ObsidianVault/SS2026/Quantum Computing/18. Fault-torerant computation/Fault-Tolerant Computation.md

We now face two problems with continuous computations:

1. Applying operations on logical qubits. Applying operations on encoded qubits would only be possible by decoding - applying - encoding again. Not optimal. Also errors can happen in decode encode.
2. Operations on encoded qubits could introduce new more complex errors.

Operations on logical/physical qubits

We begin by defining how to apply operations to encoded qubits:

! !

Fault tolerant Gates

Now we need to reduce our error probability.

!

To make this circuit fault-tolerant, we replace it with:

!

Let's look at a circuit for CNOT:

! ! !