We present how a neutrino condensate and small neutrino masses emerge from a topological formulation of gravitational anomaly. We first recapitulate how a gravitational θ-term leads to the emergence of a new bound neutrino state analogous to the η ′ meson of QCD. Then we show the consequent formation of a neutrino vacuum condensate, which effectively generates small neutrino masses. Afterwards we outline several phenomenological consequences of our neutrino mass generation model. The cosmological neutrino mass bound vanishes since we predict the neutrinos to be massless until the phase transition in the late Universe, T ∼ meV. Deviations from an equal flavor rate due to enhanced neutrino decays in extraterrestrial neutrino fluxes can be observed in future IceCube data. The current cosmological neutrino background only consists of the lightest neutrinos, which, due to enhanced neutrino-neutrino interactions, either bind up, form a superfluid, or completely annihilate into massless bosons. Strongly coupled relic neutrinos could provide a contribution to cold dark matter in the late Universe, together with the new proposed particles and topological defects, which may have formed during neutrino condensation. These enhanced interactions could also be a source of relic neutrino clustering in our Galaxy, which possibly makes the overdense cosmic neutrino background detectable in the KATRIN experiment. The neutrino condensate provides a mass for the hypothetical B − L gauge boson, leading to a gravity-competing force detectable in short-distance measurements. Gravitational waves detections have the potential to probe our neutrino mass generation mechanism.

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We numerically study the single-flavour Schwinger model in the Hamiltonian formulation with a topological θ-term corresponding to a constant electric background field. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial θ-dependence of several lattice and continuum quantities. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermion mass. In the chiral limit, we demonstrate that the continuum model becomes independent of the vacuum angle θ, thus respecting CP invariance, while lattice artifacts still depend on θ. We also confirm that negative masses can be mapped to positive masses by shifting θ → θ + π due to the axial anomaly in the continuum, while lattice artifacts non-trivially distort this mapping.

Parametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution space while maintaining a low parameter count and circuit depth. In this paper, develop a method to analyze the dimensional expressivity of parametric quantum circuits. Our technique allows for identifying superfluous parameters in the circuit layout and for obtaining a maximally expressive ansatz with a minimum number of parameters. Using a hybrid quantum-classical approach, we show how to efficiently implement the expressivity analysis using quantum hardware, and we provide a proof of principle demonstration of this procedure on IBM's quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.