Related papers: Geometric phases in superconducting qubits beyond …
When a quantum mechanical system undergoes an adiabatic cyclic evolution it acquires a geometrical phase factor in addition to the dynamical one. This effect has been demonstrated in a variety of microscopic systems. Advances in…
We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical…
Geometric phases are only dependent on evolution paths but independent of evolution details so that they own some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates have been proposed, such as…
We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution,…
We analyze the influence of a dissipative environment on geometric phases in a quantum system subject to non-adiabatic evolution. We find dissipative contributions to the acquired phase and modification of dephasing, considering the cases…
Geometric phases of scattering states in a ring geometry are studied based on a variant of the adiabatic theorem. Three time scales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a…
Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized,…
A quantum system interacting with its environment is subject to dephasing which ultimately destroys the information it holds. Using a superconducting qubit, we experimentally show that this dephasing has both dynamic and geometric origins.…
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…
The adiabatic geometric phases for general three state systems are discussed. An explicit parameterization for space of states of these systems is given. The abelian and non-abelian connection one-forms or vector potentials that would…
Quantum adiabatic transfer is widely used in quantum computation and quantum simulation. However, the transfer speed is limited by the quantum adiabatic approximation condition, which hinders its application in quantum systems with a short…
Geometric phases accompanying adiabatic quantum evolutions can be used to construct robust quantum control for quantum information processing due to their noise-resilient feature. A significant development along this line is to construct…
Quantum gates, which are the essential building blocks of quantum computers, are very fragile. Thus, to realize robust quantum gates with high fidelity is the ultimate goal of quantum manipulation. Here, we propose a nonadiabatic geometric…
Geometric quantum computation relies on the geometric phase that arises in adiabatic cyclic evolutions of non-degenerate quantum systems, enabling the design of robust quantum gates. However, the adiabatic condition requires long evolution…
When quantum mechanical qubits as elements of two dimensional complex Hilbert space are generalized to elements of even subalgebra of geometric algebra over three dimensional Euclidian space, geometrically formal complex plane becomes…
In a recent Letter [Phys. Rev. Lett. {\bf 95}, 080502 (2005)], an interesting scheme was proposed to implement a type of conditional quantum phase gates with built-in fault-tolerant feature via adiabatic evolution of dark eigenstates. In…
In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $\Lambda$ three-level system. They further…
The geometric phase acquired by the vector states under an adiabatic evolution along a noncyclic path can be calculated correctly in any instantaneous basis of a Hamiltonian that varies in time due to a time-dependent classical field.
We make use of a superconducting qubit to study the effects of noise on adiabatic geometric phases. The state of the system, an effective spin one-half particle, is adiabatically guided along a closed path in parameter space and thereby…