From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation, and which have the potential to significantly expand the breadth of quantum computing applications. A leading candidate is Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates between applying a cost-function-based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the Quantum Alternating Operator Ansatz, is the consideration of general parametrized families of unitaries rather than only those corresponding to the time-evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach to a wide variety of approximate optimization, exact optimization, and sampling problems. Here, we introduce the Quantum Alternating Operator Ansatz, lay out design criteria for mixing operators, detail mappings for eight problems, and provide brief descriptions of mappings for diverse problems.Comment: 51 pages, 2 figures. Revised to match journal pape

Birds of a feather flock together and get money from the crowd

In constructing online alternative finance instruments as a new form of financial democratization and financial inclusion, this article aims at verifying the presence of similarity effect in equity crowdfunding investments. Discussion focuses on ethnic and gender similarity between the seekers and investors that sustained the project. Our analysis is based on 5,996 personal investors that have participated in 81 equity crowdfunding campaigns, on Crowdcube, a British equity crowdfunding platform from 2011 and 2016. Results show that in equity crowdfunding gender and ethnic similarities play different role based on investors’ characteristics - gender, ethnicity and the combination of two. In particular, ethnic similarity positively influence the level of amount invested by both female and male investors belonging to an ethnic minority. Even if female investors tend to prefer male company, their preference changes if a female proponent belonging to an ethnic minority runs the company. From a practical perspective, our findings shed new light on how individual characteristics can be important factor in financing situations. Results allow entrepreneurs and equity crowdfunding platforms to understand better potential investor behaviour and highlights the role of equity crowdfunding as tool for minorities’ financial inclusion and women entrepreneur empowerment

Reversible myocardial injury aggravated by complex arrhythmias in three Toxoplasma gondii-positive dogs

Although Toxoplasma gondii represents an oft-cited cause of myocarditis in veterinary medicine, the existing literature on the pre-mortem demonstration of T. gondii-associated myocardial injury (MI) in dogs is scant. In this case series, we provide detailed clinical, laboratory, echocardiographic and electrocardiographic description of three T. gondii-positive dogs diagnosed with MI. In all cases, etiological diagnosis was based on the antibody screening test (all dogs had IgM titres ≥1:64) and MI was demonstrated by a concomitant increase of the serum concentration of cardiac troponin I (0.25-9.6 ng/ml, upper hospital limit <0.15 ng/ml). In all dogs, MI was aggravated by complex arrhythmias (ventricular in two dogs, and either ventricular and supraventricular in the remaining dog). In one case, left ventricular systolic dysfunction was also present. All dogs underwent an extensive diagnostic work-up aimed at excluding additional comorbidities, either cardiac and extra-cardiac, possibly able to contribute to MI, arrhythmias and systolic dysfunction. All dogs received appropriate antiprotozoal (i.e., clindamycin) and antiarrhythmic (i.e., amiodarone, sotalol) therapy. This was systematically followed by a simultaneous decline in T. gondii serology titres, normalisation of troponin level and left ventricular systolic function, and the resolution of clinical and electrocardiographic abnormalities. In light of this result, therapies were interrupted and subsequent controls ruled out any disease relapse. In these cases, the clinical and instrumental findings obtained at admission and rechecks strongly supported the clinical suspicion of toxoplasmic myocarditis

Edge channel mixing induced by potential steps in an integer quantum Hall system

We investigate the coherent mixing of co-propagating edge channels in a quantum Hall bar produced by step potentials. In the case of two edge channels it is found that, although a single step induces only a few percent mixing, a series of steps could yield 50% mixing. In addition, a strong mixing is found when the potential height of a single step allows a different number of edge channels on the two sides of the step. Charge density probability has been also calculated even for the case where the step is smoothened.Comment: final version: 7 pages, 6 figure