Colloquium

Speaker:   Bane Vasic, Professor, ECE Department, University of Arizona

Title:    Quantum Low-Density Parity Check Codes and Decoders Dealing with Degeneracy

Abstract:  Quantum error correction (QEC) is critical for the practical realization of fault-tolerant quantum computing. All quantum computers today use topological codes in which qubits are entangled through stabilizers locally. While this simplifies design, such codes have asymptotically diminishing rates and thus are not scalable with increasing qubits. Enabling non-local qubit connectivity is challenging with current hardware limitations, but it is the only way for scalable and fault-tolerant computing systems, and is pursued in various qubit architectures, including the one proposed by the speaker and his collaborators. 

The prime QEC code candidate in this regard is sparse non-local stabilizer codes - quantum low-density parity-check (QLDPC) codes. Despite being the quantum counterpart of extensively studied classical LDPC codes, the recognition and appreciation of QLDPC codes in their own right have only emerged relatively recently. They were proven to achieve a high encoding rate and code distance with linear scaling asymptotically. While these advantages of QLDPC codes are evident in the asymptotic regime, constructing practical finite-size QLDPC codes poses significant challenges. The stabilizer commutativity requirement primarily constrains the QLDPC code design flexibility. In addition, unreliable stabilizer measurement circuitry and long-range connectivity among qubits impose new code design constraints. Furthermore, such QLDPC codes are inherently degenerate - giving rise to more than one error having the same syndrome. 

Existing iterative decoding solutions fail to use this unique quantum feature of degeneracy and suffer both in the waterfall regime - high to moderate noise (qubit depolarizing probability) - and more so in the low noise - error floor regime. On the other hand, decoders that utilize complex and serial post-processing approaches, such as ordered statistics decoding, show good decoding performance but are impractical for implementation in quantum control hardware with stringent latency budgets. The challenge is to develop highly parallel, low-latency real-time decoders without sacrificing the error correction performance. 

In this talk we present our approach of addressing these which involves constructing finite-length QLDPC codes and developing fast and reliable low-complexity message-passing iterative decoders that leverage the inherent code structure and the degeneracy effect.