Designing the Quantum Channels Induced by Diagonal Gates

Understand

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 implementing a universal set of quantum operations.
• This paper introduces a framework that describes the process of preparing a code state, applying a diagonal physical gate, measuring a code syndrome, and applying a Pauli correction that may depend on the measured syndrome (the average logical channel induced by an arbitrary diagonal gate).
• It focuses on CSS codes, and describes the interaction of code states and physical gates in terms of generator coefficients determined by the induced logical operator.