Abstract: 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.

Abstract: Systems, computer-implemented methods, and computer program products to facilitate estimation of quantum resources to calculate an expectation value of a stochastic process using a re-parameterization method are provided. According to an embodiment, a system can comprise a processor that executes computer executable components stored in memory. The computer executable components can comprise a re-parameterization component that applies a quantum fault-tolerant operation to a variationally prepared quantum state corresponding to a probability distribution to produce a quantum state corresponding to a target probability distribution. The computer executable components can further comprise an estimation component that estimates at least one defined criterion of a quantum computer to be used to compute an expectation value of a stochastic process associated with the target probability distribution.