Principles of Superconducting Quantum Computers

10Quantum Error Correction

In Chapter 9, we discussed various sources of noise in quantum systems, and how to reduce and compensate for noise. However, noise cannot be completely eliminated. Some noise will cause errors in the quantum information used in our computations. In this chapter, we discuss how qubit errors can be detected and corrected, leading to the development of fault-tolerant quantum computing.

To deal with errors, we encode information using additional qubits. For example, we might use 12 qubits to represent 2⁸ basis states, rather than 8. This allows us to distinguish valid encodings, representing the 2⁸ “good” states, from invalid encodings, representing error states. With enough information in the extra qubits, we can determine which data qubit has an error and how to correct it.

Such error correction codes are used extensively in the classical computing realm, particularly for communicating over noisy channels or dealing with leakage errors in memory. Quantum Error Correction (QEC) codes build on these concepts, but additional features are required to deal with the nature of quantum information and errors.

10.1 Review of Classical Error Correction

Errors may occur when transmitting information across a noisy channel. A channel is any medium through which information is communicated, either through space (e.g., transmission of bits over a wire) or time (e.g., bits stored in memory). The channel sits between the transmitter of information and the receiver ...