Quantum Inf Process (2012) 11:629–631
Frank Gaitan: Quantum error correction and fault
tolerant quantum computing
Received: 15 April 2011 / Accepted: 17 August 2011 / Published online: 27 August 2011
© Springer Science+Business Media, LLC 2011
Quantum computing makes use of a quantum system to store and process information.
If a quantum system is employed for computing, one can make use of resources such
as superposition states and entangled states, which do not exist in the classical world.
These new resources give a quantum computer exponentially efﬁcient computational
power compared to its classical counterpart. Here qubits (quantum bits) are employed
instead of the bits used in classical computing. A (pure) state of a qubit is a two-
dimensional complex vector represented as a superposition of two basis vectors cor-
responding to classical 0 and 1. Physical realization of a quantum computer, however,
suffers from several serious obstacles. Decoherence is one of the most serious obstacles
among others. A quantum system employed for quantum computing has to satisfy two
seemingly contradicting requirements; it must be controllable by manipulating exter-
nal control parameters and interactions within the system and, at the same time, it
must be isolated from the rest of the world to maintain coherence. Decoherence is a
process in which a pure state of a quantum system develops into a mixed state under
interaction with its environment. Naturally decoherence is recognized as an error if it
takes place during quantum computation and must be suppressed.
There are several proposals to ﬁght decoherence. Quantum error correction, abbre-
viated as QEC in the following, is a popular strategy for this purpose. It is a natural
generalization of classical error correction, which employs redundant bits for encod-
ing. The simplest example of classical error correction employs three bits so that 0 is
encoded as 000 and 1 as 111. Assuming only one bit-ﬂip error takes place during trans-
mission, it is an easy matter to recover 000 from 100, for example, by majority vote
and decode 000 to 0. This simple encoding does not work for a qubit because of the no
cloning theorem; one cannot copy an unknown quantum state by a unitary operation.
M. Nakahara (
Department of Physics, Kinki University, Higashi-Osaka 577-8502, Japan