Nzongani, U., Zylberman, J., Doncecchi, C. E., Perez, A., Debbasch, F., & Arnault, P. (2023). Quantum circuits for discrete-time quantum walks with position-dependent coin operator. Quantum Inf. Process., 22(7), 270–46pp.
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).
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IGISOL Collaboration(Briz, J. A. et al), Algora, A., Tain, J. L., Guadilla, V., Agramunt, J., Estevez, E., et al. (2016). Total absorption spectroscopy of fission fragments relevant for reactor antineutrino spectra determination. Acta Phys. Pol. B, 47(3), 755–762.
Abstract: The contribution of each fission fragment to the reactor antineutrino spectra was determined using the summation method based on the existing information on fission yields and decay data contained in nuclear databases and the reactor evolution code MURE. The beta decay of some of the main contributors has been studied using the Total Absorption Spectroscopy (TAS) technique during two experimental campaigns at the IGISOL facility, in Jyvaskyla (Finland). Results on the decay of Rb-92, the most important contributor in the 4-8 MeV energy region are reported. The status of the analysis of the second experiment is presented as well.
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Hinarejos, M., Perez, A., Roldan, E., Romanelli, A., & de Valcarcel, G. J. (2013). Understanding and controlling N-dimensional quantum walks via dispersion relations: application to the two-dimensional and three-dimensional Grover walks-diabolical points and more. New J. Phys., 15, 073041–31pp.
Abstract: The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrodinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-dimensional Grover walks are presented.
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Hinarejos, M., Bañuls, M. C., & Perez, A. (2015). Wigner formalism for a particle on an infinite lattice: dynamics and spin. New J. Phys., 17, 013037–16pp.
Abstract: The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.
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Angles-Castillo, A., Bañuls, M. C., Perez, A., & De Vega, I. (2020). Prethermalization of quantum systems interacting with non-equilibrium environments. New J. Phys., 22(8), 083067–17pp.
Abstract: The usual paradigm of open quantum systems falls short when the environment is actually coupled to additional fields or components that drive it out of equilibrium. Here we explore the simplest such scenario, by considering a two level system coupled to a first thermal reservoir that in turn couples to a second thermal bath at a different temperature. We derive a master equation description for the system and show that, in this situation, the dynamics can be especially rich. In particular, we observe prethermalization, a transitory phenomenon in which the system initially approaches thermal equilibrium with respect to the first reservoir, but after a longer time converges to the thermal state dictated by the temperature of the second environment. Using analytical arguments and numerical simulations, we analyze the occurrence of this phenomenon, and how it depends on temperatures and coupling strengths. The phenomenology gets even richer if the system is placed between two such non-equilibrium environments. In this case, the energy current through the system may exhibit transient features and even switch direction, before the system eventually reaches a non-equilibrium steady state.
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Gomez-Vargas, G. A., Lopez-Fogliani, D. E., Muñoz, C., Perez, A. D., & Ruiz de Austri, R. (2017). Search for sharp and smooth spectral signatures of μnu SSM gravitino dark matter with Fermi- LAT. J. Cosmol. Astropart. Phys., 03(3), 047–23pp.
Abstract: The μnu SSM solves the μproblem of supersymmetric models and reproduces neutrino data, simply using couplings with right-handed neutrinos nu's. Given that these couplings break explicitly R parity, the gravitino is a natural candidate for decaying dark matter in the μnu SSM. In this work we carry out a complete analysis of the detection of μnu SSM gravitino dark matter through gamma-ray observations. In addition to the two-body decay producing a sharp line, we include in the analysis the three-body decays producing a smooth spectral signature. We perform first a deep exploration of the low-energy parameter space of the μnu SSM taking into account that neutrino data must be reproduced. Then, we compare the gamma-ray fluxes predicted by the model with Fermi-LAT observations. In particular, with the 95% CL upper limits on the total diffuse extragalactic gamma-ray background using 50 months of data, together with the upper limits on line emission from an updated analysis using 69.9 months of data. For standard values of bino and wino masses, gravitinos with masses larger than about 4 GeV, or lifetimes smaller than about 10(28) s, produce too large fluxes and are excluded as dark matter candidates. However, when limiting scenarios with large and close values of the gaugino masses are considered, the constraints turn out to be less stringent, excluding masses larger than 17 GeV and lifetimes smaller than 4 x 10(25) s.
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Arnault, P., Macquet, A., Angles-Castillo, A., Marquez-Martin, I., Pina-Canelles, V., Perez, A., et al. (2020). Quantum simulation of quantum relativistic diffusion via quantum walks. J. Phys. A, 53(20), 205303–39pp.
Abstract: Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position.
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Perez, A., & Romanelli, A. (2013). Spatially Dependent Decoherence and Anomalous Diffussion of Quantum Walks. J. Comput. Theor. Nanosci., 10(7), 1591–1595.
Abstract: We analyze the long time behavior of a discrete time quantum walk subject to decoherence with a strong spatial dependence, acting on one half of the lattice. We show that, except for limiting cases on the decoherence parameter, the quantum walk at late times behaves sub-ballistically, meaning that the characteristic features of the quantum walk are not completely spoiled. Contrarily to expectations, the asymptotic behavior is non Markovian, and depends on the amount of decoherence. This feature can be clearly shown on the long time value of the Generalized Chiral Distribution (GCD).
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Marquez-Martin, I., Di Molfetta, G., & Perez, A. (2017). Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time. Phys. Rev. A, 95(4), 042112–5pp.
Abstract: We analyze the properties of a two-and three-dimensional quantum walk that are inspired by the idea of a brane-world model put forward by Rubakov and Shaposhnikov [Phys. Lett. B 125, 136 (1983)]. In that model, particles are dynamically confined on the brane due to the interaction with a scalar field. We translated this model into an alternate quantum walk with a coin that depends on the external field, with a dependence which mimics a domain wall solution. As in the original model, fermions (in our case, the walker) become localized in one of the dimensions, not from the action of a random noise on the lattice (as in the case of Anderson localization) but from a regular dependence in space. On the other hand, the resulting quantum walk can move freely along the “ordinary” dimensions.
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Di Molfetta, G., & Perez, A. (2016). Quantum walks as simulators of neutrino oscillations in a vacuum and matter. New J. Phys., 18, 103038–8pp.
Abstract: We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing one to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to illustrate these effects in extreme conditions, such as the solar interior or supernovae.
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