Quantum error correction

Abstract

Abstract Quantum error correction is a very advanced field, and researchers have invested a great deal of time in trying to find the best ways of combating errors in quantum computers, winch occur when the computer is not properly isolated from its environment. Theoretically, quantum computation can be stabilised against any kind of influence of the environment. Classical error correction has been generalised to quantum mechanics to show that a reliable quantum computer can be constructed out of unreliable simple elements, or quantum gates. This chapter discusses the basic techniques of quantum error correction and looks at some general conditions which a quantum error correction code has to satisfy, explains how to protect qubits against general errors and achieve fault-tolerant computing, compares quantum error correction with Maxwell's demon, and performs error correction for pure states and mixed states.