Lucas K. Kovalsky | Searcharxiv

arXiv2026

Conformal Vacuum of dS$_4\times \mathbb R$ with Oppositely Oriented Boundaries

We derive a dS$_4 \times \mathbb R$ quotient spacetime that is asymptotically dS$_4$, where the quotient makes its past boundary oppositely oriented relative to its future boundary. This introduces a lightlike singularity that severs the antipodes of the spacetime and simplifies its global vacuum to a trivial product on antipodal static patches. We show that this state is conformal to the vacuum of an infinite orientable cover of a non-orientable AdS$_3$ spacetime with an S$^2$ bundle. The vacuum's separability extends to its holographic dual, which is a product of Cardy states. We find that this candidate dS$_4$ vacuum state is perturbatively unstable within quantum gravity due to a vanishing Hagedorn temperature.

hep-th↗

arXiv2023

Self-healing of Trotter error in digital adiabatic state preparation

Adiabatic time evolution can be used to prepare a complicated quantum many-body state from one that is easier to synthesize and Trotterization can be used to implement such an evolution digitally. The complex interplay between non-adiabaticity and digitization influences the infidelity of this process. We prove that the first-order Trotterization of a complete adiabatic evolution has a cumulative infidelity that scales as $\mathcal O(T^{-2} δt^2)$ instead of $\mathcal O(T^2 δt^2)$ expected from general Trotter error bounds, where $δt$ is the time step and $T$ is the total time. This result suggests a self-healing mechanism and explains why, despite increasing $T$, infidelities for fixed-$δt$ digitized evolutions still decrease for a wide variety of Hamiltonians. It also establishes a correspondence between the Quantum Approximate Optimization Algorithm (QAOA) and digitized quantum annealing.

quant-ph↗