Storing quantum information in a quantum error correction code can protect it from errors,
but the ability to transform the stored quantum information in a fault tolerant way is equally …

The challenge of quantum computing is to combine error resilience with universal
computation. Diagonal gates such as the transversal $ T $ gate play an important role in …

The Clifford hierarchy is a fundamental structure in quantum computation, classifying unitary
operators based on their commutation relations with the Pauli group. Despite its …

Physical platforms such as trapped ions suffer from coherent noise that does not follow a
simple stochastic model. Stochastic errors in quantum systems occur randomly but coherent …

Designing efficient and noise-tolerant quantum computation protocols generally begins with
an understanding of quantum error-correcting codes and their native logical operations. The …

The Clifford hierarchy plays a crucial role in the stabilizer formalism of quantum error
correction and quantum computation. Apart form the zeroth level (the discrete Heisenberg …

In this note we prove a necessary set of conditions which must be satisfied by any controlled
gate in the qubit Clifford Hierarchy. These conditions are straightforward to derive yet quite …

The challenge of quantum computing is to combine error resilience with universal
computation. There are many finite sets of gates that are universal, and a standard choice is …

Stochastic errors in quantum systems occur randomly but coherent errors may be more
damaging since they can accumulate in a particular direction. We develop a framework for …

В формализме стабилизатора квантовой коррекции ошибок и квантовых вычислений
решающую роль играет иерархия Клиффорда. За исключением нулевого уровня …