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Two Proofs of the Hamiltonian Cycle Identity
Hamilton Sawczuk, Edinah Gnang
https://arxiv.org/abs/2510.02473 https://arxiv.org/pdf/2510.02473

Two Proofs of the Hamiltonian Cycle Identity
The Hamiltonian cycle polynomial can be evaluated to count the number of Hamiltonian cycles in a graph. It can also be viewed as a list of all spanning cycles of length $n$. We adopt the latter perspective and present a pair of original proofs for the Hamiltonian cycle identity which relates the Hamiltonian cycle polynomial to the important determinant and permanent polynomials. The first proof is a more accessible combinatorial argument. The second proof relies on viewing polynomials as both l…

Adiabatic preparation of thermal states and entropy-noise relation on noisy quantum computers
Etienne Granet, Henrik Dreyer
https://arxiv.org/abs/2509.05206 https://

Adiabatic preparation of thermal states and entropy-noise relation on noisy quantum computers
We consider the problem of preparing thermal equilibrium states at finite temperature on quantum computers. Assuming thermalization, we show that states that are locally at thermal equilibrium can be prepared by evolving adiabatically an initial thermal Gibbs state of a simple Hamiltonian with an interpolating time-dependent Hamiltonian, identically to adiabatic ground state preparation. We argue that the entropy density of local density matrices is conserved during the adiabatic evolution, so …