The term “logical qubit” can be used in two contexts, with slightly different meanings. It can be meant as a mathematical concept that represents a perfect quantum bit, i.e. the fundamental unit of quantum information, that can be in any superposition of the states |0> and |1>, as opposed to a [physical qubit], which corresponds to an actual physical quantum system. In the description of abstract quantum algorithms and quantum protocols, “qubit” should always be understood as “logical qubit”.
In the context of [quantum error correction] and fault-tolerant quantum computing, “logical qubit” refers to a collection of physical qubits that are entangled with each other, following an error-correction protocol, to form a system that behaves like a qubit, but is more protected from noise and errors than the physical qubits it is composed of. It then corresponds to an [error-corrected qubit].
Frequently asked questions about logical qubits
- Is a logical qubit a perfect qubit? It depends on the context. In the first sense, yes, it’s an ideal two-level quantum system. In the context of quantum error correction, no, it’s a multi-particle system that has qubit-like properties and is more resilient to noise than its constituents.
- How many physical qubits are needed to form one logical qubit? It depends on the amount of physical noise one has to deal with, on the logical error rate one wants to achieve, and on the quantum error correcting code. A typical number would be 1000 physical qubits for one logical qubit, but more advanced codes can reduce this factor to 100, or even to 10.
- In the context of quantum error correction, can logical qubits eliminate errors completely? No, but they significantly reduce them, and by using more physical qubits, the logical error rate can be made arbitrarily small.