Low-cost error mitigation by symmetry verification

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an experiment, and develop a zero-cost post-processing protocol which is equivalent to a variant of the quantum subspace expansion. We develop methods for inserting global and local symetries into quantum algorithms, and for adjusting natural symmetries of the problem to boost their mitigation against different error channels. We demonstrate these techniques on two- and four-qubit simulations of the hydrogen molecule (using a classical density-matrix simulator), finding up to an order of magnitude reduction of the error in obtaining the ground state dissociation curve.Comment: Published versio

Not All Incentives Wash Out the Warm Glow: The Case of Blood Donation Revisited

The issue of the nature of the altruism inherent in blood donation and the perverse effects of financial rewards for blood and/or organ donation has been recently revisited in the economic literature with limited consensus. As Titmuss (1970) famously pointed out, providing monetary incentives to blood donors may crowd out blood supply as purely altruistic donors may feel less inclined to donate if a reward is involved - in addition to having the effect of reducing blood quality. In this paper we take a different approach by focusing on the nature of the rewards. That is, we examine how favouring different types of incentives are related to the likelihood of donating blood by exploiting a large sample representative of 15 European countries in 2002. Our results show that donors are less likely to favour monetary rewards for blood donation but are more likely to favour non-monetary ones. This is consistent with the idea that while monetary rewards may crowd out blood donation, non-monetary rewards do not.altruism, blood donation, incentives, nudging, recursive system, warm glow

Calculating energy derivatives for quantum chemistry on a quantum computer

Modeling chemical reactions and complicated molecular systems has been proposed as the `killer application' of a future quantum computer. Accurate calculations of derivatives of molecular eigenenergies are essential towards this end, allowing for geometry optimization, transition state searches, predictions of the response to an applied electric or magnetic field, and molecular dynamics simulations. In this work, we survey methods to calculate energy derivatives, and present two new methods: one based on quantum phase estimation, the other on a low-order response approximation. We calculate asymptotic error bounds and approximate computational scalings for the methods presented. Implementing these methods, we perform the world's first geometry optimization on an experimental quantum processor, estimating the equilibrium bond length of the dihydrogen molecule to within 0.014 Angstrom of the full configuration interaction value. Within the same experiment, we estimate the polarizability of the H2 molecule, finding agreement at the equilibrium bond length to within 0.06 a.u. (2% relative error).Comment: 19 pages, 1 page supplemental, 7 figures. v2 - tidied up and added example to appendice

Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions

The final publication is available at Springer via http://dx.doi.org/10.1007/s00013-012-0458-zWe investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H∞. Applications for composition operators on weighted Bloch spaces are given. © 2012 Springer Basel.1. The authors are thankful to the referee for pointing to us the references [15] and [16] and their relevance in the present research. 2. The research of Bonet was partially supported by MICINN and FEDER Project MTM2010-15200 and by GV project Prometeo/2008/101 and project ACOMP/2012/090.Bonet Solves, JA.; Lindström, M.; Wolf, E. (2012). Norm-attaining weighted composition operators on weighted Banach spaces of analytic functions. Archiv der Mathematik. 99(6):537-546. https://doi.org/10.1007/s00013-012-0458-zS537546996Bierstedt K.D., Bonet J., Galbis A.: Weighted spaces of holomorphic functions on bounded domains. Michigan Math. J. 40, 271–297 (1993)Bierstedt K.D., Bonet J., Taskinen J.: Associated weights and spaces of holomorphic functions. Studia Math. 127, 137–168 (1998)J. Bonet, P. Domański, and M. Lindström, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Canad, Math. Bull. 42, no. 2, (1999), 139–148Bonet J. et al.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc. Ser. A 64, 101–118 (1998)Bonet J., Lindström M, Wolf E.: Isometric weighted composition operators on weighted Banach spaces of type H ∞. Proc. Amer. Math. Soc. 136, 4267–4273 (2008)Bonet J, Wolf E.: A note on weighted spaces of holomorphic functions. Archiv Math. 81, 650–654 (2003)Contreras M.D, Hernández-Díaz A.G.: Weighted composition operators in weighted banach spaces of analytic functions. J. Austral. Math. Soc. Ser. A 69, 41–60 (2000)Cowen C., MacCluer B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)J. Diestel, Geometry of Banach Spaces. Selected Topics, Lecture Notes in Math. vol. 485, Springer, Berlin, 1975.Hammond C.: On the norm of a composition operator with linear fractional symbol. Acta Sci. Math. (Szeged) 69, 813–829 (2003)Hosokawa T., Izuchi K., Zheng D.: Isolated points and essential components of composition operators on H ∞. Proc. Amer. Math. Soc. 130, 1765–1773 (2001)Hosokava T., Ohno S.: Topological strusctures of the sets of composition operatorson the Bloch spaces. J. Math. anal. Appl. 303, 499–508 (2005)Lusky W.: On the isomorphy classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19–45 (2006)Martín M.: Norm-attaining composition operators on the Bloch spaces. J. Math. Anal. Appl. 369, 15–21 (2010)A. Montes-Rodríguez, The Pick-Schwarz lemma and composition operators on Bloch spaces, International Workshop on Operator Theory (Cefalu, 1997), Rend. Circ. Mat. Palermo (2) Suppl. 56 (1998), 167–170.Montes-Rodríguez A.: The essential norm of a composition operator on Bloch spaces. Pacific J. Math. 188, 339–351 (1999)Montes-Rodríguez A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. London Math. Soc. 61, 872–884 (2000)J.H. Shapiro, Composition Operators and Classical Function Theory, Springer, 1993.K. Zhu, Operator Theory in Function Spaces, Second Edition. Amer. Math. Soc., 2007

Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces

[EN] Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt's resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators.J. Bonet was partially supported by the research projects MTM2016-76647-P and GV Prometeo 2017/102 (Spain). M. Worku is supported by ISP project, Addis Ababa University, Ethiopia.Bonet Solves, JA.; Mengestie, T.; Worku, M. (2019). Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces. Results in Mathematics. 74(4):1-15. https://doi.org/10.1007/s00025-019-1123-7S115744Abanin, A.V., Tien, P.T.: Differentiation and integration operators on weighted Banach spaces of holomorphic functions. Math. Nachr. 290(8–9), 1144–1162 (2017)Atzmon, A., Brive, B.: Surjectivity and invariant subspaces of differential operators on weighted Bergman spaces of entire functions, Bergman spaces and related topics in complex analysis, Contemp. Math., vol. 404, Amer. Math. Soc., Providence, RI, pp. 27–39 (2006)Bayart, F., Matheron, E.: Dynamics of Linear Operators, Cambridge Tracts in Math, vol. 179. Cambridge Univ. Press, Cambridge (2009)Bermúdez, T., Bonilla, A., Peris, A.: On hypercyclicity and supercyclicity criteria. Bull. Austral. Math. Soc. 70, 45–54 (2004)Beltrán, M.J.: Dynamics of differentiation and integration operators on weighted space of entire functions. Studia Math. 221, 35–60 (2014)Beltrán, M.J., Bonet, J., Fernández, C.: Classical operators on weighted Banach spaces of entire functions. Proc. Am. Math. Soc. 141, 4293–4303 (2013)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999)Bonet, J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 26, 649–657 (2009)Bonet, J.: The spectrum of Volterra operators on weighted Banach spaces of entire functions. Q. J. Math. 66, 799–807 (2015)Bonet, J., Bonilla, A.: Chaos of the differentiation operator on weighted Banach spaces of entire functions. Complex Anal. Oper. Theory 7, 33–42 (2013)Bonet, J., Taskinen, J.: A note about Volterra operators on weighted Banach spaces of entire functions. Math. Nachr. 288, 1216–1225 (2015)Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. Lond. Math. Soc. 47, 958–963 (2015)Constantin, O., Peláez, J.-Á.: Integral operators, embedding theorems and a Littlewood–Paley formula on weighted Fock spaces. J. Geom. Anal. 26, 1109–1154 (2016)De La Rosa, M., Read, C.: A hypercyclic operator whose direct sum is not hypercyclic. J. Oper. Theory 61, 369–380 (2009)Dunford, N.: Spectral theory. I. Convergence to projections. Trans. Am. Math. Soc. 54, 185–217 (1943)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear Chaos. Springer, New York (2011)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233–247 (2008)Krengel, U.: Ergodic Theorems. Walter de Gruyter, Berlin (1985)Lyubich, Yu.: Spectral localization, power boundedness and invariant subspaces under Ritt’s type condition. Studia Mathematica 143(2), 153–167 (1999)Mengestie, T.: A note on the differential operator on generalized Fock spaces. J. Math. Anal. Appl. 458(2), 937–948 (2018)Mengestie, T.: Spectral properties of Volterra-type integral operators on Fock–Sobolev spaces. J. Kor. Math. Soc. 54(6), 1801–1816 (2017)Mengestie, T.: On the spectrum of volterra-type integral operators on Fock–Sobolev spaces. Complex Anal. Oper. Theory 11(6), 1451–1461 (2017)Mengestie, T., Ueki, S.: Integral, differential and multiplication operators on weighted Fock spaces. Complex Anal. Oper. Theory 13, 935–95 (2019)Mengestie, T., Worku, M.: Isolated and essentially isolated Volterra-type integral operators on generalized Fock spaces. Integr. Transf. Spec. Funct. 30, 41–54 (2019)Nagy, B., Zemanek, J.A.: A resolvent condition implying power boundedness. Studia Math. 134, 143–151 (1999)Nevanlinna, O.: Convergence of iterations for linear equations. Lecture Notes in Mathematics. ETH Zürich, Birkhäuser, Basel (1993)Ritt, R.K.: A condition that $$\lim _{n\rightarrow \infty } n^{-1}T^n =0$$. Proc. Am. Math. Soc. 4, 898–899 (1953)Ueki, S.: Characterization for Fock-type space via higher order derivatives and its application. Complex Anal. Oper. Theory 8, 1475–1486 (2014)Yosida, K.: Functional Analysis. Springer, Berlin (1978)Yosida, K., Kakutani, S.: Operator-theoretical treatment of Marko’s process and mean ergodic theorem. Ann. Math. 42(1), 188–228 (1941

Overview of ERA Integrated Technology Demonstration (ITD) 51A Ultra-High Bypass (UHB) Integration for Hybrid Wing Body (HWB)

The NASA Environmentally Responsible Aircraft Project (ERA) was a ve year project broken into two phases. In phase II, high N+2 Technical Readiness Level demonstrations were grouped into Integrated Technology Demonstrations (ITD). This paper describes the work done on ITD-51A: the Vehicle Systems Integration, Engine Airframe Integration Demonstration. Refinement of a Hybrid Wing Body (HWB) aircraft from the possible candidates developed in ERA Phase I was continued. Scaled powered, and unpowered wind- tunnel testing, with and without acoustics, in the NASA LARC 14- by 22-foot Subsonic Tunnel, the NASA ARC Unitary Plan Wind Tunnel, and the 40- by 80-foot test section of the National Full-Scale Aerodynamics Complex (NFAC) in conjunction with very closely coupled Computational Fluid Dynamics was used to demonstrate the fuel burn and acoustic milestone targets of the ERA Project

Thermodynamics of viscous dark energy in an RSII braneworld

We show that for an RSII braneworld filled with interacting viscous dark energy and dark matter, one can always rewrite the Friedmann equation in the form of the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon. In addition, the generalized second law of thermodynamics can fulfilled in a region enclosed by the apparent horizon on the brane for both constant and time variable 5-dynamical Newton's constant $G_5$. These results hold regardless of the specific form of the dark energy. Our study further support that in an accelerating universe with spatial curvature, the apparent horizon is a physical boundary from the thermodynamical point of view.Comment: 11 page

Analysis of the coating integrityduring a coronary stent deployment

Las afecciones cardiovasculares constituyen en la actualidad una causa frecuente de muerte. Una de estas afecciones es la ateroesclerosis, la cual provoca la reducción de la luz arterial. En aras de solucionar tal afección se han desarrollado varios tratamientos, ganando terreno la Angioplastia Coronaria Transluminar Percutánea (PTCA) con colocación de estent. En la actualidad muchos de estos dispositivos son recubiertos para aumentar la biocompatibilidad y disminuir los riesgos de reestenosis. Dado la posibilidad de fallas o roturas de los recubrimientos y los riesgos asociados a estas, es de gran importancia el estudio del comportamiento de la unión estentrecubrimiento durante la fase de expansión del estent. En esta investigación se estudia la posible ocurrencia de delaminación del recubrimiento durante la expansión de un estent y la influencia de parámetros como el espesor y el material del mismo. El estudio parte de la obtención de un modelo geométrico de una celda del estent Sirius Carbostent para su posterior procesamiento por el Método de Elementos Finitos. La simulación por tal método, se desarrolló, aplicando restricciones al movimiento de forma tal que la celda modelada simule su comportamiento durante la expansión de un estent. Considerando estos aspectos fue posible evaluar la integridad del recubrimiento. Con los modelos desarrollados se logró predecir la ocurrencia de delaminación durante la expansión del estent y se determinó que al aumentar el espesor del recubrimiento aumenta el riesgo de ocurrencia de la misma. Se obtuvo además una ecuación general que permite determinar el esfuerzo máximo de contacto para celdas en forma de U.The cardiovascular diseases constitute one of the main causes of death worldwide. One of the main diseases is atherosclerosis, which causes narrowing of the arterial lumen. In order to solve this condition, several treatments have been developed, and Percutaneous Transluminal Coronary Angioplasty (PTCA) with the placement of stent have gained relevancy. Many of these devices are currently coated to increase the biocompatibility and to decrease the restenosis risks. The biomechanical studies of the stent-coating interface behavior are necessary given the associated risks to possibility of failures or breakages of the coating during stent deployment. In this study the possible occurrence of coating delamination during stent deployment and the influence of parameters as the thickness and material were studied. The study starts by obtaining a geometric model of a stent unit of the Sirius Carbostent stent for the further processing by the Finite Element Method. The simulation was developed by applying restrictions so that the modeled stent hinge simulates his behavior during stent deployment. Considering these aspects it was possible to evaluation the coating integrity. With this model it was possible to predict the occurrence of delamination during stent deployment and to determine that the delamination risks increases with increasing the coating thickness. Finally, it was obtained a general function that allows to determine the maximal contact stress for a stent hinge with an U shape.Peer Reviewe