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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Encoding a qubit in a molecule

Victor V. Albert, Jacob P. Covey, John P. Preskill

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Quantum error-correcting codes are constructed embedding a finite-dimensional codespace in the infinite-dimensional state space of rotational degrees of freedom of rigid bodies. Such codes protect against orientational diffusion and kicks in the body’s angular momentum.
DOI
10.1364/cqo.2019.m5a.11

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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 propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. We then discuss the feasibility of this scheme and suggest several candidates for its implementation. The proposed scheme is immediately generalizable to qudits of any finite dimension.
We present a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error‐correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. Finally, we propose a possible realization of qubits encoded in orbital angular momentum of a single photon.