TurboQuant

Rotation-based vector quantization algorithm from Google Research. Zandieh et al., 2026 (arXiv:2504.19874). Now ships in Qdrant 1.18 with production extensions. Part of the Vector Quantization family; in the same design space as RaBitQ.

Core Algorithm

1. Random orthogonal rotation — every vector is rotated; redistributes per-coordinate variance evenly so coordinates approximate N(0, 1) post-rotation
2. Coordinate-wise quantization — fixed Lloyd-Max codebook for the standard normal distribution; universal — no per-dataset training, no calibration set, no stored codebooks; one lookup table works across all embeddings and dimensionalities
3. Scoring — reconstruct dot product directly from codebook indices; orthogonal rotation preserves dot products and L2 distances

Two Paper Variants

Variant	Description	Trade-off
MSE	Literal recipe; codebook lookup only	Symmetric: any pair of stored vectors can be scored from indices alone
PROD	Adds QJL random projection to cancel per-vector length bias	Better bias correction; splits bit budget between codebook and projection

Qdrant ships MSE: symmetric scoring is required for HNSW graph construction; the length bias is fixed more cheaply via RaBitQ renormalization.

Compression Operating Points

Variant	Bits/dim	Compression
4-bit	4	8× vs float32
2-bit	2	16×
1.5-bit	1.5	~21×
1-bit	1	32×

Performance vs. Alternatives (Qdrant benchmarks, 10 datasets)

• TQ 4-bit vs SQ (4×): competitive — within 2 pp on 9/10 datasets; beats SQ on 3/10 (up to +4.6 pp); half the storage
• TQ 2-bit vs BQ 2-bit: +9–24 pp recall on every dataset
• TQ 1-bit vs BQ 1-bit: +9–21 pp recall on every dataset; still beats asymmetric BQ

Qdrant’s Production Extensions

Beyond the paper: Qdrant adds length renormalization from RaBitQ (per-vector scalar, 4 bytes), per-coordinate anisotropy compensation (P-Square quantile calibration per segment, free at query time), full L2/dot/cosine support (stores original L2 norm), and SIMD kernels (AVX-VNNI/AVX-512/NEON).

vs. Related Algorithms

Algorithm	Quantization approach	Key difference
RaBitQ	Rotation + binarization	Length rescaling + bit-plane scoring; complements TurboQuant
BBQ / OSQ	Binary + centering	Elasticsearch; uniform integer grid; SIMD-optimized
Product Quantization	Sub-vector codebooks	Per-dataset trained; high compression, higher build cost

Articles

• TurboQuant in Qdrant — Qdrant 1.18 implementation, production extensions, full benchmarks
• Elasticsearch BBQ Optimized Scalar Quantization vs TurboQuant — Elastic’s OSQ vs TurboQuant benchmarks

People

• Ivan Pleshkov — Qdrant; TurboQuant implementation
• Thomas Veasey — Elastic; OSQ/BBQ comparison benchmarks

Related Concepts

• Vector Quantization — parent concept
• Scalar Quantization — baseline at 4× compression; TurboQuant 4-bit achieves 8× at comparable recall
• Binary Quantization — baseline at 16–32×; TurboQuant beats BQ by 9–24 pp at same storage
• RaBitQ — companion rotation-based algorithm; contributes length renormalization and 1-bit scoring
• BBQ — Elasticsearch’s approach
• HNSW — TurboQuant’s MSE variant chosen for HNSW compatibility (symmetric scoring)
• Dense Vector Retrieval
• ANN

Mathematical Deep Dive

• The Mathematics of Google’s TurboQuant — Prateek Chandra Jha; first-principles derivation of PolarQuant + QJL; Beta distribution, Lloyd-Max quantizer, Johnson-Lindenstrauss lemma; within 2.7x of information-theoretic limit