# QBit

`QBit` stores a numeric vector with a fixed element type and dimension. Its distance functions let a query choose how much precision to use when comparing the vector with a reference array.

## Creating QBit

```text
QBit(T, N)
QBit(T, N, stride)
```

## Parameters

* `T` — `Int8`, `BFloat16`, `Float32` or `Float64`.
* `N` — A positive number of coordinates. Every input must contain exactly `N` non-`NULL` coordinates.
* `stride` — A positive group size dividing `N`. The default is `N`. A smaller stride must be a multiple of eight.

Coordinates are converted to `T`. Use JSON array text or an array value as input.

## Vector search functions

`l2_distance_transposed`, `cosine_distance_transposed` and `dot_product_transposed` accept a QBit vector, an Array reference and a precision from 1 through the element bit width.

A full-precision probe recovers the stored coordinate values. A lower precision can change the result. The optional `used_dims` argument must be a positive multiple of stride and cannot exceed `N`; omitting it requires a reference for the full dimension.

Results are Float64. SQL `NULL` propagates, nonfinite coordinates raise an error, and cosine distance with a zero-norm vector returns `NULL`.

## Examples

### Euclidean distance

The vectors differ by one unit in their final coordinate:

```sql
SELECT l2_distance_transposed(
    CAST('[1,2,3]' AS QBit(Float32, 3)),
    array(1, 2, 4),
    32
)
FORMAT csv;
```

```text
1.0
```

### An identical reference

```sql
SELECT l2_distance_transposed(
    CAST('[1,2,3]' AS QBit(Float32, 3)),
    array(1, 2, 3),
    32
)
FORMAT csv;
```

```text
0.0
```

See [vector distance functions](https://coordinatordb.com/docs/reference/functions/regular-functions/distance-functions) for the complete function signatures and aliases.