Autoregressive decoding remains a key bottleneck for LLM inference, due to its token-by-token nature. Speculative decoding is proposed to reduce latency by drafting multiple tokens and verifying them with fewer target-model passes. However, existing methods either incur auxiliary-drafter overhead or rely on brittle lexical span reuse. In structured tasks (e.g., code generation and text editing), we observe significant locality of reference and semantic redundancy for potential semantic context reuse. In light of this, we present Semantic Retrieval Speculative Decoding (SRSD), a training-free scheme that treats intermediate-layer hidden states as an in-context semantic index. At each decoding step, SRSD retrieves semantically similar past positions. Multiple candidates are merged into a compact tree and verified jointly in a single forward pass. SRSD requires no auxiliary models or external datastores. Across a variety of popular LLMs, SRSD achieves up to 5.42× throughput speedups over state-of-the-art training-free methods and parametric drafters. The code is available at https://github.com/Secbrain/SRSD.

Large language models have recently advanced automated program repair, yet most existing approaches provide only post-hoc natural-language explanations that are neither executable nor verifiable. This limitation is especially critical for quantum programs, where correctness hinges on subtle semantic properties such as circuit equivalence and fidelity preservation. We propose Explainable Quantum Program Repair, a framework that couples repair generation with machine-checkable executable explanations. Given a buggy quantum circuit, a language model proposes candidate repairs together with structured transformation rationales, which are compiled into proof traces and validated using formal verification backends, including circuit equivalence checking, ZX-calculus reasoning, stabilizer analysis, and quantum simulation. Only repairs whose explanations are fully verified are accepted. Experiments on QASMBench with mutation-generated quantum program bugs demonstrate that our approach achieves competitive repair success while substantially improving semantic precision and explanation faithfulness over baselines that rely on unconstrained or purely natural-language explanations.