Abstract: A method for quantum computing-assisted portfolio selection may include a classical computer program: (1) receiving a plurality of asset selection parameters for an asset portfolio; (2) initializing a current selection of assets from a plurality of available assets; (3) setting a risk upper bound value to a risk upper bound initial value, and a risk lower bound value to a risk lower bound initial value; (4) instructing a quantum computer to solve a first sub-problem; (5) calculating an objective functional value; (6) setting the risk upper bound value to the objective functional value; (7) instructing the quantum computer to determine a new selection of assets by solving a second sub-problem using a second quantum algorithm; and (8) returning an optimal portfolio selection.

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 and methods for quantum computing-based summarization are disclosed. A method for quantum computing-based summarization may include a classical computer program: receiving a document having a plurality of sentences; receiving a summary parameter that represents a subset of the plurality of sentences to include in a summary of the document; generating a vector for each sentence; calculating a centrality value for each vector; calculating a similarity value to other vectors for each vector; creating a cost function using the similarity values, the centrality values, a number of the plurality of sentences in the document, and the summary parameter; instructing a quantum computer to optimize the cost function using a quantum algorithm; receiving a dictionary comprising a plurality of distributions of the plurality of sentences and a probability for each distribution; and generating a summary comprising a subset of the plurality sentences based on a distribution having a highest probability.

Abstract: Embodiments use quantum conditional logic in the Quantum Phase Estimation Algorithm (QPEA) to compute eigenvalues prior to inversion. Embodiments estimate the eigenvalues of a unitary, U=eiÂt, generated by a N×N Hermitian matrix Â. The binary representations of the n-bit estimations of eigenvalues of  may be encoded in these states: |?i=|b1b2 . . . bn; ?i is an estimation of the i-th eigenvalue, excluding degeneracy, and .b1b2 . . . bn is its binary representation. To perform the eigenvalue inversion, an n-qubit controlled Ry rotation with angle ?i/2(n?1) conditioned on seeing |b1b2 . . . bn is applied for each possible n-bit binary string b1b2 . . . bn (2n values). The overall unitary is called a “uniformly controlled Ry rotation” in literature.

Abstract: A method may include: a computer program populating a Hermitian matrix A with input data; calculating an upper bound a for a maximum eigenvalue for the Hermitian matrix A; initializing a time evolution value t=1/a; generating a first quantum computer program using the time evolution value t; communicating the first quantum computer program to a quantum computer; receiving a result including a binary value for each n-bit string and a probability for each binary value; converting each binary value into an integer; identifying a maximum absolute value of the integers; determining a value x for the maximum absolute value of all of the integers; updating the time evolution value t based on the value of x; generating a second quantum computer program using the updated time evolution value t; and communicating, by the classical computer program, the second quantum computer program to the quantum computer.