Abstract: In this disclosure, quantum algorithms are presented for simulating Hamiltonian time-evolution e?i(A+B)t in the interaction picture of quantum mechanics on a quantum computer. The interaction picture is a known analytical tool for separating dynamical effects due to trivial free-evolution A from those due to interactions B. This is especially useful when the energy-scale of the trivial component is dominant, but of little interest. Whereas state-of-art simulation algorithms scale with the energy ?A+B???A?+?B? of the full Hamiltonian, embodiments of the disclosed approach generally scale linearly with the sum of the Hamiltonian coefficients from the low-energy component B and poly-logarithmically with those from A.

Abstract: A method of training a quantum computer employs quantum algorithms. The method comprises loading, into the quantum computer, a description of a quantum Boltzmann machine, and training the quantum Boltzmann machine according to a protocol, wherein a classification error is used as a metric for the protocol.

Abstract: In this disclosure, quantum algorithms are presented for simulating Hamiltonian time-evolution e?i(A+B)t in the interaction picture of quantum mechanics on a quantum computer. The interaction picture is a known analytical tool for separating dynamical effects due to trivial free-evolution A from those due to interactions B. This is especially useful when the energy-scale of the trivial component is dominant, but of little interest. Whereas state-of-art simulation algorithms scale with the energy ?A+B???A?+?B? of the full Hamiltonian, embodiments of the disclosed approach generally scale linearly with the sum of the Hamiltonian coefficients from the low-energy component B and poly-logarithmically with those from A.

Abstract: Methods for preparing a Gibbs state in a qubit register of a quantum computer include applying one or more quantum gates to one or more qubits of the qubit register to prepare a trial quantum state spanning the one or more qubits, the trial quantum state being defined as a function of parameters {right arrow over (?)} and being selected to provide an initial estimate of the Gibbs state. The methods further include evaluating the Gibbs free energy of the trial quantum state, adjusting the parameters {right arrow over (?)}, re-applying the one or more quantum gates to the one or more qubits to refine the trial quantum state according to the parameters {right arrow over (?)} as adjusted, and re-evaluating the Gibbs free energy of the trial quantum state.

Abstract: Quantum neural nets, which utilize quantum effects to model complex data sets, represent a major focus of quantum machine learning and quantum computing in general. In this application, example methods of training a quantum Boltzmann machine are described. Also, examples for using quantum Boltzmann machines to enable a form of quantum state tomography that provides both a description and a generative model for the input quantum state are described. Classical Boltzmann machines are incapable of this. Finally, small non-stoquastic quantum Boltzmann machines are compared to traditional Boltzmann machines for generative tasks, and evidence presented that quantum models outperform their classical counterparts for classical data sets.

Abstract: Existing methods for dynamical simulation of physical systems use either a deterministic or random selection of terms in the Hamiltonian. In this application, example approaches are disclosed where the Hamiltonian terms are randomized and the precision of the randomly drawn approximation is adapted as the required precision in phase estimation increases. This reduces both the number of quantum gates needed and in some cases reduces the number of quantum bits used in the simulation.

Abstract: The disclosed technology concerns example embodiments for estimating eigenvalues of quantum operations using a quantum computer. Such estimations are useful in performing Shor's algorithm for factoring, quantum simulation, quantum machine learning, and other various quantum computing applications. Existing approaches to phase estimation are sub-optimal, difficult to program, require prohibitive classical computing, and/or require too much classical or quantum memory to be run on existing devices. Embodiments of the disclosed approach address one or more (e.g., all) of these drawbacks. Certain examples work by using a random walk for the estimate of the eigenvalue that (e.g., only) keeps track of the current estimate and the measurement record that it observed to reach that point.

Abstract: In this disclosure, a number of ways that quantum information can be used to help make quantum classifiers more secure or private are disclosed. In particular embodiments, a form of robust principal component analysis is disclosed that can tolerate noise intentionally introduced to a quantum training set. Under some circumstances, this algorithm can provide an exponential speedup relative to other methods. Also disclosed is an example quantum approach for bagging and boosting that can use quantum superposition over the classifiers or splits of the training set to aggregate over many more models than would be possible classically. Further, example forms of k-means clustering are disclosed that can be used to prevent even a powerful adversary from even learning whether a participant even contributed data to the clustering algorithm.

Abstract: Embodiments of a new approach for training a class of quantum neural networks called quantum Boltzmann machines are disclosed. in particular examples, methods for supervised training of a quantum Boltzmann machine are disclosed using an ensemble of quantum states that the Boltzmann machine is trained to replicate. Unlike existing approaches to Boltzmann training, example embodiments as disclosed herein allow for supervised training even in cases where only quantum examples are known (and not probabilities from quantum measurements of a set of states). Further, this approach does not require the use of approximations such as the Golden-Thompson inequality.

Abstract: Methods for preparing a Gibbs state in a qubit register of a quantum computer include applying one or more quantum gates to one or more qubits of the qubit register to prepare a trial quantum state spanning the one or more qubits, the trial quantum state being defined as a function of parameters {right arrow over (?)} and being selected to provide an initial estimate of the Gibbs state. The methods further include evaluating the Gibbs free energy of the trial quantum state, adjusting the parameters {right arrow over (?)}, re-applying the one or more quantum gates to the one or more qubits to refine the trial quantum state according to the parameters {right arrow over (?)} as adjusted, and re-evaluating the Gibbs free energy of the trial quantum state.

Abstract: Existing methods for dynamical simulation of physical systems use either a deterministic or random selection of terms in the Hamiltonian. In this application, example approaches are disclosed where the Hamiltonian terms are randomized and the precision of the randomly drawn approximation is adapted as the required precision in phase estimation increases. This reduces both the number of quantum gates needed and in some cases reduces the number of quantum bits used in the simulation.

Abstract: Methods to train a quantum Boltzmann machine (QBM) having one or more visible nodes and one or more hidden nodes. The methods comprise associating each visible and each hidden node of the QBM to a different corresponding qubit of a plurality of qubits of a quantum computer, wherein a state of each of the plurality of qubits contributes to a global energy of the QBM according to a set of weighting factors, and wherein the plurality of qubits include one or more output qubits corresponding to one or more visible nodes of the QBM. The methods further comprise providing a distribution of training data over the one or more output qubits, estimating a gradient of a quantum relative entropy between the output qubits and the distribution of training data, and training the set of weighting factors based on the estimated gradient using the quantum relative entropy as a cost function.

Abstract: A method for tuning a quantum gate of a quantum computer comprises interrogating one or more qubits of the quantum computer using stored control-parameter values and yielding new data. The method further comprises computing an objective function quantifying operational quality of the quantum gate at the stored control-parameter values, such computing employing the new data in addition to a prior distribution over features used to compute the objective function. Here, the prior distribution may be obtained by previous adaptive or non-adaptive interrogation of the one or more qubits, for instance. The method further comprises updating the stored control-parameter values, expanding the prior distribution to incorporate uncertainty in the objective function at the updated control-parameter values, re-interrogating the one or more qubits using the updated control-parameter values, and re-computing the objective function using the expanded prior distribution.

Abstract: In this disclosure, quantum algorithms are presented for simulating Hamiltonian time-evolution e?i(A+B)t in the interaction picture of quantum mechanics on a quantum computer. The interaction picture is a known analytical tool for separating dynamical effects due to trivial free-evolution A from those due to interactions B. This is especially useful when the energy-scale of the trivial component is dominant, but of little interest. Whereas state-of-art simulation algorithms scale with the energy ?A+B???A?+?B? of the full Hamiltonian, embodiments of the disclosed approach generally scale linearly with the sum of the Hamiltonian coefficients from the low-energy component B and poly-logarithmically with those from A.

Abstract: This application relates generally to quantum computing. In particular, this application discloses example tools and techniques for performing phase arithmetic in quantum computer environments. Embodiments of the disclosed technology allow one to multiply N phases within error ? using (N2 log(N/?) log log(1/?)) queries to the circuits that output the N constituent phases using (N(log(N)+log log(1/?))) ancillary qubits. Also disclosed are example applications of these techniques to synthesizing specific functions of phase and new error bounds for robust amplitude amplification that is quadratically better than the standard bound.

Abstract: The disclosed technology concerns example embodiments for estimating eigenvalues of quantum operations using a quantum computer. Such estimations are useful in performing Shor's algorithm for factoring, quantum simulation, quantum machine learning, and other various quantum computing applications. Existing approaches to phase estimation are sub-optimal, difficult to program, require prohibitive classical computing, and/or require too much classical or quantum memory to be run on existing devices. Embodiments of the disclosed approach address one or more (e.g., all) of these drawbacks. Certain examples work by using a random walk for the estimate of the eigenvalue that (e.g., only) keeps track of the current estimate and the measurement record that it observed to reach that point.

Abstract: In this disclosure, a number of ways that quantum information can be used to help make quantum classifiers more secure or private are disclosed. In particular embodiments, a form of robust principal component analysis is disclosed that can tolerate noise intentionally introduced to a quantum training set. Under some circumstances, this algorithm can provide an exponential speedup relative to other methods. Also disclosed is an example quantum approach for bagging and boosting that can use quantum superposition over the classifiers or splits of the training set to aggregate over many more models than would be possible classically. Further, example forms of k-means clustering are disclosed that can be used to prevent even a powerful adversary from even learning whether a participant even contributed data to the clustering algorithm.

Abstract: Quantum neural nets, which utilize quantum effects to model complex data sets, represent a major focus of quantum machine learning and quantum computing in general. In this application, example methods of training a quantum Boltzmann machine are described. Also, examples for using quantum Boltzmann machines to enable a form of quantum state tomography that provides both a description and a generative model for the input quantum state are described. Classical Boltzmann machines are incapable of this. Finally, small non-stoquastic quantum Boltzmann machines are compared to traditional Boltzmann machines for generative tasks, and evidence presented that quantum models outperform their classical counterparts for classical data sets.