Abstract: A method for building a quantum computing circuit optimizes qubit routing in the circuit. A computer processor receives a plurality of qubits and an initial input circuit layer. Layers of quantum sub-circuits are extracted from the initial input circuit layer. Adjacency matrices are built for the layers of quantum sub-circuits. A cost function is determined for the extracted layers, based on the number of constraints violations determined by the doubly stochastic matrices. In addition, a final quantum circuit topology is selected based on the cost function of the extracted layers.

Abstract: A sub-graph isomorphism determination method comprising the steps of: determining, by the classical computer, a first adjacency matrix of a first graph and a second adjacency matrix of a second graph; wherein the first graph comprises a greater number of vertices than the second graph; determining, by the classical computer, an objective optimization problem subject to one or more constraints; wherein an objective of the objective optimization problem is to determine a partial permutation matrix; determining, by the classical computer, a QUBO matrix suitable for implementing the objective optimization problem; solving, by a quantum computer, a QUBO formulation including the QUBO matrix, thereby providing the partial permutation matrix; applying, by the classical computer, the partial permutation matrix to the first adjacency matrix, thereby producing a partially permuted first adjacency matrix; wherein the partially permuted first adjacency matrix corresponds to a sub-graph of the first graph that is isomorph

Abstract: A routing optimization computer implemented method is provided, comprising: determining a non-convex sub-problem and a convex sub-problem of a constrained optimization problem; generating a smart contract corresponding to the non-convex sub-problem; transmitting the smart contract to a distributed ledger; broadcasting the smart contract to a plurality of solvers; receiving a first binary solution to the non-convex sub-problem from a first solver; receiving a further binary solution to the non-convex sub-problem from a second solver; determining a more suitable solution of the first binary solution and the further binary solution; transmitting a payment associated with the smart contract; transmitting the more suitable binary solution; determining a time solution to the convex sub-problem using the more suitable binary solution; repeating steps using the time solution as the continuous variable, until a threshold is met; and mapping the binary solution and the time solution to the constrained optimization prob

Abstract: A computer implemented method for optimising, an objective optimisation problem. The methods begins by receiving the objective optimisation problem. The objective optimisation problem is represented by an L×L objective matrix comprising a plurality of matrix components A set of frozen variables is received. The method determines a set of freezable matrix components corresponding to the set of frozen variables. Then, a contribution vector is determined based on the set of freezable matrix components and the set of frozen variables An equivalent optimisation problem is determined based on the contribution vector and the objective optimisation problem. The equivalent optimisation problem excludes the freezable matrix components such that the equivalent optimisation problem may be solved on a quantum computer using fewer quantum bits than the objective optimisation problem would require.

Abstract: The computer implemented image matching method involves the use of a quantum computer communicating with a classical computer. The method includes the following steps: (a) The classical computer receives input data. (b) The classical computer generates an input graph representing the input data, (c) The classical computer augments the input graph, (d) An iteration block is performed. (e) The iteration block is repeated using the new permutation parameter, the permuted first adjacency matrix, and a new existing graph until a threshold is met. In the first iteration of the iteration block, the accumulated permutation is the identity, making the permuted first adjacency matrix equal to the first adjacency matrix. The first graph is isomorphic with the second graph when the loss is minimized, indicating a match between the first data and the existing data.

Abstract: A system and computer-implemented method for allocating a plurality of transactions to a plurality of networks comprising: receiving from a router at a classical computer a plurality of first information associated with a respective one of the plurality of transactions; receiving from a router at the classical computer a plurality of second information associated with a respective one of the plurality of networks; determining in the classical computer a switching characteristic to be optimised by the allocation of the plurality of transactions to the plurality of networks; expressing by the classical computer in at least one expression to a quantum computer, the plurality of first information, the plurality of second information and the switching characteristic; resolving in the quantum computer the at least one expression to determine the allocation of the plurality of transactions to the plurality of networks; and providing the allocation to the router.

Abstract: A system and computer-implemented method for optimising, by a quantum computer, an allocation of opportunities to recipients comprising: determining a plurality of opportunities to be allocated; determining a plurality of recipients to be allocated at least one of the plurality of opportunities; determining a respective acceptance likelihood of each of the plurality of recipients accepting each of the plurality of opportunities; determining a first constraint associated with a cost acceptance of each of the plurality of opportunities by the plurality of recipients; and determining an optimised allocation of the opportunities to the recipients based on the respective likelihoods and the first constraint, in the quantum computer.

Abstract: An internal flow determination method comprising the steps of: receiving, at a classical computer, an input flow vector comprising a plurality of input entries. Then, receiving an output flow vector comprising a plurality of output entries. Said output entries are indicative of a monetary amount exiting the processing node. Determining an objective optimization problem subject to one or more constraints, wherein an objective of the objective optimization problem is to determine: an input flow matrix and an output flow matrix. Then, determining a quadratic unconstrained binary optimization (QUBO) formulation suitable for implementing the objective optimization problem. Solving, by a quantum computer, the QUBO formulation, thereby providing a solution representative of the input flow matrix and the output flow matrix. Finally, generating, by the classical computer, a probability matrix indicative of a probability that an internal flow of the processing node connects an input entry to an output entry.