Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial
Quantum computers have the potential to provide exponential speedups over
their classical counterparts. Quantum principles are being applied to fields
such as communications, information processing, and artificial intelligence to
achieve quantum advantage. However, quantum bits are extremely noisy and prone
to decoherence. Thus, keeping the qubits error free is extremely important
toward reliable quantum computing. Quantum error correcting codes have been
studied for several decades and methods have been proposed to import classical
error correcting codes to the quantum domain. However, circuits for such
encoders and decoders haven't been explored in depth. This paper serves as a
tutorial on designing and simulating quantum encoder and decoder circuits for
stabilizer codes. We present encoding and decoding circuits for five-qubit code
and Steane code, along with verification of these circuits using IBM Qiskit. We
also provide nearest neighbour compliant encoder and decoder circuits for the
five-qubit code.
Arijit Mondal Keshab K. Parhi