Related papers: Nodal free geometric phases: Concept and applicati…
It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases…
The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
Nonadiabatic geometric quantum computation (NGQC) has emerged as an excellent proposal for achieving fast and robust quantum control against control errors. However, previous NGQC protocols could not be strongly resilient against the noise…
Field theories with combinatorial non-local interactions such as tensor invariants are interesting candidates for describing a phase transition from discrete quantum-gravitational to continuum geometry. In the so-called cyclic-melonic…
We discuss the desired criteria for a two-qubit phase gate and present a method for realising such a gate for quantum computation that is measurement-free and low error. The gate is implemented between qubits via an intermediate bus mode.…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
Besides the intrinsic noise resilience property, nonadiabatic geometric phases are of the fast evolution nature, and thus can naturally be used in constructing quantum gates with excellent performance, i.e., the so-called nonadiabatic…
Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. However, previous NHQC gates require the driving Hamiltonian to satisfy a set of rather restrictive…
In open quantum systems, we study the geometric phases acquired for a two-level atom coupled to a bath of fluctuating vacuum massless scalar fields due to linear acceleration and circular motion without and with a boundary. In free space,…
Quantum connections are defined by parallel transport operators acting on a Hilbert space. They transport tangent operators along paths in parameter space. The metric tensor of a Riemannian manifold is replaced by an inner product of pairs…
In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also…
We present a method to enact a deterministic, measurement-free, optically generated controlled-phase gate on two qubits defined by single electrons trapped in large-area quantum dots in a planar microcavity. This method is robust to optical…
We present an approach for eliminating the gauge freedom for derivative couplings in nonadiabatic dynamics in the presence of geometric phase effects. This approach relies on a bottom-up construction of a parametric quantum Hamiltonian in…
Nonadiabatic holonomic quantum computation is a promising approach for implementing quantum gates that offers both efficiency and robustness against certain types of errors. A key element of this approach is a geometric constraint known as…
As primitives for entanglement generation, controlled phase gates take a central role in quantum computing. Especially in ideas realizing instances of quantum computation in linear optical gate arrays a closer look can be rewarding. In such…
Recent proposals using heterostructures of superconducting and either topologically insulating or semiconducting layers have been put forth as possible platforms for topological quantum computation. These systems are predicted to contain…