Large computations, either classical or quantum, require each of their operations to have a low logical error rate in order to succeed. Otherwise, the incorrect results of a few operations can be fed forward, and the whole computation will output random results. This is an example of the well-known “Garbage In, Garbage Out” principle from computer science.

To prevent this, it is necessary to encode the states of the qubits we want to use to compute into quantum error-correcting codes. These codes allow errors to be detected and their effects to be reversed, preventing error propagation. In this lecture, Professor Barbara Terhal will introduce a few of the most popular quantum codes currently used.

Main takeaways

• Large-scale computations require much lower logical error rates than those we can produce directly in hardware.
• A variety of encoding schemes exist to protect qubits against external noise, and the effects of imprecise control. More redundancy in the encoding scheme tends to lead to better protection against errors.
• Measuring individual qubits to determine whether an error has occurred will destroy the superposition necessary to maintain a logical state, so measurements which detect errors must be done indirectly, using ancilla qubits.
• There are two fundamental types of errors on qubits: X and Z.