We introduce the characterization of a class of quantum PageRank algorithms in a scenario in which some kind of quantum network is realizable out of the current classical internet web, but no quantum computer is yet available. This class represents a quantization of the PageRank protocol currently employed to list web pages according to their importance. We have found an instance of this class of quantum protocols that outperforms its classical counterpart and may break the classical hierarchy of web pages depending on the topology of the web.

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Google in a Quantum Network

COVID-19 is a novel virus that affects the upper respiratory tract, as well as the lungs. The scale of the global COVID-19 pandemic, its spreading rate, and deaths are increasing regularly. Computed tomography (CT) scans can be used carefully to detect and analyze COVID-19 cases. In CT images/scans, ground-glass opacity (GGO) is found in the early stages of infection. While in later stages, there is a superimposed pulmonary consolidation. This research investigates the quantum machine learning (QML) and classical machine learning (CML) approaches for the analysis of COVID-19 images. The recent developments in quantum computing have led researchers to explore new ideas and approaches using QML. The proposed approach consists of two phases: in phase I, synthetic CT images are generated through the conditional adversarial network (CGAN) to increase the size of the dataset for accurate training and testing. In phase II, the classification of COVID-19/healthy images is performed, in which two models are proposed: CML and QML. The proposed model achieved 0.94 precision (Pn), 0.94 accuracy (Ac), 0.94 recall (Rl), and 0.94 F1-score (Fe) on POF Hospital dataset while 0.96 Pn, 0.96 Ac, 0.95 Rl, and 0.96 Fe on UCSD-AI4H dataset. The proposed method achieved better results when compared to the latest published work in this domain.

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Quantum Machine Learning Architecture for COVID-19 Classification Based on Synthetic Data Generation Using Conditional Adversarial Neural Network.

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrodinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

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Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register.

Efficient state preparation for a register of quantum bits (13 pages)

Among several tasks in Machine Learning, is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of such problem is the task of inferring the Hidden Markov Model underlying a given stochastic process. This is known as the positive realization problem (PRP) [Benvenuti,Farina(2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory [Luenberger(1979)].

We consider the scenario where the latent variables are quantum (e.g., quantum states of a finite-dimensional system), and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument-if any-yields the process at hand by iterative application.

We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the Hidden Markov Model, or the iterated quantum instrument, is however devoid from any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The Completely-Positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists.

We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [Guta(2011), Guta&Yamamoto(2013)].

Quantum Learning of Classical Stochastic Processes: The Completely-Positive Realization Problem

Humans are experts at recognising patterns in past experience and applying them to new tasks. For example, after seeing pictures of a face we can usually tell if another image contains the same person or not. Machine learning is a research discipline at the intersection of computer science, statistics and mathematics that investigates how pattern recognition can be performed by machines and for large amounts of data. Since a few years machine learning has come into the focus of quantum computing in which information processing based on the laws of quantum theory is explored. Although large scale quantum computers are still in the first stages of development, their theoretical description is well-understood and can be used to formulate ‘quantum software’ or ‘quantum algorithms’ for pattern recognition. Researchers can therefore analyse the impact quantum computers may have on intelligent data mining. This approach is part of the emerging research discipline of quantum machine learning that harvests synergies between quantum computing and machine learning. The research objective of this thesis is to understand how we can solve a slightly more specific problem called supervised pattern recognition based on the language that has been developed for universal quantum computers. The contribution it makes is twofold: First, it presents a methodology that understands quantum machine learning as the combination of data encoding into quantum systems and quantum optimisation. Second, it proposes several quantum algorithms for supervised pattern recognition. These include algorithms for convex and non-convex optimisation, implementations of distance-based methods through quantum interference, and the preparation of quantum states from which solutions can be derived via sampling. Amongst the machine learning methods considered are least-squares linear regression, gradient descent and Newton’s method, k-nearest neighbour, neural networks as well as ensemble methods. Together with the growing body of literature, this thesis demonstrates that quantum computing offers a number of interesting tools for machine learning applications, and has the potential to create new models of how to learn from data.

Maria. Schuld

Papers

Quantum machine learning for supervised pattern recognition.