Cavity quantum electrodynamics (CQED)-based quantum LDPC encoders and decoders

Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment, resulting in errors. Moreover, the quantum gates are imperfect so that the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing. The QECC is also important in quantum communication and teleportation applications. The most critical gate, i.e., the CNOT gate, has been implemented recently as a probabilistic device by using integrated optics. CNOT gates from linear optics provide only probabilistic outcomes and, as such, are not suitable for any meaningful quantum computation (on the order of thousand qubits and above). In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, which are needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). Moreover, in CQED technology, the use of the controlled-$Z$ gate instead of the CNOT gate is more appropriate. We then show that encoders/decoders for quantum low-density parity-check (LDPC) codes can be implemented based on Hadamard and controlled-$Z$ gates only using CQED. We also discuss quantum dual-containing and entanglement-assisted codes and show that they can be related to combinatorial objects known as balanced incomplete block designs (BIBDs). In particular, a special class of BIBDsSteiner triple systems (STSs)yields to low-complexity quantum LDPC codes. Finally, we perform simulations and evaluate the performance of several classes of large-girth quantum LDPC codes suitable for implementation in CQED technology against that of lower girth entanglement-assisted codes and dual-containing quantum codes.