[jhj]

PQ is just a vector compression/quantization method, not an approximate k-NN search algorithm (like cell-probe or bucketing based methods such as IVF or LSH, or graph-based methods such as HNSW). HNSW can be used together with PQ encoding, for instance.

However PQ does have the nice property that distance computation can be performed with lookup-adds instead of multiply-adds but in practice performance is lower than normal brute-force multiply-add inner product because lookup table gather is slow on CPU or GPU relative to arithmetic. The gain of PQ is by dimensionality reduction (a 128 dimensional vector can be compressed as 8 PQ codes resulting in 8 lookup-adds, versus 128 FMAs for the brute-force inner product, say).