t b a b a

All these achievements continuously showed us the computational potential of quantum
computer over classic computer.
Quantum information theory, like classical information theory, deals with information
which can be transmitted by using quantum systems as carriers. Modern classical comput-
ers guard against error largely by being digital instead of analog. At each time step the
hardware corrects the bit to standard 0 and 1 (digital instead of analog). This prevents
small errors from building up into large errors, which are therefore drastically reduced. The
same technique cannot be used in a quantum computer, because measurement on a single
qubit would destroy the entanglements that distinguish a quantum computer from a classical
one. Unlike the classic digital circuits, quantum operations are fully linear and reversible
and therefore will quickly accumulate noise. The no-cloning property makes it more difficult
to implement a reliable quantum communication.
Decoherence, the alteration of the quantum state as a result of the interaction with
the environment, is probably the most challenging problem faced by quantum computation
and quantum communication [Pre98]. Quantum error correcting codes, like classical error
correcting codes, allow us to deal algorithmically with decoherence. Over time, researchers
have come up with several codes: Peter Shor’s 9-qubit-code, also named the Shor code,
encodes 1 logical qubit in 9 physical qubits and can correct for one bit flip and one phase
flip error; Steane implemented the same code using 7 instead 9 qubits, named Steane code;
In 1996, Robert Calderband, Peter Shor and Andrew Steane discovered an important class
6