Problem
Research questions and friction points this paper is trying to address.
quantum LDPC codes
practical constraints
rate-distance tradeoff
finite-length codes
CSS codes
Multi-agent discovery of practical quantum LDPC codes
🤖 AI Summary
This work addresses the ongoing challenge of efficiently discovering high-performance finite-length quantum low-density parity-check (qLDPC) codes under practical constraints—specifically, code length $n \leq 400$ and weight $w \leq 10$. To this end, it introduces, for the first time, a structured multi-agent search framework that integrates expert proposal and review mechanisms, persistent scientific memory, and closed-loop deterministic evaluation. This framework enables the construction of coset-orbit balanced product codes under non-regular subgroup actions, substantially expanding the searchable design space while preserving hardware feasibility. The approach yields several novel CSS codes, including [[288,16,18]] with $w=7$ and [[234,28,18]] with $w=10$, which demonstrate state-of-the-art logical error rate performance under depolarizing noise.
📝 Abstract
Quantum low-density parity-check (qLDPC) codes can encode multiple logical qubits using sparse parity checks, yet searching for useful finite-length instances remains a challenging design problem because code performance must be optimized while satisfying practical constraints. Motivated by recent advances in artificial-intelligence agents for scientific discovery, we develop a multi-agent framework for discovering practical qLDPC codes. The framework combines specialist proposal and review, persistent scientific memory, long-horizon evolution of executable programs, and deterministic construction and evaluation within a closed-loop search. These programs instantiate coset-orbit balanced-product codes, providing a search space that includes bicycle and lifted-product constructions as well as non-normal subgroup actions. To incorporate practical constraints, we restrict the search to binary CSS codes with block length $n\leq400$ and overall weight $w\leq10$. Within this regime, the framework discovers codes with leading or competitive rate--distance performance in every weight class considered, with representative instances including $[[288,16,18]]$ at $w=7$, $[[288,18,18]]$ at $w=9$, and $[[234,28,18]]$ at $w=10$. The search also uncovers structurally distinct, high-performing constructions, including a $[[336,12,\leq24]]$ candidate and a $[[368,18,16]]$ code, both of which are genuine balanced-product constructions with non-normal subgroup actions. When evaluated under code-capacity depolarizing noise using a common BP-OSD decoding protocol, the discovered codes also exhibit low logical failure rates. Together, these results provide hardware-relevant finite-length candidates for further experimental evaluation and show how structured agentic search can contribute to scientific discovery.
Innovation
Methods, ideas, or system contributions that make the work stand out.
multi-agent discovery
quantum LDPC codes
balanced-product construction
non-normal subgroup actions
structured agentic search
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