Logical Qubit

Many proposals exist for the implementation of quantum error correction. A popular approach is to compute with sets of entangled physical qubits, called “logical qubits”, that enable the detection and correction of errors without breaking quantum physics’ rules about measurement and how it affects systems.

Copying quantum information is not possible due to the no cloning theorem. In classical computers, error correction often employs redundancy: for example, if you duplicate each bit 10 times then it is easy to detect and correct a single bit flip. To get around the no cloning theorem in quantum error correction you can spread the (logical) information of one logical qubit onto a highly entangled state of several (physical) qubits. Peter Shor first discovered this method of formulating a quantum error correcting code by storing the information of one qubit onto an entangled state of nine qubits.

Working with entangled units of qubits also allows one to circumvent quantum mechanics’ measurement problem: when a qubit is measured, its delicate quantum information is collapsed into a specific state and the richness of information is lost, therefore, one must measure the errors and not the qubits themselves.