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We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence Hamiltonian, which is of the more general form of the nonstationary forced bosonic oscillator. If however one admits Grassmann variables as Hamiltonian parameters then the coherence Hamiltonian takes again the form of (Grassmannian fermionic) forced oscillator.
In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilises perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we provide a gener
The definition of accessible coherence is proposed. Through local measurement on the other subsystem and one way classical communication, a subsystem can access more coherence than the coherence of its density matrix. Based on the local accessible co
Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the Hamiltonian involve
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical inference to glean