Abelian and non-Abelian quantum geometric tensor

Non-abelian Tensor-multiplet Anomalies

We use the anomaly cancellation of the M-theory fivebrane to derive the R-symmetry anomalies of the AN (0, 2) tensor-multiplet theories. This result leads to a simple derivation of black hole entropy in d = 4,N = 2 compactifications of M -theory. We also show how the formalism of normal bundle anomaly cancellation clarifies the Kaluza-Klein origin of Chern-Simons terms in gauged supergravity th...

Abelian and non-Abelian geometric phases in adiabatic open quantum systems

We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases, based on an adiabatic approximation developed within an inherently open-systems approach. This expression provides a natural generalization of the analogous one...

Fast non-Abelian geometric gates via transitionless quantum driving

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric ph...

Non-Abelian geometric effect in quantum adiabatic transitions.

Quantum Error-Correction Codes on Abelian Groups

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.