Solovay–Kitaev Approximations of Special Orthogonal Matrices

The circuit-gate framework of quantum computing relies on the fact that an arbitrary quantum gate in the form of a unitary matrix of unit determinant can be approximated to a desired accuracy by a fairly short sequence of basic gates, of which the exact bounds are provided by the Solovay–Kitaev theorem. In this work, we show that a version of this theorem is applicable to orthogonal matrices with unit determinant as well, indicating the possibility of using orthogonal matrices for efficient computation. We further develop a version of the Solovay–Kitaev algorithm and discuss the computational experience.

Robust Optimization Model for Runway Configurations Management

The Runway Configuration Management problem governs what combinations of airport runways are in use at a given time for an airport or a collection of airports. Runway configurations (groupings of runways), operate under Runway Configuration Capacity Envelopes (RCCEs) which limit arrival and departure capacities. The RCCE identifies unique capacity constraints based on which runways are used for arrivals, departures, and their direction of travel. When switching between RCCEs, due to a change in weather conditions or a change in the demand pattern, a decrement in arrival and departure capacities is incurred during the transition. This paper reports computational experience with two distinct models—a robust optimization model that addresses uncertainty in the arrival demand, and a previously studied model that does not include uncertainty in any of the parameters. Test case scenarios are based on data from the John F. Kennedy international airport in New York.