RaBitQ

Rotation-based binary vector quantization algorithm. Gao & Long, SIGMOD 2024 (arXiv:2405.12497). Shares the same “rotate then quantize” foundation as TurboQuant but with different choices: pure binarization instead of Lloyd-Max codebook, and asymmetric 1-bit scoring.

Core Ideas

1. Random orthogonal rotation before quantization — same as TurboQuant; equalizes coordinate variance
2. Per-vector length rescaling — store one scalar per vector recording how much quantization shrank the length; multiply back at score time. Fixes the systematic length bias of rotation-based methods at cost of 4 bytes/vector (one multiplication). More efficient than TurboQuant PROD’s full QJL projection.
3. 1-bit asymmetric scoring — data stored as one bit/coordinate (sign after rotation); query stored as B-bit scalar quantization transposed into B bit-planes. Inner product = AND + popcount per bit-plane, weighted by 2^b

Relationship to TurboQuant

	TurboQuant (MSE)	RaBitQ
Rotation	Random orthogonal	Random orthogonal
Quantization	Lloyd-Max codebook (universal, no training)	Pure binarization (sign)
Length correction	PROD variant (QJL, expensive)	Per-vector scalar (4 bytes, cheap)
1-bit scoring	Codebook lookup	Bit-plane AND + popcount

Qdrant’s TurboQuant implementation borrows RaBitQ’s length renormalization and 1-bit bit-plane scoring, combining them with TurboQuant’s MSE codebook and anisotropy compensation.

Where Used

• Qdrant borrows length renormalization and 1-bit scoring for the TurboQuant 1.18 implementation

Articles

• TurboQuant in Qdrant — explains how RaBitQ ideas are incorporated

A Special Case of ASH

ASH (2026) reframes RaBitQ as one corner of a larger design space: RaBitQ is what you get from ASH when you drop the dimensionality reduction, use a single cluster, and take a random rotation instead of a learned one. Extended RaBitQ is the same with more than one bit per dimension.

The reframing sharpens what RaBitQ trades away. The random rotation is why it needs no training and carries a theoretical error bound — but that bound assumes the data is spread evenly over the sphere, and real embeddings are not, so a rotation fitted to the corpus can do better. ASH measures 2.3–7.1 points higher terminal recall at the same compression.

Related Concepts

• ASH — generalizes RaBitQ with a learned projection and dimensionality reduction
• ITQ — the older learned rotation for binarization
• TurboQuant — companion rotation-based algorithm; different quantization approach
• Binary Quantization — RaBitQ is a rotation-enhanced variant of binary quantization
• Vector Quantization — parent concept
• BBQ — Elasticsearch’s binary quantization (different design space)
• HNSW — the index RaBitQ-style quantization operates with
• Dense Vector Retrieval