Unitary dynamics for quantum codewords

Abstract

A quantum codeword is a redundant representation of a logical qubit by means of several physical qubits. It is constructed in such a way that if one of the physical qubits is perturbed, for example if it gets entangled with an unknown environment, there still is enough information encoded in the other physical qubits to restore the logical qubit, and disentangle it from the environment. The recovery procedure may consist of the detection of an error syndrome, followed by the correction of the error, as in the classical case. However, it can also be performed by means of unitary operations, without having to know the error syndrome. Since quantum codewords span only a restricted subspace of the complete physical Hilbert space, the unitary operations that generate quantum dynamics (that is, the computational process) are subject to considerable arbitrariness, similar to the gauge freedom in quantum field theory. Quantum codewords can thus serve as a toy model for investigating the quantization of constrained dynamical systems.