An introduction to quantum error correction and fault-tolerant quantum computation
Daniel Gottesman · Proceedings of symposia in applied mathematics · 2010
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers.The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes.Many quantum codes can be described in terms of the stabilizer of the codewords.The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code.The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements.To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum errorcorrecting code.The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error rate per physical gate or time step is below some constant threshold value.