Construction of Quantum LDPC Codes From Classical Row-Circulant QC-LDPCs

Classical row-circulant quasi-cyclic (QC) low-density parity check (LDPC) matrices are known to generate efficient high-rate short and moderate-length QC-LDPC codes, while the comparable random structures exhibit numerous short cycles of length-4. Therefore, we conceive a general formalism for constructing nondual-containing Calderbank–Shor–Steane (CSS)-type quantum low-density parity check (QLDPC) codes from arbitrary classical row-circulant QC-LDPC matrices. We apply our proposed formalism to the classical balanced incomplete block design (BIBD)-based row-circulant QC-LDPC codes for demonstrating that our designed codes outperform their dual-containing CSS-type counterparts as well as the entanglement-assisted (EA)-QLDPC codes.

I. Introduction

Quantum-domain parallel processing provides a plausible solution for achieving full-search based multi-stream detection [1], which is vital for future gigabit-wireless systems. The peculiar laws of quantum mechanics have also spurred interest in the absolutely-secure quantum-based communication systems [2], [3]. Unfortunately, quantum decoherence imposes a hitherto insurmountable impairment on the practical implementation of quantum computation as well as on quantum communication systems. More specifically, decoherence perturbs the fragile quantum states, which may be characterized either by bit-flips or phase-flips - or in fact possibly both - inflicted on the constituent qubits. Analogously to the classical error correction codes, these detrimental effects of decoherence may be overcome with the aid of efficient quantum error correction codes (QECCs).