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Paper 1

Qutrit codes within representations of SU(3)

Xzavier Herbert, Jonathan Gross, Michael Newman

Year
2023
Journal
arXiv preprint
DOI
arXiv:2312.00162
arXiv
2312.00162

We describe a quantum error-detecting and error-correcting code embedded within irreducible representations of SU(3). These logical qutrits inherit the He(3) symmetries induced by the representation, while protecting against small SU(3) displacements. We explore the general methodology for finding codes from structure-inducing representations of groups, together with symmetries inherited from finite subgroups, extending the case of spin representations of SU(2).

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Paper 2

Quantum optimization with arbitrary connectivity using Rydberg atom arrays

Minh-Thi Nguyen, Jin-Guo Liu, Jonathan Wurtz, Mikhail D. Lukin, Sheng-Tao Wang, Hannes Pichler

Year
2022
Journal
arXiv preprint
DOI
arXiv:2209.03965
arXiv
2209.03965

Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including: maximum weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.

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