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Quantum physics holds the promise of enabling certain tasks with better performance than possible when only classical resources are employed. The quantum phenomena present in many experiments signify nonclassical behavior, but do not always…

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that…

A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…

We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…

Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…

Stochastic processes underlie a vast range of natural and social phenomena. Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g. traffic congestion, are effectively probabilistic because we…

The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that…

Quantum computing is a growing field where the information is processed by two-levels quantum states known as qubits. Current physical realizations of qubits require a careful calibration, composed by different experiments, due to noise and…

State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…

In this work we introduce a general scheme for measurement based quantum computation in continuous variables. Our approach does not necessarily rely on the use of ancillary cluster states to achieve its aim, but rather on the detection of a…

The standard approach to quantum measurement discrimination is to perform the given unknown measurement on a probe state, possibly entangled with an auxiliary system, and make a decision based on the measurement outcome obtained. In this…

A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case.…

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum…

This paper proposes a general quantum algorithm that can be applied to any classical computer program. Each computational step is written using reversible operators, but the operators remain classical in that the qubits take on values of…

Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this…

Quantum chemistry calculations are important applications of quantum annealing. For practical applications in quantum chemistry, it is essential to estimate a ground state energy of the Hamiltonian with chemical accuracy. However, there are…

Estimating nonlinear functions of quantum states, such as the moment $\tr(\rho^m)$, is of fundamental and practical interest in quantum science and technology. Here we show a quantum-classical hybrid framework to measure them, where the…

This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter…

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…

Measurement based quantum computation (MBQC), which requires only single particle measurements on a universal resource state to achieve the full power of quantum computing, has been recognized as one of the most promising models for the…