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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…
We introduce a twisted Heisenberg-type interaction Hamiltonian, a Heisenberg-type spin interaction where the coordinates of the second qubit are twisted according to a unitary gate. We develop parallelizable adiabatic gate teleportation…
We present a general approach to speed up the adiabatic process without adding the traditional counterdiabatic driving (CD) Hamiltonian. The strategy is to design an easy-to-get intermediate Hamiltonian to connect the original Hamiltonian…
Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
Open quantum systems described by a non-Hermitian Hamiltonian exhibit rich dynamics due to the topology of their complex energy spectrum. By encircling an exceptional point degeneracy, this topology allows for topological state transport,…
We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We…
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a…
In this work, we present a new algorithm for generating quantum circuits that efficiently implement continuous time quantum walks on arbitrary simple sparse graphs. The algorithm, called matching decomposition, works by decomposing a…
We propose a new method for simulating certain type of time-dependent Hamiltonian $H(t) = \sum_{i=1}^m \gamma_i(t) H_i$ where $\gamma_i(t)$ (and its higher order derivatives) is bounded, computable function of time $t$, and each $H_i$ is…
An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. In…
In quantum information processing, the development of fast and robust control schemes remains a central challenge. Although quantum adiabatic evolution is inherently robust against control errors, it typically demands long evolution times.…
We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This…
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the…
Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest.…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Consider a path of non-degenerate eigenstates of unitary operators or Hamiltonians with minimum eigenvalue gap G. The eigenpath traversal problem is to transform one or more copies of the initial to the final eigenstate. Solutions to this…
We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated…
The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic…
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We…