Abstract: Methods and apparatus for quantum assisted optimization. In one aspect, a method includes obtaining a set of initial input states, applying one or more of (i) dynamical thermal fluctuations and (ii) cluster update algorithms to the set of input states and subsequent input states when the states evolve within the classical information processors, applying dynamical quantum fluctuations to the set of input states and subsequent states when the states evolve within the quantum systems and repeating the application steps until a desirable output state is obtained.

Abstract: Methods, systems, and apparatus, for totally corrective boosting with cardinality penalization are described. One of the methods includes obtaining initialization data identifying training examples, a dictionary of weak classifiers, and an active weak classifier matrix. Iterations of a totally corrective boosting with cardinality penalization process are performed, wherein each iteration performs operations comprising selecting a weak classifier from the dictionary of weak classifiers that most violates a constraint of a dual of the primal problem. The selected weak classifier is included in the active weak classifier matrix. The primal problem is optimized, and a discrete weight vector is determined. Weak classifiers are identified from the active weak classifier matrix with respective discrete weights greater than a threshold. The regularized risk is optimized, and a continuous weight vector is determined.

Abstract: In one aspect, a method includes identifying (i) a computational problem that is a candidate for a quantum computation, and (ii) one or more numerical algorithms for solving the candidate computational problem; providing input task data identifying (i) the candidate computational problem, and (ii) the one or more numerical algorithms, to a numerical quantum experimentation system, wherein the numerical quantum experimentation system comprises multiple universal numerics workers, a universal numerics worker, of the multiple universal numerics workers being configured to solve the candidate computational problem using the one or more numerical algorithms; receiving, from the numerical quantum experimentation system, data representing results of the one or more numerical algorithms to solve the candidate computational problem; and determining whether the received data indicates that a quantum computation applied to the candidate computational problem has a greater efficacy at a solution than a classical computat

Abstract: A system comprises a network of computers comprising a master computer and slave computers. For a machine learning problem that is partitioned into a number of correlated sub-problems, each master computer is configured to store tasks associated with the machine learning problem, and each of the slave computers is assigned one of the correlated sub-problems. Each slave computer is configured to store variables or parameters or both associated with the assigned one of the correlated sub-problems; obtain information about one or more tasks stored by the master computer without causing conflict with other slave computers with regard to the information; perform computations to update the obtained information and the variables or parameters or both of the assigned sub-problem; send the updated information to the master computer to update the information stored at the master computer; and store the updated variables or parameters or both of the assigned sub-problem.

Abstract: Methods, systems, and apparatus, for totally corrective boosting with cardinality penalization are described. One of the methods includes obtaining initialization data identifying training examples, a dictionary of weak classifiers, and an active weak classifier matrix. Iterations of a totally corrective boosting with cardinality penalization process are performed, wherein each iteration performs operations comprising selecting a weak classifier from the dictionary of weak classifiers that most violates a constraint of a dual of the primal problem. The selected weak classifier is included in the active weak classifier matrix. The primal problem is optimized, and a discrete weight vector is determined. Weak classifiers are identified from the active weak classifier matrix with respective discrete weights greater than a threshold. The regularized risk is optimized, and a continuous weight vector is determined.

Abstract: Methods and apparatus for quantum assisted optimization. In one aspect, a method includes obtaining a set of initial input states, applying one or more of (i) dynamical thermal fluctuations and (ii) cluster update algorithms to the set of input states and subsequent input states when the states evolve within the classical information processors, applying dynamical quantum fluctuations to the set of input states and subsequent states when the states evolve within the quantum systems and repeating the application steps until a desirable output state is obtained.

Abstract: Methods and apparatus for quantum assisted optimization. In one aspect, a method includes obtaining a set of initial input states, applying one or more of (i) dynamical thermal fluctuations and (ii) cluster update algorithms to the set of input states and subsequent input states when the states evolve within the classical information processors, applying dynamical quantum fluctuations to the set of input states and subsequent states when the states evolve within the quantum systems and repeating the application steps until a desirable output state is obtained.

Abstract: In one aspect, a method includes identifying (i) a computational problem that is a candidate for a quantum computation, and (ii) one or more numerical algorithms for solving the candidate computational problem; providing input task data identifying (i) the candidate computational problem, and (ii) the one or more numerical algorithms, to a numerical quantum experimentation system, wherein the numerical quantum experimentation system comprises multiple universal numerics workers, a universal numerics worker, of the multiple universal numerics workers being configured to solve the candidate computational problem using the one or more numerical algorithms; receiving, from the numerical quantum experimentation system, data representing results of the one or more numerical algorithms to solve the candidate computational problem; and determining whether the received data indicates that a quantum computation applied to the candidate computational problem has a greater efficacy at a solution than a classical computat

Abstract: Methods, systems, and apparatus for numerical quantum experimentation.

Abstract: A system comprises a network of computers comprising a master computer and slave computers. For a machine learning problem that is partitioned into a number of correlated sub-problems, each master computer is configured to store tasks associated with the machine learning problem, and each of the slave computers is assigned one of the correlated sub-problems. Each slave computer is configured to store variables or parameters or both associated with the assigned one of the correlated sub-problems; obtain information about one or more tasks stored by the master computer without causing conflict with other slave computers with regard to the information; perform computations to update the obtained information and the variables or parameters or both of the assigned sub-problem; send the updated information to the master computer to update the information stored at the master computer; and store the updated variables or parameters or both of the assigned sub-problem.

Abstract: Methods, systems, and apparatus for numerical quantum experimentation.

Abstract: Methods and apparatus for quantum assisted optimization. In one aspect, a method includes obtaining a set of initial input states, applying one or more of (i) dynamical thermal fluctuations and (ii) cluster update algorithms to the set of input states and subsequent input states when the states evolve within the classical information processors, applying dynamical quantum fluctuations to the set of input states and subsequent states when the states evolve within the quantum systems and repeating the application steps until a desirable output state is obtained.