Abstract: The aim of this paper is to build quantum circuits that implement discrete-time quantum walks having an arbitrary position-dependent coin operator. The position of the walker is encoded in base 2: with n wires, each corresponding to one qubit, we encode 2(n) position states. The data necessary to define an arbitrary position-dependent coin operator is therefore exponential in n. Hence, the exponentiality will necessarily appear somewhere in our circuits. We first propose a circuit implementing the position-dependent coin operator, that is naive, in the sense that it has exponential depth and implements sequentially all appropriate position-dependent coin operators. We then propose a circuit that “transfers” all the depth into ancillae, yielding a final depth that is linear in n at the cost of an exponential number of ancillae. Themain idea of this linear-depth circuit is to implement in parallel all coin operators at the different positions. Reducing the depth exponentially at the cost of having an exponential number of ancillae is a goal which has already been achieved for the problem of loading classical data on a quantum circuit (Araujo in Sci Rep 11:6329, 2021) (notice that such a circuit can be used to load the initial state of the walker). Here, we achieve this goal for the problem of applying a position-dependent coin operator in a discrete-time quantum walk. Finally, we extend the result of Welch (New J Phys 16:033040, 2014) from position-dependent unitaries which are diagonal in the position basis to position-dependent 2 x 2-block-diagonal unitaries: indeed, we show that for a position dependence of the coin operator (the block-diagonal unitary) which is smooth enough, one can find an efficient quantum-circuit implementation approximating the coin operator up to an error epsilon (in terms of the spectral norm), the depth and size of which scale as O(1/epsilon). A typical application of the efficient implementation would be the quantum simulation of a relativistic spin-1/2 particle on a lattice, coupled to a smooth external gauge field; notice that recently, quantum spatial-search schemes have been developed which use gauge fields as the oracle, to mark the vertex to be found (Zylberman in Entropy 23:1441, 2021), (Fredon arXiv:2210.13920). A typical application of the linear-depth circuit would be when there is spatial noise on the coin operator (and hence a non-smooth dependence in the position).

Abstract: Deviations from unitarity in the three-neutrino mixing canonical picture are expected in many physics scenarios beyond the Standard Model. The mixing of new heavy neutral leptons with the three light neutrinos would in principle modify the strength and flavour structure of charged-current and neutral-current interactions with matter. Non-unitarity effects would therefore have an impact on the neutrino decoupling processes in the early Universe and on the value of the effective number of neutrinos, Neff. We calculate the cosmological energy density in the form of radiation with a non-unitary neutrino mixing matrix, addressing the possible interplay between parameters. Highly accurate measurements of Neff from forthcoming cosmological observations can provide independent and complementary limits on the departures from unitarity. For completeness, we relate the scenario of small deviations from unitarity to non-standard neutrino interactions and compare the forecasted constraints to other existing limits in the literature.

Abstract: Dark-matter particles that annihilate or decay can undergo complex sequences of processes, including strong and electromagnetic radiation, hadronisation, and hadron de-cays, before particles that are stable on astrophysical time scales are produced. Antiprotons produced in this way may leave footprints in experiments such as AMS-02. Several groups have reported an excess of events in the antiproton flux in the rigidity range of 10-20 GV. However, the theoretical modeling of baryon production is not straightforward and relies in part on phenomenological models in Monte Carlo event generators. In this work, we assess the impact of QCD uncertainties on the spectra of antiprotons from dark-matter annihila-tion. As a proof-of-principle, we show that for a two-parameter model that depends only on the thermally-averaged annihilation cross section ((o -v)) and the dark-matter mass (Mx), QCD uncertainties can affect the best-fit mass by up to ti 14% (with large uncertainties for large DM masses), depending on the choice of Mx and the annihilation channel (bb over bar or W+W-), and (o -v) by up to ti 10%. For comparison, changes to the underlying diffusion parameters are found to be within 1%-5%, and the results are also quite resilient to the choice of cosmic-ray propagation model. These findings indicate that QCD uncertainties need to be included in future DM analyses. To facilitate full-fledged analyses, we provide the spectra in tabulated form including QCD uncertainties and code snippets to perform mass interpolations and quick DM fits. The code can be found in this GitHub [1] repository.