Related papers: Hamiltonian of Homonucleus Molecules for NMR Quant…
In this dissertation a simple Hamiltonian for a system of inter-acting molecules and radiation field is developed from a model of N Two-Level Molecules interacting, via a dipole approximation, with a single mode, quantized radiation field.…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the…
In creating a large-scale quantum information processor, the ability to construct control pulses for implementing an arbitrary quantum circuit in a scalable manner is an important requirement. For liquid-state nuclear magnetic resonance…
Optimal control techniques provide a means to tailor the control pulses required to generate customized quantum gates, which helps to improve the resilience of quantum simulations to gate errors and device noise. However, the significant…
We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented…
Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the…
The response of a quadrupolar nucleus (nuclear spin with I>1/2) to an oscillating radio-frequency (RF) pulse/field is delicately dependent on the ratio of the quadrupolar coupling constant to the amplitude of the pulse in addition to its…
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of…
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
In recent decades the field of quantum computation has seen remarkable development. While much progress has been made toward the realization of a fully digital, scalable, and fault tolerant quantum computer, there are still many essential…
Quantum simulation presents itself as one of the biggest advantages of developing quantum computers. Simulating a quantum system classically is almost impossible beyond a certain system size whereas a controllable quantum system inherently…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
The propagation of excitation along a one-dimensional chain of atoms is simulated by means of NMR. The physical system used as an analog quantum computer is a nucleus of 133-Cs (spin 7/2) in a liquid crystalline matrix. The Hamiltonian of…
We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system - a qubit - onto n "copy" qubits initially all prepared in the down state. In terms of spin components, for spin-1/2 particle spin…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…