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Paper 1

Yoked surface codes

Craig Gidney, Michael Newman, Peter Brooks, Cody Jones

Year
2023
Journal
arXiv preprint
DOI
arXiv:2312.04522
arXiv
2312.04522

We nearly triple the number of logical qubits per physical qubit of surface codes in the teraquop regime by concatenating them into high-density parity check codes. These "yoked surface codes" are arrayed in a rectangular grid, with parity checks (yokes) measured along each row, and optionally along each column, using lattice surgery. Our construction assumes no additional connectivity beyond a nearest neighbor square qubit grid operating at a physical error rate of $10^{-3}$.

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Paper 2

Nonstandard Hubbard model and electron pairing

M. Zendra, F. Borgonovi, G. L. Celardo, S. Gurvitz

Year
2023
Journal
arXiv preprint
DOI
arXiv:2307.16737
arXiv
2307.16737

We present a non-standard Hubbard model applicable to arbitrary single-particle potential profiles and inter-particle interactions. Our approach involves a novel treatment of Wannier functions, free from the ambiguities of conventional methods and applicable to finite systems without periodicity constraints. To ensure the consistent evaluation of Wannier functions, we develop a perturbative approach, utilizing the barrier penetration coefficient as a perturbation parameter. With the newly defined Wannier functions as a basis, we derive the Hubbard Hamiltonian, revealing the emergence of density-induced and pair tunneling terms alongside standard contributions. Our investigation demonstrates that long-range inter-particle interactions can induce a novel mechanism for repulsive particle pairing. This mechanism relies on the effective suppression of single-particle tunneling due to density-induced tunneling. Contrary to expectations based on the standard Hubbard model, an increase in inter-particle interaction does not lead to an insulating state. Instead, our proposed mechanism implies the coherent motion of correlated electron pairs, similar to bound states within a multi-well system, resistant to decay from single-electron tunneling transitions. These findings carry significant implications for various phenomena, including the formation of flat bands, the emergence of superconductivity in twisted bilayer graphene, and the possibility of a novel metal-insulator transition.

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