Microsoft Technology Licensing, LLC

Nathan O Wiebe

Guang Hao Low

Krysta Marie Svore

Christopher Granade

Ashish Kapoor

Alexei V Bocharov

Martin Henri Roetteler

Vadym Kliuchnikov

Matthias Troyer

John King Gamble, Iv

Ram Shankar Siva Kumar

Maria Kieferova

Paul Smolensky

Ian Kivlichan

Ilia Zintchenko

Anirban Ch Narayan Chowdhury

Yuan Su

Natalie M Klco

Christopher Evan Granade

John King Iv Gamble

In this disclosure, quantum algorithms are presented for simulating Hamiltonian time-evolution ein 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 &#x2225;A+B&#x2225;&#x2264;&#x2225;A&#x2225;+&#x2225;B&#x2225; 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.

Hamiltonian simulation in the interaction picture

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.

Quantum algorithms for supervised training of quantum boltzmann machines

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 (&#x3b8;)} 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 (&#x3b8;)}, 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 (&#x3b8;)} as adjusted, and re-evaluating the Gibbs free energy of the trial quantum state.

Variational quantum Gibbs state preparation

A quantum computer and methods of operating the quantum computer, such that the quantum computer is enabled to fully simulate molecular chemistry, are described. The circuit depth of the quantum computer is reduced by at least an order of magnitude, as compared to conventional quantum computing methods. Parallelized qubit or fermionic swap networks are employed to render the non-local terms of the second quantized Hamiltonian, as local on consecutive qubits of the computer. Thus, non-local quantum dynamics are rendered local. By localizing the non-local interactions, the quantum computations may be significantly parallelized and a single template circuit, simulating the time-evolution operator for 4-qubit interactions, may be applied to the localized groupings of four qubits. In addition to chemistry, the quantum computer and the methods of operating the quantum computer may be employed to localize any many-body interaction, while reducing the required circuit depth, via parallelizations of the localized computations.

Swap networks for quantum computation

Boltzmann machines are trained using an objective function that is evaluated by sampling quantum states that approximate a Gibbs state. Classical processing is used to produce the objective function, and the approximate Gibbs state is based on weights and biases that are refined using the sample results. In some examples, amplitude estimation is used. A combined classical/quantum computer produces suitable weights and biases for classification of shapes and other applications.

Quantum deep learning

Examples are disclosed relating to obtaining a solution to a multiproduct formula of order m to solve a quantum computing problem comprising a product formula. One example provides a method comprising selecting a set of exponents k, wherein each kis a real number and is an exponent in a linear combination of product formulas. Based on the set of exponents k, a set of pre-factors ais determined based on an underdetermined solution to an m&#xd7;M system of linear equations, where M is a number of lower-order product formulas in the linear combination of product formulas. The set of exponents kand the set of pre-factors aare used to solve the quantum computing problem comprising the product formula. By minimizing the set of exponents kand the set of pre-factors a, sparse solutions to the multiproduct formula are generated, reducing computational time and scaling.

Methods for obtaining solutions to multiproduct formulas

Methods and apparatus are provided that permit estimation of eigenphase or eigenvalue gaps in which random or pseudo-random unitaries are applied to a selected initial quantum state to produce a random quantum state. A target unitary is then applied to the random quantum state one or more times, or an evolution time is allowed to elapse after application of the target unitary. An inverse of the pseudo-random unitary used to produce the random quantum state is applied, and the resultant state is measured with respect to the initial quantum state. Measured values are used to produce Bayesian updates, and eigenvalue/eigenvector gaps are estimated. In some examples, the disclosed methods are used in amplitude estimate and control map determinations. Eigenvalue gaps for time-dependent Hamiltonians can be evaluated by adiabatic evolution of the Hamiltonian from an initial Hamiltonian to a final Hamiltonian.

Randomized gap and amplitude estimation

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.

Tomography and generative data modeling via quantum boltzmann training

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.

Phase estimation with randomized hamiltonians

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.

Using random walks for iterative phase estimation

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.

Adversarial quantum machine learning

Nearest neighbor distances are obtained by coherent majority voting based on a plurality of available distance estimates produced using amplitude estimation without measurement in a quantum computer. In some examples, distances are Euclidean distances or are based on inner products of a target vector with vectors from a training set of vectors. Distances such as mean square distances and distances from a data centroid can also be obtained.

Method and system for computing distance measures on a quantum computer

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.

Bayesian tuning for quantum logic gates

Quantum circuits and associated methods use Repeat-Until-Success (RUS) circuits to perform approximate multiplication and approximate squaring of input values supplied as rotations encoded on ancilla qubits. So-called gearbox and programmable ancilla circuits are coupled to encode even or odd products of input values as a rotation of a target qubit. In other examples, quantum RUS circuits provide target qubit rotations that are associated with reciprocals using series expansion representations.

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Seattle, WA, United States of America

Nathan O Wiebe