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Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics

Programming quantum annealing computers using machine learning

Elizabeth Behrman, James E. Steck

Published Oct 1, 2017• 0 citations
Publisher

Abstract

Commercial quantum annealing (QA) machines are now being built with hundreds of quantum bits (qubits). These are used as analog computers, to solve optimization problems by annealing to an unknown ground state (the solution), given the Hamiltonian for that problem. We propose and develop a new approach, in which we use machine learning to do the inverse problem: to find the Hamiltonian that will produce a given, desired ground state. We demonstrate successful learning to produce a desired fully entangled state for a two-qubit system, then bootstrap to do the same for three, four, five and six qubits; the amount of additional learning necessary decreases. With these new capabilities the computing possibilities for QA arrays are greatly expanded.

DOI
10.1109/smc.2017.8122617

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Commercial quantum annealing (QA) machines are now being built with hundreds of quantum bits (qubits). These are used as analog computers, to solve optimization problems by annealing to an unknown ground state (the solution), given the Hamiltonian for that problem. We propose and develop a new approach, in which we use machine learning to do the inverse problem: to find the Hamiltonian that will produce a given, desired ground state. We demonstrate successful learning to produce a desired fully entangled state for a two-qubit system, then bootstrap to do the same for three, four, five and six qubits; the amount of additional learning necessary decreases. With these new capabilities the computing possibilities for QA arrays are greatly expanded.
We propose and develop a new procedure, whereby a quantum system can learn to anneal to a desired ground state. We demonstrate successful learning to produce an entangled state for a two-qubit system, then demonstrate generalizability to larger systems. The amount of additional learning necessary decreases as the size of the system increases. Because current technologies limit measurement of the states of quantum annealing machines to determination of the average spin at each site, we then construct a "broken pathway" between the initial and desired states, at each step of which the average spins are nonzero, and show successful learning of that pathway. Using this technique we show we can direct annealing to multiqubit GHZ and W states, and verify that we have done so. Because quantum neural networks are robust to noise and decoherence we expect our method to be readily implemented experimentally; we show some preliminary results which support this.
We propose and develop a new procedure, whereby a quantum system can learn to anneal to a desired ground state. We demonstrate successful learning to produce an entangled state for a two-qubit system, then demonstrate generalizability to larger systems. The amount of additional learning necessary decreases as the size of the system increases. Because current technologies limit measurement of the states of quantum annealing machines to determination of the average spin at each site, we then construct a “broken pathway” between the initial and desired states, at each step of which the average spins are nonzero, and show successful learning of that pathway. Using this technique we show we can direct annealing to multiqubit GHZ and W states, and verify that we have done so. Because quantum neural networks are robust to noise and decoherence we expect our method to be readily implemented experimentally; we show some preliminary results which support this.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
Abstract Noisy intermediate-scale quantum (NISQ) devices are spearheading the second quantum revolution. Of these, quantum annealers are the only ones currently offering real world, commercial applications on as many as 5000 qubits. The size of problems that can be solved by quantum annealers is limited mainly by errors caused by environmental noise and intrinsic imperfections of the processor. We address the issue of intrinsic imperfections with a novel error correction approach, based on machine learning methods. Our approach adjusts the input Hamiltonian to maximize the probability of finding the solution. In our experiments, the proposed error correction method improved the performance of annealing by up to three orders of magnitude and enabled the solving of a previously intractable, maximally complex problem.
This paper explores the applications of quantum annealing (QA) and classical simulated annealing (SA) to a suite of combinatorial optimization problems in machine learning, namely feature selection, instance selection, and clustering. We formulate each task as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement both quantum and classical solvers to compare their effectiveness. For feature selection, we propose several QUBO configurations that balance feature importance and redundancy, showing that quantum annealing (QA) produces solutions that are computationally more efficient. In instance selection, we propose a few novel heuristics for instance-level importance measures that extend existing methods. For clustering, we embed a classical-to-quantum pipeline, using classical clustering followed by QUBO-based medoid refinement, and demonstrate consistent improvements in cluster compactness and retrieval metrics. Our results suggest that QA can be a competitive and efficient tool for discrete machine learning optimization, even within the constraints of current quantum hardware.
Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.