In one example described herein a system can receive, by a scheduler of a server, a request to execute a quantum algorithm. The system can determine, by the scheduler, a quantum computer system of a plurality of quantum computer systems to execute the quantum algorithm based on a database that stores associations between each quantum computer system of the plurality of quantum computer systems, at least one parameter associated with the quantum algorithm, and error information. The system can transmit, by the scheduler, the request to the quantum computer system for executing the quantum algorithm.

In one example described herein a system can receive, by a scheduler of a server, a request to execute a quantum algorithm. The system can determine, by the scheduler, a quantum computer system of a plurality of quantum computer systems to execute the quantum algorithm based on a database that stores associations between each quantum computer system of the plurality of quantum computer systems, at least one parameter associated with the quantum algorithm, and error information. The system can transmit, by the scheduler, the request to the quantum computer system for executing the quantum algorithm.

One example method includes receiving a computation workflow defined by a graph that includes quantum computing nodes, receiving a catalogue of quantum computing instances that are available in a hybrid classic-quantum computation infrastructure, transforming the graph to create a first graph transformation, and each of the quantum computing nodes is assigned a respective candidate resource allocation that identifies candidate resources operable to execute a respective quantum algorithm associated with that quantum computing node, and the transforming is performed using information from the catalogue, and optimizing the computation workflow by selecting, for each of the quantum computing nodes, a resource from the candidate resource allocation associated with that quantum computing node, and the optimizing includes transforming the first graph transformation to create a second graph transformation that specifies the selected resources for each node.

One example method includes receiving a computation workflow defined by a graph that includes quantum computing nodes, receiving a catalogue of quantum computing instances that are available in a hybrid classic-quantum computation infrastructure, transforming the graph to create a first graph transformation, and each of the quantum computing nodes is assigned a respective candidate resource allocation that identifies candidate resources operable to execute a respective quantum algorithm associated with that quantum computing node, and the transforming is performed using information from the catalogue, and optimizing the computation workflow by selecting, for each of the quantum computing nodes, a resource from the candidate resource allocation associated with that quantum computing node, and the optimizing includes transforming the first graph transformation to create a second graph transformation that specifies the selected resources for each node.

Quantum branch-and-bound algorithms with heuristics are disclosed. A method may include: receiving a branch and bound problem; setting an upper bound, a best bound, an incumbent, and a counter i; executing a subtree estimation procedure that returns branch_m that represents a tree of size m; determining branch_i and cost_i for branch_m; setting cost_feas to a value COST(N) for feasible nodes N, and to +∞ for unfeasible nodes; instructing a quantum computer to execute a QuantumMinimumLeaf procedure to get a node N and setting incumbent′ to COST(N); instructing the quantum computer to execute the QuantumMinimumLeaf procedure to get a node N′ and to setting best bound′ to equal COST(N′); and returning the node N when an absolute value of a difference between a minimum of incumbent and incumbent′ and a minimum of best bound and best bound′ is less than the approximation margin.

Quantum branch-and-bound algorithms with heuristics are disclosed. A method may include: receiving a branch and bound problem; setting an upper bound, a best bound, an incumbent, and a counter i; executing a subtree estimation procedure that returns branch_m that represents a tree of size m; determining branch_i and cost_i for branch_m; setting cost_feas to a value COST(N) for feasible nodes N, and to +∞ for unfeasible nodes; instructing a quantum computer to execute a QuantumMinimumLeaf procedure to get a node N and setting incumbent′ to COST(N); instructing the quantum computer to execute the QuantumMinimumLeaf procedure to get a node N′ and to setting best bound′ to equal COST(N′); and returning the node N when an absolute value of a difference between a minimum of incumbent and incumbent′ and a minimum of best bound and best bound′ is less than the approximation margin.

A method includes providing a first quantum state at a first node, transforming the first quantum state to obtain a first plurality of transformed quantum states, and measuring the first plurality of transformed quantum states to obtain a first set of measurement results. The method further includes providing a second quantum state at a second node, transforming the second quantum state to obtain a second plurality of transformed quantum states, the second plurality of unitary operations corresponding to the first plurality of unitary operations, and measuring the second plurality of transformed quantum states to obtain a second set of measurement results. A similarity measure between the first quantum state and the second quantum state is determined in terms of the first set of measurement results and the second set of measurement results, the similarity measure including a trace product of the first quantum state and the second quantum state.

A method includes providing a first quantum state at a first node, transforming the first quantum state to obtain a first plurality of transformed quantum states, and measuring the first plurality of transformed quantum states to obtain a first set of measurement results. The method further includes providing a second quantum state at a second node, transforming the second quantum state to obtain a second plurality of transformed quantum states, the second plurality of unitary operations corresponding to the first plurality of unitary operations, and measuring the second plurality of transformed quantum states to obtain a second set of measurement results. A similarity measure between the first quantum state and the second quantum state is determined in terms of the first set of measurement results and the second set of measurement results, the similarity measure including a trace product of the first quantum state and the second quantum state.

Systems and methods for efficiently routing qubits in a quantum computing system include selecting bubble nodes and routing qubits to the bubble nodes. The systems and methods further include dividing a system of nodes into regions and selecting a bubble node for each region. The systems and methods further include using super bubble nodes with reliable links connected to other super bubble nodes and bubble nodes to improve cross-region operations.

Systems and methods for efficiently routing qubits in a quantum computing system include selecting bubble nodes and routing qubits to the bubble nodes. The systems and methods further include dividing a system of nodes into regions and selecting a bubble node for each region. The systems and methods further include using super bubble nodes with reliable links connected to other super bubble nodes and bubble nodes to improve cross-region operations.