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Paper 1

Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources

Alejandro Borda, Julian Rincon, César Galindo

Year
2025
Journal
arXiv preprint
DOI
arXiv:2512.20787
arXiv
2512.20787

The Clifford group is efficiently classically simulable, and universality is obtained by supplementing it with non-Clifford resources. We determine which single-qudit gates suffice to achieve universality. We show that the structure of such resources is governed by the prime factorization of the qudit dimension $d$. Using the adjoint action on the space of complex trace-zero matrices, we relate density to irreducibility together with an infiniteness criterion, yielding a trichotomy based on the factorization of $d$. When $d$ is prime, any non-Clifford gate generates a dense subgroup of the determinant-one unitaries. If $d$ is a prime power, the adjoint action is reducible, and universality requires gates that couple the resulting invariant subspaces. For composite $d$ with pairwise coprime factors, generalized intra-qudit controlled-NOT gates connecting the factors already suffice. These findings suggest that ``composite architectures'' -- hybrid registers combining incommensurate dimensions -- offer a route to bypass the standard overhead associated with magic-state injection.

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Paper 2

A note on the non-planar corrections for the Page curve in the PSSY model via the IOP matrix model correspondence

Norihiro Iizuka, Mitsuhiro Nishida

Year
2024
Journal
arXiv preprint
DOI
arXiv:2410.04679
arXiv
2410.04679

We develop a correspondence between the PSSY model and the IOP matrix model by comparing their Schwinger-Dyson equations, Feynman diagrams, and parameters. Applying this correspondence, we resum specific non-planar diagrams involving crossing in the PSSY model by using a non-planar analysis of a two-point function in the IOP matrix model. We also compare them with Page's formula on entanglement entropy and discuss the contributions of extra-handle-in-bulk diagrams.

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