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There are well developed theoretical tools to analyse how quantum dynamics can solve computational problems by varying Hamiltonian parameters slowly, near the adiabatic limit. On the other hand, there are relatively few tools to understand…
Quantum probes are atomic-sized devices mapping information of their environment to quantum mechanical states. By improving measurements and at the same time minimizing perturbation of the environment, they form a central asset for quantum…
Quantum annealing is a promising approach to heuristically solving difficult combinatorial optimization problems. However, the connectivity limitations in current devices lead to an exponential degradation of performance on general…
Quantum annealing is a generic solver for optimization problems that uses fictitious quantum fluctuation. The most groundbreaking progress in the research field of quantum annealing is its hardware implementation, i.e., the so-called…
To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult…
State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It…
We describe simulations of the quantum dynamics of a confocal cavity QED system that realizes an intrinsically driven-dissipative spin glass. A close connection between open quantum dynamics and replica symmetry breaking is established, in…
The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm,…
The glass phase and its quantum analog are prominent challenges of current non-equilibrium statistical mechanics and condensed matter physics. As a model system to study the transition from classical to quantum glassy dynamics, we propose a…
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of…
Semiconductor quantum dots (QDs) offer a platform to explore the physics of quantum electronics including spins. Electron spins in QDs are considered good candidates for quantum bits in quantum information processing, and spin control and…
Quantum annealing was originally proposed as an approach for solving combinatorial optimisation problems using quantum effects. D-Wave Systems has released a production model of quantum annealing hardware. However, the inherent noise and…
Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated…
Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from…
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…
Spin glass dynamics is a strong function of spatial dimensionality $D$. The lower critical dimension is close to 2.5, so that, in two dimensions, the condensation temperature $T_\text{g}=0$, and only fluctuations are present at finite…
Eigenstates of quantum many-body systems are often used to define phases of matter in and out of equilibrium; however, experimentally accessing highly excited eigenstates is a challenging task, calling for alternative strategies to…
We study various annealing dynamics, both classical and quantum, for simple mean-field models and explain how to describe their behavior in the thermodynamic limit in terms of differential equations. In particular we emphasize the…
The aim of this work is to prove that it is possible to realise an optical system which produces as output a light intensity that can be expressed in the same mathematical form of the spin glass Hamiltonian. The optical system under study…