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A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
We consider the unitary time evolution of a one-dimensional quantum system which is in a stationary state for negative times and then undergoes a sudden change (quench) of a parameter of its Hamiltonian at t=0. For systems possessing a…
The fundamental importance of the chiral oscillator is elaborated. Its quantum invariants are computed. As an application the Zeeman effect is analysed. We also show that the chiral oscillator is the most basic example of a duality…
Quantum technology has been rapidly growing due to its potential revolutionary applications. In particular, superconducting qubits provide a strong light-matter interaction as required for quantum computation and in principle can be scaled…
The classical and quantum oscillator model on Lie-algebraically deformed nonrelativistic space-time is introduced and analyzed. The corresponding equations of motions are studied using mostly numerical methods. The time-dependent energy…
Owing to their long-lifetimes at cryogenic temperatures, mechanical oscillators are recognized as an attractive resource for quantum information science and as a testbed for fundamental physics. Key to these applications is the ability to…
Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically…
We discuss whether, to what extent and how a quantum computing device can be evaluated and simulated using classical tools.
This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with $O_{h}$ symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates…
Quantum annealing provides a promising way to solve combinational optimization problems where the solutions correspond to the ground state of the Ising Hamiltonian. We can implement quantum annealing using the Kerr non-linear resonators,…
Sextic polynomial oscillator is probably the best known quantum system which is partially exactly {\it alias} quasi-exactly solvable (QES), i.e., which possesses closed-form, elementary-function bound states $\psi(x)$ at certain couplings…
The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we…
We analyse the one dimensional quartic oscillator using the effective operator methodology of Lee and Suzuki. We reproduce known results for low lying energy eigenvalues.
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or…
This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…
We investigate the feasibility of performing quantum non-demolition (QND) measurements in relativistic quantum systems, using the one-dimensional Dirac oscillator as a specific example. We derive general expressions for its QND observables…
The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
We provide a brief overview of what is known about Quadratic Gravity, which includes terms quadratic in the curvatures in the fundamental action. This is proposed as a renormalizeable UV completion for quantum gravity which continues to use…
Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g.…