Abstract: Fault tree analysis is performed using a combination of digital computer systems and quantum processing devices. For example, quantum annealers may be configured to analyze a fault tree for minimal cut sets. The quantum annealer may be particular good at identifying smaller minimal cut sets. Digital computer systems may be used to identify the remaining minimal cut sets. If the quantum annealer identifies one of the minimal cut sets of smallest size (i.e., lowest cardinality), this can be used as a constraint for the digital computer system, thus speeding up its search for other minimal cut sets.

Abstract: Fault tree analysis is performed using a combination of digital computer systems and quantum processing devices. For example, quantum annealers may be configured to analyze a fault tree for minimal cut sets. The quantum annealer may be particular good at identifying smaller minimal cut sets. Digital computer systems may be used to identify the remaining minimal cut sets. If the quantum annealer identifies one of the minimal cut sets of smallest size (i.e., lowest cardinality), this can be used as a constraint for the digital computer system, thus speeding up its search for other minimal cut sets.

Abstract: An improved method uses quantum processing devices to optimize a portfolio of financial assets. In one approach, a list of lots available for purchase is received. Each lot specifies financial assets included in the lot and a price to purchase the lot. A budget for the portfolio is also received. An objective function is formulated based on the list of lots and on the budget. The objective function has a form suitable for solution by a quantum processing device, which is used to optimize the objective function, thereby determining which lots are to be purchased.

Abstract: An improved method uses quantum processing devices to determine optimal sets of bids in combinatorial auctions. In one approach, a list of bids is received. Each bid specifies a price for a package of one or more items offered in the auction. The bids may be conflicting. An objective function based on the list of bids is formulated. The objective function has a form suitable for solution by a quantum processing device, which is used to optimize the objective function, thereby determining which bids are accepted.