An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper we propose a hybrid quantum-classical algorithm to solve optimization problems with an adiabatic machine assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular we present a technique to learn the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm. Moreover the output of the proposed algorithm can be used to learn efficient adiabatic algorithms from examples.
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper we propose a hybrid quantum-classical algorithm to solve optimization problems with an adiabatic machine assuming restrictions on the class of available problem Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular we present a technique to learn the encoding of a given optimization problem into a problem Hamiltonian and we prove the convergence of the algorithm. Moreover the output of the proposed algorithm can be used to learn efficient adiabatic algorithms from examples.
Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand us to accelerate the evolution so that the adiabatic errors can be prevented from accumulation. Here, by treating this trade-off task as a multiobjective optimization problem, we propose a gradient-free learning algorithm with pulse smoothing technique to search optimal adiabatic quantum pathways and apply it to the Landau-Zener Hamiltonian and Grover search Hamiltonian. Numerical comparisons with a linear schedule, local adiabatic theorem induced schedule, and gradient-based algorithm searched schedule reveal that the proposed method can achieve significant performance improvements in terms of the adiabatic time and the instantaneous ground-state population maintenance. The proposed method can be used to solve more complex and real adiabatic quantum computation problems.
Quantum adiabatic optimization is a quantum algorithm for solving classical optimization problems (E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser. Quantum computation by adiabatic evolution, 2000. arXiv:quant-ph/0001106). The solution to an optimization prob-lem is encoded in the ground state of a "problem Hamiltonian " Hp which acts on the Hilbert space of n spin 1/2 particles and is diagonal in the Pauli z basis. To produce this ground state, one first initializes the quantum system in the ground state of a different Hamiltonian and then adiabatically changes the Hamiltonian into Hp. Farhi et al suggest the interpolating Hamiltonian i where the parameter s is slowly changed as a function of time between 0 and 1. The running time of this algorithm is related to the minimum spectral gap of H(s) for s E (0, 11. We study such transverse field spin Hamiltonians using both analytic and numerical techniques. Our approach is example-based, that is, we study some specific choices for the problem Hamiltonian Hp which illustrate the breadth of phenomena which can occur. We
Adiabatic quantum computing (AQC) is a computation protocol to solve difficult problems exploiting quantum advantage, directly applicable to optimization problems. In performing the AQC, different configurations of the Hamiltonian path could lead to dramatic differences in the computation efficiency. It is thus crucial to configure the Hamiltonian path to optimize the computation performance of AQC. Here we apply a reinforcement learning approach to configure AQC for integer programming, where we find the learning process automatically converges to a quantum algorithm that exhibits scaling advantage over the trivial AQC using a linear Hamiltonian path. This reinforcement-learning-based approach for quantum adiabatic algorithm design for integer programming can well be adapted to the quantum resources in different quantum computation devices, due to its built-in flexibility.
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite (and currently small) number of qubits, however, poses the risk of finding only the optimum within the restricted space supported by this Hamiltonian. We describe an iterative algorithm in which a solution obtained with such a restricted problem Hamiltonian is used to define a new problem Hamiltonian that is better suited than the previous one. In numerical examples of the shortest vector problem, we show that the algorithm with a sequence of improved problem Hamiltonians converges to the desired solution.
Machine learning is a branch of Artificial Intelligence that seeks to make machines learn from data. It is being applied for solving real world problems with huge amount of data. Though, Machine Learning is receiving wide acceptance, however, execution time is one of the major concerns in practical implementations of Machine Learning techniques. It largely comprises of a set of techniques that trains a model by reducing the error between the desired or actual outcome and an estimated or predicted outcome, which is often called as loss function. Thus, training in machine learning techniques often requires solving a difficult optimization problem, which is the most expensive step in the entire model-building process and its applications. One of the possible solutions in near future for reducing execution time of training process in Machine learning techniques is to implement them on quantum computers instead of classical computers. It is conjectured that quantum computers may be exponentially faster than classical computers for solving problems which involve matrix operations. Some of the machine learning techniques like support vector machines make extensive use of matrices, which can be made faster by implementing them on quantum computers. However, their efficient implementation is non-trivial and requires existence of quantum memories. Thus, another possible solution in near term is to use a hybrid of Classical Quantum approach, where a machine learning model is implemented in classical computer but the optimization of loss function during training is performed on quantum computer instead of classical computer. Several Quantum optimization algorithms have been proposed in recent years, which can be classified as gradient based and gradient free optimization techniques. Gradient based techniques require the nature of optimization problem being solved to be convex, continuous and differentiable otherwise if the problem is non-convex then they can find local optima only whereas gradient free optimization techniques work well even with non-continuous, non-linear and nonconvex optimization problems. This chapter discusses a global optimization technique based on Adiabatic Quantum Computation (AQC) to solve minimization of loss function without any restriction on its structure and the underlying model, which is being learned. Further, it is also shown that in the proposed framework, AQC based approach would be superior to circuit-based approach in solving global optimization problems.
Machine learning brings the promise of deriving meaning from different data, which is widely used for medicine and computer science. Quantum computing exploits the phenomena of quantum states to realize parallel computing, which believed to be significantly faster than classical computers. Quantum machine learning is the integration of quantum algorithms within machine learning programs, thereby improving classical machine learning techniques. Quantum control such as gate decomposition and Hamiltonian control is an essential problem to solve in quantum dynamics. Here we present a hybrid quantum machine learning model to conduct quantum control optimization. Firstly, according to Bloch theorem, any single-qubit unitary gate can be specified by three vector rotations. We find the optimal decomposition of the given gate, which is the optimal control sequence. Secondly, we build a hybrid quantum-classical neural networks to solve gate decomposition problem utilizing supervised learning. And we prepare the training data and train the hybrid supervised model. Finally, we demonstrate the quantum control optimization results in hybrid model on quantum gates.