Generative sequence models have shown strong results in recommendation. Applying them to search ranking is more challenging. Search behavior is inherently query-driven. Each query switch introduces a sharp topic shift in the user's interaction history. Existing generative methods flatten queries and items into a single token sequence. They do not distinguish query boundaries. This causes the model to mix different query intents into one prediction target, resulting in noisy supervision. We present Query-Conditioned Generative Search (QGS). QGS encodes each interaction as a (query, item) pair token. It trains with a query-conditioned next-item objective. The prediction target changes from a noisy marginal P(item_{t+1}|context_{<=t}) to a clean conditional P(item_{t+1}|context_{<=t}, query_{t+1}). This directly removes the semantic discontinuity caused by query switches. Encoding long interaction histories with standard attention has quadratic cost. This is impractical under strict online latency budgets. We introduce a Linear HSTU encoder. It replaces full attention with causal linear recurrence. Per-layer complexity drops from O(L^2) to O(L) with no loss in ranking quality. Traditional search ranking depends on hand-crafted features like text-matching scores, statistical signals, and behavioral features. We propose HFG-Attention to preserve them in the generative framework. It organizes heterogeneous features into semantic groups and fuses them through a dedicated attention block. This bridges sparse engineered signals with dense sequential representations. QGS is deployed in the ranking module of Quark Search, a major commercial search engine in China. Online A/B tests show statistically significant gains: +0.62% CTR, +0.38% Click-Search Ratio, and +3.55% PV Duration over the production deep learning baseline.

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