A magic gate is a fault-tolerant quantum operation unavailable directly from a logical architecture. Magic states supply these operations, extending the supported gate set so programs can approximate arbitrary gates. section 9.3 section 9.8
A typical magic-gate implementation involves:
- Preparing rough approximations of magic states. section 9.3
- Refining those states through magic state distillation. section 9.3
- Using the distilled states with supported logical gates to construct the required operations. section 9.3
The T gate
The T gate is a standard magic gate: T = diag(1, e^{iπ/4}). Its matching magic state is |T⟩ = T|+⟩ = (|0⟩ + e^{iπ/4}|1⟩)/√2. Combined with simple architecture-supported gates, T enables arbitrarily precise approximations of any single-qubit gate. section 9.3
Magic state distillation runs alongside the main computation in a separate area and can become a major resource cost, depending on the program’s gate requirements. section 9.3 section 9.8
Figure 9.5 Physical qubits are noisy, they support a limited set of gates, and these gates are slow. We have to use error correction to enable reliable computation on noisy qubits. We also have to use a special process to implement arbitrary logical gates on logical qubits. These factors affect both the run time of algorithms on the quantum computers and the numbers of qubits required to run them.
Physical-qubit noise, error correction, limited gate sets, and magic-gate construction jointly affect execution time and qubit requirements. section 9.8
