International Journal of Quantum Information

The goal of this work is to define a notion of a “quantum neural network” to classify data, which exploits the low-energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data and then test its performance on a simple classification task. More specifically, we use Microsoft’s quantum simulator, LIQ$Ui|〉$, to construct local Hamiltonians that can encode trained classifier functions in their ground space, and which can be probed by measuring the overlap with test states corresponding to the data to be classified. To obtain such a classifier Hamiltonian, we further propose a training scheme based on quantum annealing which is completely closed-off to the environment and which does not depend on external measurements until the very end, avoiding unnecessary decoherence during the annealing procedure. For a network of size $n$, the trained network can be stored as a list of $O(n)$ coupling strengths. We address the question of which interactions are most suitable for a given classification task, and develop a qubit-saving optimization for the training procedure on a simulated annealing device. Furthermore, a small neural network to classify colors into red versus blue is trained and tested, and benchmarked against the annealing parameters.

Quantum many-body systems realize many different phases of matter characterized by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies that the physics is dictated by an interacting Hamiltonian. The interaction distance has been successfully used to quantify the effect of interactions in a variety of states of matter via the entanglement spectrum [C. J. Turner, K. Meichanetzidis, Z. Papic and J. K. Pachos, Nat. Commun. 8 (2017) 14926, Phys. Rev. B 97 (2018) 125104]. The computation of the interaction distance reduces to a global optimization problem whose goal is to search for the free-fermion entanglement spectrum closest to the given entanglement spectrum. In this work, we employ techniques from machine learning in order to perform this same task. In a supervised learning setting, we use labeled data obtained by computing the interaction distance and predict its value via linear regression. Moving to a semi-supervised setting, we train an autoencoder to estimate an alternative measure to the interaction distance, and we show that it behaves in a similar manner.

Quantum machine learning is the aspect of quantum computing concerned with the design of algorithms capable of generalized learning from labeled training data by effectively exploiting quantum effects. Error-correcting output codes (ECOC) are a standard setting in machine learning for efficiently rendering the collective outputs of a binary classifier, such as the support vector machine, as a multi-class decision procedure. Appropriate choice of error-correcting codes further enables incorrect individual classification decisions to be effectively corrected in the composite output. In this paper, we propose an appropriate quantization of the ECOC process, based on the quantum support vector machine. We will show that, in addition to the usual benefits of quantizing machine learning, this technique leads to an exponential reduction in the number of logic gates required for effective correction of classification error.

We present strategies for the training of a qubit network aimed at the ancilla-assisted synthesis of multi-qubit gates based on a set of restricted resources. By assuming the availability of only time-independent single and two-qubit interactions, we introduce and describe a supervised learning strategy implemented through momentum-stochastic gradient descent with automatic differentiation methods. We demonstrate the effectiveness of the scheme by discussing the implementation of nontrivial three qubit operations, including a QFT and a half-adder gate.

This paper proposes a quantum-classical algorithm to evaluate and select classical artificial neural networks architectures. The proposed algorithm is based on a probabilistic quantum memory (PQM) and the possibility to train artificial neural networks (ANN) in superposition. We obtain an exponential quantum speedup in the evaluation of neural networks. We also verify experimentally through a reduced experimental analysis that the proposed algorithm can be used to select near-optimal neural networks.

Quantum compiling means fast, device-aware implementation of quantum algorithms (i.e. quantum circuits, in the quantum circuit model of computation). In this paper, we present a strategy for compiling IBM Q-aware, low-depth quantum circuits that generate Greenberger–Horne–Zeilinger (GHZ) entangled states. The resulting compiler can replace the QISKit compiler for the specific purpose of obtaining improved GHZ circuits. It is well known that GHZ states have several practical applications, including quantum machine learning. We illustrate our experience in implementing and querying a uniform quantum example oracle based on the GHZ circuit, for solving the classically hard problem of learning parity with noise.

Representing a given problem as a QUBO problem implies the possibility of running it in a quantum computational environment (generic or specific). The well-known problem of looking for similar functions in biological structures, especially of proteins, is of great interest in the field of Bioinformatics. We give a QUBO formulation for CMO protein problem. Experimental results validate this approach as an alternative to classical methods via combinatorial optimization. For the accomplishment of such experiments, we use the qbsolv tool.

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [G. Carleo and M. Troyer, Science 355(6325) (2017) 602.]. States represented in this way, called Neural Network States (NNSs), were shown to display interesting properties like the ability to efficiently capture long-range quantum correlations. However, identifying an optimal neural network representation of a given state might be challenging, and so far this problem has been addressed with stöchastic optimization techniques. In this work, we explore a different direction. We study how the action of elementary quantum operations modifies NNSs. We parametrize a family of many body quantum operations that can be directly applied to states represented by Unrestricted Boltzmann Machines, by just adding hidden nodes and updating the network parameters. We show that this parametrization contains a set of universal quantum gates, from which it follows that the state prepared by any quantum circuit can be expressed as a Neural Network State with a number of hidden nodes that grows linearly with the number of elementary operations in the circuit. This is a powerful representation theorem (which was recently obtained with different methods) but that is not directly useful, since there is no general and efficient way to extract information from this unrestricted description of quantum states. To circumvent this problem, we propose a step-wise procedure based on the projection of Unrestricted quantum states to Restricted quantum states. In turn, two approximate methods to perform this projection are discussed. In this way, we show that it is in principle possible to approximately optimize or evolve Neural Network States without relying on stochastic methods such as Variational Monte Carlo, which are computationally expensive.

Computer vision has a wide range of applications from medical image analysis to robotics. Over the past few years, the field has been transformed by machine learning and stands to benefit from potential advances in quantum computing. The main challenge for processing images on current and near-term quantum devices is the size of the data such devices can process. Images can be large, multidimensional and have multiple color channels. Current machine learning approaches to computer vision that exploit quantum resources require a significant amount of manual pre-processing of the images in order to be able to fit them onto the device. This paper proposes a framework to address the problem of processing large scale data on small quantum devices. This framework does not require any dataset-specific processing or information and works on large, grayscale and RGB images. Furthermore, it is capable of scaling to larger quantum hardware architectures as they become available. In the proposed approach, a classical autoencoder is trained to compress the image data to a size that can be loaded onto a quantum device. Then, a Restricted Boltzmann Machine (RBM) is trained on the D-Wave device using the compressed data, and the weights from the RBM are then used to initialize a neural network for image classification. Results are demonstrated on two MNIST datasets and two medical imaging datasets.

Supervised learning algorithms take as input a set of labeled examples and return as output a predictive model. Such models are used to estimate labels for future, previously unseen examples, drawn from the same generating distribution. In this paper, we investigate the possibility of using supervised learning to estimate the dimension of a non-Markovian quantum environment. Our approach uses an ensemble learning method, the Random Forest Regressor, applied to classically simulated datasets. Our results indicate this is a promising line of research.

We propose an application of a quantum-inspired version of the Nearest Mean Classifier (NMC) (G. Sergioli, E. Santucci, L. Didaci, J. A. Miszczak and R. Giuntini, A quantum inspired version of the NMC classifier, Soft Comput. 22(3) (2018) 691. G. Sergioli, G. M. Bosyk, E. Santucci and R. Giuntini, A quantum-inspired version of the classification problem, Int. J. Theo. Phys. 56(12) (2017) 3880. E. Santucci and G. Sergioli, Classification problem in a quantum framework, in quantum foundations, probability and information, Proc. Quantum and Beyond Conf., 13–16 June 2016, Vaxjo, Sweden, A. Khrennikov and T. Bourama, Springer-Berlin, Germany, 2018 (in press, 2018). E. Santucci, Quantum minimum distance classifier, Entropy 19(12) (2017) 659.) to a biomedical context. In particular, we benchmark the performances of such a quantum-variant of NMC against NMC and other (nonlinear) classifiers with respect to the problem of classifying the probability of survival for patients affected by idiopathic pulmonary fibrosis (IPF).

In many-body physics, renormalization techniques are used to extract aspects of a statistical or quantum state that are relevant at large scale, or for low energy experiments. Recent works have proposed that these features can be formally identified as those perturbations of the states whose distinguishability most resist coarse-graining. Here, we examine whether this same strategy can be used to identify important features of an unlabeled dataset. This approach indeed results in a technique very similar to kernel PCA (principal component analysis), but with a kernel function that is automatically adapted to the data, or “learned”. We test this approach on handwritten digits, and find that the most relevant features are significantly better for classification than those obtained from a simple Gaussian kernel.

In this work, we examine a recently proposed distance-based classification method designed for near-term quantum processing units with limited resources. We study possibilities to reduce the quantum resources without any efficiency decrease. We show that only a part of the information undergoes coherent evolution and this fact allows us to introduce an algorithm with significantly reduced quantum system size requirements. Additionally, considering only partial information at a time, we propose a classification protocol with information distributed among a number of agents. Finally, we show that the information evolution during a measurement can lead to a better solution and that the accuracy of the algorithm can be improved by harnessing the state after the final measurement.