README.md

---
license: mit
configs:
- config_name: static-embedding-v0
  data_files:
  - split: train
    path: "metadata/static-embedding-v0.parquet"
- config_name: universal-geometry-v1
  data_files:
  - split: train
    path: "metadata/universal-geometry-v1.parquet"
- config_name: universal-geometry-v2
  data_files:
  - split: train
    path: "metadata/universal-geometry-v2.parquet"
tags:
- quantum
- superconducting
- qiskit-metal
- gds
- layout
- embedding
- geometry
- computer-vision
pretty_name: SQuADDS Layout Embeddings
size_categories:
- 10K<n<100K
---

<center>
  <img src="https://github.com/LFL-Lab/SQuADDS/blob/master/docs/_static/images/squadds_logo_dark_name.png?raw=true" width="80%" alt="SQuADDS Logo" />
</center>

# SQuADDS Layout Embeddings

Versioned layout representations for the 24,106 GDS artifacts in
[SQuADDS/SQuADDS_Layouts](https://huggingface.co/datasets/SQuADDS/SQuADDS_Layouts).

## Static embedding model `v0`

`static-embedding-v0` implements the original SQuADDS proof-of-concept model:

```text
v0 = parameter_sum + geometric_moments + flattened_shape_bitmap
```

Each unit-normalized vector has **9,227 dimensions**:

| Block | Dimensions | Contents |
| --- | ---: | --- |
| Parameter sum | 1 | Permutation- and parameter-count-invariant sum of numerical design options, converted to micrometers where units are present |
| Geometric moments | 10 | Functional area, perimeter, aspect ratio, occupancy, centroid, second central moments, and eccentricity |
| Shape tensor | 9,216 | Row-major flattened 96×96 signed bitmap of functional GDS geometry |

The bitmap uses `+1` for conductor, `-1` for etch, `+0.5` for explicit port
geometry, and `0` for background. Geometry is cropped to its functional bounds,
centered without distortion, supersampled at 4×, and reduced to 96×96. The
large simulation-domain ground rectangle on layer `(1, 0)` is excluded so it
does not hide the component shape.

This is a deterministic static embedding, not a learned model. It remains a
transparent baseline and a stable input for similarity search.

The exact block offsets, moment order, raster semantics, normalization
statistics, and source schema are frozen in
`metadata/static-embedding-v0.schema.json`.

## Universal geometry model `v1`

`universal-geometry-v1` is an additive 1,024-dimensional standard built from only
a GDS file, a functional layer-role mapping, and the native design-parameter
dictionary. Simulation targets are never embedded.

| Block | Dimensions | Contents |
| --- | ---: | --- |
| Geometry metrics | 32 | Centered physical and morphological metrics; availability remains metadata rather than distorting cosine distance |
| Multiscale shape | 768 | Target-blind, variance-selected full-spectrum 2D DCT coefficients from 96×96 signed-material and boundary-distance rasters |
| Parameter controls | 224 | Stable signed feature hashing of canonical parameter paths after per-parameter centering and scaling |

The metric block retains physical scale and role-specific conductor, etch, and
port measurements. The shape block captures finger topology and boundary detail
without storing a dense pixel tensor. Each block is normalized and explicitly
weighted, and every fitted statistic and selected spectral frequency is frozen
in the schema.

Parameter identity is retained on every row through `parameter_names`,
`parameter_values`, `parameter_hash_indices`, and `parameter_hash_signs`.
`models/universal-geometry-v1/control-map.parquet` provides the global,
auditable bridge back to the originating layout controls.

This first v1 configuration contains all **20,062**
`GeneralizedCapNInterdigital` designs. The encoder accepts foreign GDS layouts
when their `(layer, datatype)` pairs are mapped to `conductor`, `etch`, or
`port`; the cross-component reference normalization will be frozen in a later
release after it is calibrated on the full SQuADDS catalogue.

The complete input contract, block offsets, transforms, normalization
statistics, and invariances are frozen in
`models/universal-geometry-v1/schema.json`.

The earlier 512-dimensional v1.0 candidate was rejected before release because
its 8×8 low-pass shape crop lost finger detail and its common offsets collapsed
cosine similarities. V1.1 passed paired topology, parameter-locality, shape,
held-out capacitance-locality, and similarity-dynamic-range gates against v0
across five deterministic held-out samples. Capacitance was never used to fit
the embedding.

## Universal geometry model `v2`

`universal-geometry-v2` is additive and answers a question v0 and v1 cannot: how
does a contributor who has never seen this catalogue produce a vector that is
directly comparable to it?

Both earlier standards are **fit on write**. Their normalization statistics, and
in v1 the selected spectral frequencies, come from whichever rows are written
together, so an outside group running the same builder lands in a different
space even though the vectors share a length. v2 removes that coupling: every
one of its 512 coordinates is a physical measurement in micrometers, inverse
micrometers, or farads per meter, accumulated onto frozen bin edges. The encoder
is a pure function of one GDS file and one design-option mapping.

| Block | Dimensions | Contents |
| --- | ---: | --- |
| Physical metrics | 48 | Absolute extent, per-role area and perimeter, conductor width percentiles, gap integrals, symmetry |
| Coupling spectrum | 192 | Facing boundary length per terminal pair per absolute separation, plus each terminal against ground |
| Shape spectrum | 128 | Two-point correlation, terminal cross-correlation, conductor width distribution, contour harmonics |
| Parameter statistics | 96 | Dimension-typed order statistics with dimension-scoped signed hashing |
| Physics proxy | 48 | Two-dimensional boundary-element capacitance matrix and dilation topology |

Terminals are discovered as connected components of the conductor layer and
ordered by port marker, never declared, so a foreign layout with different pin
names still yields terminal 0 and terminal 1. The parameter block classifies each
option by physical dimension rather than by name, which lets a 28-parameter
foreign schema and a 40-parameter local one occupy the same 96 coordinates.

v2 is deliberately **not** scale invariant. v0 and v1 crop each layout to its own
functional bounds, so a design and its exact enlargement produce identical shape
blocks; because conductor separation in micrometers is the dominant variable for
capacitance, v2 measures distances absolutely.

Simulation targets are never embedding inputs.

### Rebuilt on the unified layout convention

`TransmonCross` and `CapNInterdigitalTee` were regenerated in
[SQuADDS/SQuADDS_Layouts](https://huggingface.co/datasets/SQuADDS/SQuADDS_Layouts)
to adopt the `GeneralizedCapNInterdigital` layer convention: a ground plane with a
fixed **169 um per-side margin**, the etch expressed as a hole in that plane
rather than as layer `1/11`, and two ordered ports bridging the moat from each
terminal to ground. Their v2 rows are rebuilt from that geometry.

The margin is absolute rather than proportional to the device. Padding in the
reference `GeneralizedCapNInterdigital` sweep is essentially uncorrelated with
conductor width (Pearson -0.10), so an earlier proportional rule placed the
ground plane furthest from the largest device, which is the opposite of what an
absolutely anchored coupling spectrum needs. 169 um is the pooled median of the
per-side paddings measured from that sweep.

**Every one of the 14,899 rows for the families that were not regenerated is
byte-identical to the previous release.** Correcting two component families
changed nothing for the other two, because no v2 coordinate is derived from
catalogue statistics. This is the fit-on-write property being absent, verified
against a real geometry change rather than asserted.

`layout_id` changed for the regenerated rows, matching the layouts dataset;
`design_id` and `source_id` are unchanged.

The correction is not cosmetic: it moves held-out cross-component prediction
substantially, and it is what makes all four families share one reference frame.
Current figures are reported in the SQuADDS tutorials rather than restated here,
so they cannot drift out of step with the notebooks that produce them. See
Tutorial 20 (cross-class study) and Tutorial 21 (transfer protocol).

`static-embedding-v0` is **unchanged** and still reflects the pre-correction
geometry together with its original role map, which recognizes ports only for
`GeneralizedCapNInterdigital` and discards the `TransmonCross` etch layer. It is
fit on write, so rebuilding it would alter all 24,106 vectors including families
that were never touched. A port-complete role profile is available in the SQuADDS
package for users who want to rebuild it themselves.

### Coverage of this v2 table

This release contains **17,727** designs spanning **all four** component
families, so v2 is the first standard here that covers the whole catalogue with
a single encoder and no per-family configuration.

The `GeneralizedCapNInterdigital` count is 13,683 rather than the 20,062 that v0
and v1 hold for that family. The reason is upstream:
[SQuADDS/SQuADDS_Layouts](https://huggingface.co/datasets/SQuADDS/SQuADDS_Layouts)
currently publishes 10,000 of the 16,379 `q3d_cap` GDS artifacts that its own
`metadata/manifest.parquet` lists, so the remaining 6,379 layouts cannot be
encoded from released geometry. v0 and v1 were generated before that gap
appeared. `models/universal-geometry-v2/release-manifest.json` records the count
as `layouts_without_downloadable_gds`. Restoring the missing artifacts and
re-running the builder is the only step needed for full coverage; the encoder
does not change.

Every one of the 13,683 vectors published in the previous v2 release is
**byte-identical** in this one. Adding three component families changed none of
them, because no coordinate is derived from catalogue statistics. That is the
fit-on-write property being absent, demonstrated rather than asserted, and it is
the property that lets an outside contribution be concatenated with this table
instead of requiring a rebuild.

### Evidence

Under an identical model, split policy, and label budget over the 13,683 paired
designs, with 13 finger-count domains and 12 stratified holdouts:

| Held-out macro R² | 1% labels | 10% labels | 100% labels |
| --- | ---: | ---: | ---: |
| `static-shape-v0` (155 compact features) | 0.235 | 0.888 | 0.984 |
| `universal-geometry-v2` | 0.780 | 0.9915 | 0.9998 |
| `universal-geometry-v2`, geometry block only | 0.754 | 0.9896 | 0.9996 |

The third row is the control that matters: it receives no design parameters at
all and still beats the whole of v0, which does include v0's parameter sum, so
the improvement is geometric rather than an artifact of v2 retaining more
parameter detail.

A single unfitted coordinate, the facing-boundary integral
`log1p_primary_inverse_gap_integral`, reaches Spearman +0.941 against the
simulated mutual capacitance; the boundary-element proxy reaches +0.920. The
minimum gap on its own reaches only −0.165, because gap alone does not set
capacitance — gap weighted by facing boundary length does.

Known limits: only one component class is measured so far; extrapolating to
devices larger than any in training the advantage narrows to 0.810 against v0's
0.769; and raw cosine similarity has a compressed spread, so a frozen whitening
transform should be published as a separate metric layer before v2 similarity is
used as a headline number.

The complete input contract, block offsets, transforms, bin edges, and
invariances are frozen in `models/universal-geometry-v2/schema.json`.

### Cross-component evidence

Because v2 now covers every family, three of them - `GeneralizedCapNInterdigital`,
`CapNInterdigitalTee`, and `TransmonCross` - can be joined into one supervised
task, since each reports a mutual capacitance between two conductors
(`north_to_south`, `top_to_bottom`, and `cross_to_claw`). Across those three the
design-option vocabularies intersect in exactly one name, `orientation`, a
placement angle, so no parameter-schema baseline exists for a three-class model.

On a class-balanced cohort of 894 designs each, a model trained on two families
and given **zero labels** from the third reaches macro R2 0.859 and 0.422 in two
of the three rotations, where `static-shape-v0` reaches -7.7 and -17.6. A
brand-new component family needs roughly ten labeled designs to pass macro R2
0.94.

Two limits are worth stating with the result. The third rotation,
`TransmonCross`, stays negative at -1.891, and cross-class cosine similarity has
the wrong sign on every class pair involving that qubit family. Similarity is a
reliable applicability signal within a component family and is not yet reliable
across one.

## Similarity metric `metric-v1`

v2 coordinates are non-negative log-magnitudes in absolute physical units, so
every device shares a large common direction and a **raw cosine saturates**:
within `TransmonCross` the whole family spans a similarity standard deviation of
0.0005, and nearest-neighbour queries return 1.0000 for their top matches. The
vectors are not wrong. A raw cosine is simply the wrong metric for a
non-negative, absolutely anchored representation.

`metric-v1` is a frozen transform that fixes this while keeping the two concerns
separate, which is the point of the design:

* the **vectors** stay catalogue-free and byte-stable forever;
* the **metric** is fitted once on the reference catalogue, frozen, published,
  and versioned independently.

A newcomer applies the published transform and never refits it, so two
contributions remain directly comparable, exactly as with the vectors.

| Property | Value |
| --- | --- |
| Transform | centre, scale, shrinkage-regularized ZCA whitening, then cosine |
| Shrinkage | 0.70, selected by sweeping against within- and cross-family rank correlation |
| Fitted rows | 17,727 across all four families |
| Retained dimensions | 303 of 512 |

The 209 discarded coordinates are constant across the entire catalogue. Most are
the five unused terminal-pair slots and two unused terminal-to-ground slots: the
encoder reserves capacity for four terminals and six pairs, and every design
published so far is two-terminal. Those coordinates are reserved, not broken,
and a multi-terminal family would populate them.

Effect on within-family similarity spread:

| Family | Raw cosine sd | `metric-v1` sd |
| --- | ---: | ---: |
| TransmonCross | 0.0005 | 0.2776 |
| CavityClawRouteMeander | 0.0195 | 0.3016 |
| CapNInterdigitalTee | 0.0411 | 0.1971 |
| GeneralizedCapNInterdigital | 0.0415 | 0.1987 |

Mean cross-family similarity falls to approximately zero while within-family
similarity stays positive, which is the behaviour a retrieval metric needs and
which the raw cosine does not provide.

```python
from squadds.layouts import LayoutEmbeddingClient

client = LayoutEmbeddingClient()
client.nearest(design_id, model="universal-geometry-v2", metric="whitened")
```

Files: `models/universal-geometry-v2/metric-v1.json` (contract and checksum) and
`models/universal-geometry-v2/metric-v1.npz` (arrays).


## Coverage and links

| Component | `v0` | `v1` | `v2` |
| --- | ---: | ---: | ---: |
| `GeneralizedCapNInterdigital` | 20,062 | 20,062 | 13,683 |
| `CapNInterdigitalTee` | 894 | — | 894 |
| `CavityClawRouteMeander` | 1,216 | — | 1,216 |
| `TransmonCross` | 1,934 | — | 1,934 |

Every row retains `layout_id`, `artifact_id`, `design_id`, `component_name`,
and `source_id`, plus the raw parameter sum, geometric moments, functional
bounds, and a SHA-256 hash of the 96×96 bitmap.

The normalization statistics in this release are fit across all four component
families. Existing layout identities and shape bitmaps remain stable; vectors
are republished together so cosine similarity remains comparable across the
complete catalogue.

## Access

```python
from squadds.layouts import LayoutEmbeddingClient, StaticEmbeddingClient

v0 = StaticEmbeddingClient()  # Backward-compatible alias
v1 = LayoutEmbeddingClient(version="v1")
v2 = LayoutEmbeddingClient(version="v2")

record = v2.get("layout:sha256:<layout hash>")
neighbors = v2.nearest(record["layout_id"], limit=10)
schema = v2.schema()
```

Because v2 consults no catalogue statistics, a layout that is not in this
dataset can be encoded directly into the same space:

```python
from squadds.layouts import encode

vector = encode("my_capacitor.gds", {"digit_pitch": "5.5um", "digit_population": 9})
```

SQuADDS_DB rows can resolve the same vector directly with
`SQuADDS_DB.get_layout_embedding(row, embedding_version="v2")`. Omitting the
version preserves the v0 default. The SQuADDS MCP server also provides
`get_layout_embedding` and `find_similar_layouts`.

## Provenance

Raw GDS artifacts, layer semantics, checksums, and geometry features live in
[SQuADDS/SQuADDS_Layouts](https://huggingface.co/datasets/SQuADDS/SQuADDS_Layouts).
Simulation results and design options live in
[SQuADDS/SQuADDS_DB](https://huggingface.co/datasets/SQuADDS/SQuADDS_DB).
The generalized-capacitor dataset was contributed by Saikat Das of the
Levenson-Falk Lab at USC.

## Citation

If you use this dataset, cite SQuADDS:

```bibtex
@article{Shanto2024squaddsvalidated,
  doi = {10.22331/q-2024-09-09-1465},
  title = {{SQ}u{ADDS}: {A} validated design database and simulation workflow for superconducting qubit design},
  author = {Shanto, Sadman and Kuo, Andre and Miyamoto, Clark and Zhang, Haimeng and Maurya, Vivek and Vlachos, Evangelos and Hecht, Malida and Shum, Chung Wa and Levenson-Falk, Eli},
  journal = {{Quantum}},
  volume = {8},
  pages = {1465},
  year = {2024}
}
```

This dataset is licensed under the [MIT License](https://github.com/LFL-Lab/SQuADDS/blob/master/LICENSE).