Quantum computing has the potential to revolutionize the field of computing, but with hardware and algorithms unlike any in use today. Due to the primitive state of existing quantum hardware, simulation is one of the most effective methods for studying quantum computing issues. Our team previously developed a general-purpose simulator capable of modeling arbitrary quantum algorithms executing on any hardware device. The simulator performs over a thousand matrix multiplications per step as part of its operations. To improve the simulator performance, optimizations were designed to dynamically restructure the problem. The resulting calculations were then distributed across a cluster. These enhancements reduced both the order of the simulator operations and the memory overhead, achieving an overall performance improvement of 99.94% from the initial implementation of a key quantum algorithm, reducing the simulator run time for this algorithm from two days on a single processor to under two minutes on a cluster.

MOTIVATION: To be valuable to biological or biomedical research, in silico methods must be scaled to complex pathways and large numbers of interacting molecular species. The correct method for performing such simulations, discrete event simulation by Monte Carlo generation, is computationally costly for large complex systems. Approximation of molecular behavior by continuous models fails to capture stochastic behavior that is essential to many biological phenomena. RESULTS: We present a novel approach to building hybrid simulations in which some processes are simulated discretely, while other processes are handled in a continuous simulation by differential equations. This approach preserves the stochastic behavior of cellular pathways, yet enables scaling to large populations of molecules. We present an algorithm for synchronizing data in a hybrid simulation and discuss the trade-offs in such simulation. We have implemented the hybrid simulation algorithm and have validated it by simulating the statistical behavior of the well-known lambda phage switch. Hybrid simulation provides a new method for exploring the sources and nature of stochastic behavior in cells.

An iterative mincut heuristic for partitioning networks is presented whose worst case computation time, per pass, grows linearly with the size of the network. In practice, only a very small number of passes are typically needed, leading to a fast approximation algorithm for mincut partitioning. To deal with cells of various sizes, the algorithm progresses by moving one cell at a time between the blocks of the partition while maintaining a desired balance based on the size of the blocks rather than the number of cells per block. Efficient data structures are used to avoid unnecessary searching for the best cell to move and to minimize unnecessary updating of cells affected by each move.

The problem of designing a properly functioning parallel hardware or software system is considerably more difficult than that of designing a similar sequential system. In this paper we formulate criteria which a design methodology for parallel systems should satisfy and explore the use of various models as the basis for such a design tool.