d harrow operator algebra quantum error correction

Auxilliary degrees of freedom are also constantly measured, to detect signs of errors and allow their effects to be removed. The encoding is maintained by constantly putting the physical qubits through a highly entangling circuit. This will be done through the process of quantum error correction, in which logical qubits are encoded in a large number of physical qubits. For the future era of fault-tolerance, however, we must find ways to build logical qubits from physical qubits. In the current era of quantum computing, we seek to use physical qubits despite their imperfections, by designing custom algorithms and using error mitigation effects. Instead, we refer to them as physical qubits. These qubits will always be much too imprecise to serve directly as logical qubits. However, the imperfections can never be removed entirely. The last few decades have also seen great advances in finding physical systems that behave as qubits, with better quality qubits being developed all the time. Qubits that obey these assumptions are often known as logical qubits. Most quantum algorithms developed over the past few decades have assumed that these qubits are perfect: they can be prepared in any state we desire, and be manipulated with complete precision. Quantum computing requires us to encode information in qubits.

D harrow operator algebra quantum error correction