Entanglement-assisted quantum low-density parity-check codes

This article develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error-correction performance, high rates, and low decoding complexity. The proposed method produces several infinite families of codes with a wide variety of parameters and entanglement requirements. Our framework encompasses the previously known entanglement-assisted quantum LDPC codes having the best error-correction performance and many other codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.

Figure 1

Performance of type I EAQECCs.

Figure 2

Performance of type II EAQECCs.

Figure 3

Performance of type II EAQECCs.

Figure 4

Performance of high-rate type II EAQECCs.

Figure 5

Performance of EAQECCs obtained by deleting subdesigns from ${\mathrm{AG}}_1(3,3)$.