Related papers: Nodal free geometric phases: Concept and applicati…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay…
Non Abelian geometric phases are attracting increasing interest because of possible experimental application in quantum computation. We study the effects of the environment (modelled as an ensemble of harmonic oscillators) on a holonomic…
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…
The phase estimation algorithm, which is at the heart of a variety of quantum algorithms, including Shor's factoring algorithm, allows a quantum computer to accurately determine an eigenvalue of an unitary operator. Quantum nondemolition…
It is shown that a family of analytically solvable pulses can be used to obtain high fidelity quantum phase gates with surprising robustness against imperfections in the system or pulse parameters. Phase gates are important because they can…
Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a…
The nonadiabatic geometric quantum computation is promising as it is robust against certain types of local noises. However, its experimental implementation is challenging due to the need of complex control on multi-level and/or multiple…
The geometric phase requires the multivaluedness of solutions to Fuchsian second-order equations. The angle, or its complement, is given by half the area of a spherical triangle in the case of three singular points, or half the area of a…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
It is shown that geometric phase in non-relativistic quantum mechanics is not Galilean invariant.
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
In this thesis we revise the concept of phase space in modern physics and devise a way to explicitly incorporate physical dimension into geometric mechanics. A historical account of metrology and phase space is given to illustrate the…
High-fidelity two-logical-qubit gates are essential for realizing fault-tolerant quantum computation with bosonic codes, yet experimentally reported fidelities have rarely exceeded 90\%. Here, we propose a geometric phase engineering…
We investigate a class of cyclic evolutions for %the cyclic evolution of driven two-level quantum systems (effective spin-1/2) with a particular focus on the geometric characteristics of the driving and their specific imprints on the…
We demonstrate the formation of confinement potentials in suspended nanostructures induced by the geometry of the devices. We then propose a setup for measuring the resulting geometric phase change of electronic wave functions in such a…
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric…
Geometric phases are robust against certain types of local noises, and thus provide a promising way towards high-fidelity quantum gates. However, comparing with the dynamical ones, previous implementations of nonadiabatic geometric quantum…
Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large scale entangled states is challenging in the presence of decoherence. We present a…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…