and methods might enable robust sensing or even fault-tolerant quantum computing using the rotation of individual molecules.
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We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinitedimensional Hilbert space of rotational states of a rigid body.These codes, which protect against both drift in the body's orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule.Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms.We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.
We construct a general family of quantum codes that protect against all emission, absorption, dephasing, and raising or lowering errors up to an arbitrary fixed order. Such codes are known in the literature as absorption-emission (AE) codes. We derive simplified error correction conditions for a general AE code and show that any permutation-invariant code that corrects ttt or fewer errors can be mapped to an AE code that corrects up to order-ttt transitions. Carefully tuning the parameters of permutationally invariant codes, we construct several examples of efficient AE codes, hosted in systems with low total angular momentum. Our results also imply that spin codes can be mapped to AE codes, enabling us to characterize logical operators for certain subclasses of such codes.
The physical symmetries of a system play a central role in quantum error correction. In this work we encode a qubit in a collection of systems with angular momentum symmetry (spins), extending the tools developed by Gross [J. A. Gross, Phys. Rev. Lett. 127, 010504 (2021)] for single large spins. By considering large spins present in atomic systems and focusing on their collective symmetric subspace, we develop codes with octahedral symmetry capable of correcting errors up to second order in angular momentum operators. These errors include the most physically relevant noise sources such as microwave control errors and optical pumping. We additionally explore qubit codes that exhibit distance scaling commensurate with the surface code while permitting transversal single-qubit Clifford operations.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. The present code has a high encoding efficiency, since only one auxiliary qubit is needed for one message qubit on average. In addition, we note that the code can also work even in a worse case that the interaction with the environment causes a leakage out of the qubit space. The code may have some applications in the storage of quantum information for small-scale quantum computing, quantum information processing, and quantum communication.