Mixed-Integer Programming for a Class of Robust Submodular Maximization Problems

We consider robust submodular maximization problems (RSMs), where given a set of $m$ monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes two variants of robust submodular maximization problems in the literature, depending on the choice of the scaling vector. On one hand, by using unit scaling, we obtain a usual robust submodular maximization problem. On the other hand, by letting the scaling vector be the optimal objective function of each individual (NP-hard) submodular maximization problem, we obtain a second variant. While the robust version of the objective is no longer submodular, we reformulate the problem by exploiting the submodularity of each function. We conduct a polyhedral study of the resulting formulation and provide conditions under which the submodular inequalities are facet-defining for a key mixed-integer set. We investigate several strategies for incorporating these inequalities within a delayed cut generation framework to solve the problem exactly. For the second variant, we provide an algorithm to obtain a feasible solution along with its optimality gap. We apply the proposed methods to a sensor placement optimization problem in water distribution networks using real-world datasets to demonstrate the effectiveness of the methods

Modelling and Analysis of Traffic Light Control Systems Using Timed Coloured Petri nets

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Separation Enhancement of Mechanical Filters by Adding Negative Air Ions

The purpose of this work is to combine negative air ions (NAIs) and mechanical filters for removal of indoor suspended particulates. Various factors, including aerosol size (0.05-0.45 μm), face velocity (10 and 20 cm/s), species of aerosol (potassium chloride and dioctyl phthalate), relative humidity (30% and 70%), and concentrations of NAIs (2 ´ 104, 1 ´ 105, and 2 ´ 105 NAIs/cm3) were considered to evaluate their effects on the aerosol collection characteristics of filters. Results show that the aerosol penetration through the mechanical filter is higher than that through the mechanical filters cooperated with NAIs. This finding implies that the aerosol removal efficiency of mechanical filters can be improved by NAIs. Furthermore, the aerosol penetration through the mechanical filters increased with the aerosol size when NAIs were added. That is due to that the aerosol is easier to be charged when its size gets larger. The results also indicate the aerosol penetration decreased with the NAIs concentration increased. Reversely, aerosol penetration through the mechanical filters increased with the face velocity under the influence of NAIs. The aerosol penetration through the filter with NAIs was no affected with relative humidity. Finally, The penetration through the filter with NAIs against solid aerosol was lower than that against liquid aerosol

Qubit Mapping Toward Quantum Advantage

Qubit Mapping is a pivotal stage in quantum compilation flow. Its goal is to convert logical circuits into physical circuits so that a quantum algorithm can be executed on real-world non-fully connected quantum devices. Qubit Mapping techniques nowadays still lack the key to quantum advantage, scalability. Several studies have proved that at least thousands of logical qubits are required to achieve quantum computational advantage. However, to our best knowledge, there is no previous research with the ability to solve the qubit mapping problem with the necessary number of qubits for quantum advantage in a reasonable time. In this work, we provide the first qubit mapping framework with the scalability to achieve quantum advantage while accomplishing a fairly good performance. The framework also boasts its flexibility for quantum circuits of different characteristics. Experimental results show that the proposed mapping method outperforms the state-of-the-art methods on quantum circuit benchmarks by improving over 5% of the cost complexity in one-tenth of the program running time. Moreover, we demonstrate the scalability of our method by accomplishing mapping of an 11,969-qubit Quantum Fourier Transform within five hours

Identification and Mitigation of Conducting Package Losses for Quantum Superconducting Devices

Low-loss superconducting microwave devices are required for quantum computation. Here, we present a series of measurements and simulations showing that conducting losses in the packaging of our superconducting resonator devices affect the maximum achievable internal quality factors (Qi) for a series of thin-film Al quarter-wave resonators with fundamental resonant frequencies varying between 4.9 and 5.8 GHz. By utilizing resonators with different widths and gaps, we sampled different electromagnetic energy volumes for the resonators affecting Qi. When the backside of the sapphire substrate of the resonator device is adhered to a Cu package with a conducting silver glue, a monotonic decrease in the maximum achievable Qi is found as the electromagnetic sampling volume is increased. This is a result of induced currents in large surface resistance regions and dissipation underneath the substrate. By placing a hole underneath the substrate and using superconducting material for the package, we decrease the ohmic losses and increase the maximum Qi for the larger size resonators