We improve the quality of quantum circuits on superconducting quantum computing systems, as measured by the quantum volume (QV), with a combination of dynamical decoupling, compiler optimizations, shorter two-qubit gates, and excited state promoted readout. This result shows that the path to larger QV systems requires the simultaneous increase of coherence, control gate fidelities, measurement fidelities, and smarter software which takes into account hardware details, thereby demonstrating the need to continue to co-design the software and hardware stack for the foreseeable future.
We study a capacity expansion problem that arises in telecommunication network design. Given a capacitated network and a tra c demand matrix, the objective is to add capacity to the edges, in modularityes of various modularities, and route tra c, so that the overall cost is minimized. We study the polyhedral structure of a mixed-integer formulation of the problem and develop a cutting-plane algorithm using facet de ning inequalities. The algorithm produces an extended formulation providing both a very good lower bound and a starting point for branch and bound. The overall algorithm appears e ective when applied to problem instances using real-life data.
Abstract. We study mixed integer nonlinear programs (MINLP)s that are driven by a collection of indicator variables where each indicator variable controls a subset of the decision variables. An indicator variable, when it is "turned off", forces some of the decision variables to assume fixed values, and, when it is "turned on", forces them to belong to a convex set. Many practical MINLPs contain integer variables of this type. We first study a mixed integer set defined by a single separable quadratic constraint and a collection of variable upper and lower bound constraints, and a convex hull description of this set is derived. We then extend this result to produce an explicit characterization of the convex hull of the union of a point and a bounded convex set defined by analytic functions. Further, we show that for many classes of problems, the convex hull can be expressed via conic quadratic constraints, and thus relaxations can be solved via second-order cone programming. Our work is closely related with the earlier work of Ceria and Soares (1999) as well as recent work by Frangioni and Gentile (2006) and, Aktürk, Atamtürk and Gürel (2007). Finally, we apply our results to develop tight formulations of mixed integer nonlinear programs in which the nonlinear functions are separable and convex and in which indicator variables play an important role. In particular, we present computational results for three applications -quadratic facility location, network design with congestion, and portfolio optimization with buy-in thresholds -that show the power of the reformulation technique.
Mixed-integer rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixed-integer programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities.Given a mixed-integer region S and a collection of valid "base" mixed-integer inequalities, we develop a procedure for generating new valid inequalities for S. The starting point of our procedure is to consider the MIR inequalities related with the base inequalities. For any subset of these MIR inequalities, we generate two new inequalities by combining or "mixing" them. We show that the new inequalities are strong in the sense that they fully describe the convex hull of a special mixed-integer region associated with the base inequalities.We discuss how the mixing procedure can be used to obtain new classes of strong valid inequalities for various mixed-integer programming problems. In particular, we present examples for production planning, capacitated facility location, capacitated network design, and multiple knapsack problems. We also present preliminary computational results using the mixing procedure to tighten the formulation of some difficult integer programs. Finally we study some extensions of this mixing procedure.
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