The quantum computing devices of today have tens to hundreds of qubits that are highly
susceptible to noise due to unwanted interactions with their environment. The theory of …

Quantum error correction and symmetries play central roles in quantum information science
and physics. It is known that quantum error-correcting codes that obey (are covariant with …

Some form of quantum error correction is necessary to produce large-scale fault-tolerant
quantum computers and finds broad relevance in physics. Most studies customarily assume …

Quantum computing has been a fascinating research field in quantum physics. Recent
progresses motivate us to study in depth the universal quantum computing models …

Error-correction codes are central for fault-tolerant information processing. Here we develop
a rigorous framework to describe various coding models based on quantum resource theory …

Quantum error correction (QEC) is a key concept in quantum computation as well as many
areas of physics. There are fundamental tensions between continuous symmetries and …

A modern computer system, based on the von Neumann architecture, is a complicated
system with several interactive modular parts. It requires a thorough understanding of the …

We systematically study the fundamental competition between quantum error correction
(QEC) and continuous symmetries, two key notions in quantum information and physics, in a …

A quantum channel is covariant with respect to a group if it commutes with the action of the
group. In general, a quantum channel may not be covariant with respect to a given group …

In this work, we develop universal quantum computing models that form a family of quantum
von Neumann architectures, with modular units of memory, control, CPU, and internet …