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Recent advances in quantum technology have led to the development and the manufacturing of programmable quantum annealers that promise to solve certain combinatorial optimization problems faster than their classical counterparts. Semi-supervised learning is a machine learning technique that makes use of both labeled and unlabeled data for training, which enables a good classifier with only a small amount of labeled data. In this paper, we propose and theoretically analyze a graph-based semi-supervised learning method with the aid of the quantum annealing technique, which efficiently utilize the quantum resources while maintaining a good accuracy. We illustrate two classification examples, suggesting the feasibility of this method even with a small portion (20%) of labeled data is involved.
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New annealing schedules for quantum annealing are proposed based on the adiabatic theorem. These schedules exhibit faster decrease of the excitation probability than a linear schedule. To derive this conclusion, the asymptotic form of the excitation probability for quantum annealing is explicitly obtained in the limit of long annealing time. Its first-order term, which is inversely proportional to the square of the annealing time, is shown to be determined only by the information at the initial and final times. Our annealing schedules make it possible to drop this term, thus leading to a higher order (smaller) excitation probability. We verify these results by solving numerically the time-dependent Schrodinger equation for small size systems
The popularisation of neural networks has seen incredible advances in pattern recognition, driven by the supervised learning of human annotations. However, this approach is unsustainable in relation to the dramatically increasing size of real-world datasets. This has led to a resurgence in self-supervised learning, a paradigm whereby the model generates its own supervisory signal from the data. Here we propose a hybrid quantum-classical neural network architecture for contrastive self-supervised learning and test its effectiveness in proof-of-principle experiments. Interestingly, we observe a numerical advantage for the learning of visual representations using small-scale quantum neural networks over equivalently structured classical networks, even when the quantum circuits are sampled with only 100 shots. Furthermore, we apply our best quantum model to classify unseen images on the ibmq_paris quantum computer and find that current noisy devices can already achieve equal accuracy to the equivalent classical model on downstream tasks.
Classical and quantum annealing are two heuristic optimization methods that search for an optimal solution by slowly decreasing thermal or quantum fluctuations. Optimizing annealing schedules is important both for performance and fair comparisons between classical annealing, quantum annealing, and other algorithms. Here we present a heuristic approach for the optimization of annealing schedules for quantum annealing and apply it to 3D Ising spin glass problems. We find that if both classical and quantum annealing schedules are similarly optimized, classical annealing outperforms quantum annealing for these problems when considering the residual energy obtained in slow annealing. However, when performing many repetitions of fast annealing, simulated quantum annealing is seen to outperform classical annealing for our benchmark problems.
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function and then transforming the k-bit coupling ($kgeq 3$) terms to quadratic terms using ancillary variables. The method is efficient and uses $mathcal{O}(text{log}^2(N))$ binary variables (qubits) for finding the factors of integer $N$. The method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. As examples, we present quantum annealing results for factoring 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits respectively. The method is general and could be used to factor larger numbers
Boltzmann Machines constitute a class of neural networks with applications to image reconstruction, pattern classification and unsupervised learning in general. Their most common variants, called Restricted Boltzmann Machines (RBMs) exhibit a good trade-off between computability on existing silicon-based hardware and generality of possible applications. Still, the diffusion of RBMs is quite limited, since their training process proves to be hard. The advent of commercial Adiabatic Quantum Computers (AQCs) raised the expectation that the implementations of RBMs on such quantum devices could increase the training speed with respect to conventional hardware. To date, however, the implementation of RBM networks on AQCs has been limited by the low qubit connectivity when each qubit acts as a node of the neural network. Here we demonstrate the feasibility of a complete RBM on AQCs, thanks to an embedding that associates its nodes to virtual qubits, thus outperforming previous implementations based on incomplete graphs. Moreover, to accelerate the learning, we implement a semantic quantum search which, contrary to previous proposals, takes the input data as initial boundary conditions to start each learning step of the RBM, thanks to a reverse annealing schedule. Such an approach, unlike the more conventional forward annealing schedule, allows sampling configurations in a meaningful neighborhood of the training data, mimicking the behavior of the classical Gibbs sampling algorithm. We show that the learning based on reverse annealing quickly raises the sampling probability of a meaningful subset of the set of the configurations. Even without a proper optimization of the annealing schedule, the RBM semantically trained by reverse annealing achieves better scores on reconstruction tasks.
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