Written comprehensive exam: Quantum LDPC Codes

On the non-existance for quantum LDPC codes of type IEEE802.16e with rates 1/2 and 2/3B

In this paper, we discuss a construction of CSS codes derived from pairs of practical irregular LDPC codes. Intersection studies between quantum error-correcting codes and LDPC codes are current hot research topics [1], [3], [4], [5], [6], [7], [8], [9]. One of aims of quantum error-correcting code theory is to construct quantum error-correcting codes with small length and high error-correcting...

On the non-existence for quantum LDPC codes of type IEEE802.16e with rates 1/2 and 2/3B

In this paper, we discuss a construction of CSS codes derived from pairs of practical irregular LDPC codes. Intersection studies between quantum error-correcting codes and LDPC codes are current hot research topics [1], [3], [4], [5], [6], [7], [8], [9]. One of aims of quantum error-correcting code theory is to construct quantum error-correcting codes with small length and high error-correcting...

Fault-Tolerance of ”Bad” Quantum Low-Density Parity Check Codes

Quantum low-density parity check (LDPC) codes such as generalized toric codes with finite rate suggested by Tillich and Zémor offer an alternative route for quantum computation. Here, we study LDPC codes and show that any family of LDPC codes, quantum or classical, where distance scales as a positive power of the block length, has a finite error threshold. Based on that, we conclude that quantu...

Good quantum codes with low-weight stabilizers

Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their potential applications in fault-tolerant quantum computing. However, all families of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good families of LDPC ...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes