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Fermionic Hamiltonians without trivial low-energy states

https://doi.org/10.1103/PhysRevA.109.052431

Herasymenko, Yaroslav; Anshu, Anurag; Terhal, Barbara M; Helsen, Jonas (May 2024, Physical Review A)

We construct local fermionic Hamiltonians with no low-energy trivial states (NLTS), providing a fermionic counterpart to the NLTS theorem. Distinctly from the qubit case, we define trivial states via finite-depth fermionic quantum circuits. We furthermore allow free access to Gaussian fermionic operations, provided they involve at most O(n) ancillary fermions. The desired fermionic Hamiltonian can be constructed using any qubit Hamiltonian which itself has the NLTS property via well-spread distributions over bitstrings, such as the construction in [ABN22]. We define a fermionic analogue of the class quantum PCP and discuss its relation with the qubit version.
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Quantum error correction with the toric Gottesman-Kitaev-Preskill code

https://doi.org/10.1103/PhysRevA.99.032344

Vuillot, Christophe; Asasi, Hamed; Wang, Yang; Pryadko, Leonid P.; Terhal, Barbara M. (March 2019, Physical Review A)

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Performance and structure of single-mode bosonic codes

https://doi.org/10.1103/PhysRevA.97.032346

Albert, Victor V.; Noh, Kyungjoo; Duivenvoorden, Kasper; Young, Dylan J.; Brierley, R. T.; Reinhold, Philip; Vuillot, Christophe; Li, Linshu; Shen, Chao; Girvin, S. M.; et al (March 2018, Physical Review A)

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