gate.directory

Gate Directory is a website dedicated to cataloging quantum gates used across the field of quantum information and computation.

Local Development

The website is built with static site generator 11ty, and to build it locally, you'll need Node.js.

1. Clone the repository:

   git clone git@github.com:natestemen/gate.directory.git
   cd gate.directory

2. Install dependencies:

   npm install

3. Start the development server:

   npm run serve

4. The npm run serve command will indicate which port the pages are being served from on your machine.

When deploying to GitHub Pages the build uses a path prefix of /gate.directory/ so asset URLs resolve correctly. Locally you can override this with the PATH_PREFIX environment variable:

PATH_PREFIX=/ npm run build

Writing math

Anything between $…$ or $$…$$ is handed to KaTeX untouched (see lib/markdown-math.js), so write plain LaTeX: \\ for matrix rows, \, for thin spaces, \{, and _ wherever you like. No Markdown escaping is needed inside math.

Gate definitions

Each gate's front matter carries a machine-readable definition that drives the "unitary, drawn" panel, the JSON API and the consistency checks:

params:
  theta: { label: \theta, default: 1/2, range: [0, 2] }   # angles; defaults and ranges in units of π
matrix:
  - ["cos(theta/2)", "-i sin(theta/2)"]                    # expressions: inside them a parameter
  - ["-i sin(theta/2)", "cos(theta/2)"]                    #   stands for the angle in radians
matrix_note: d = 3                                         # optional: the instance shown for n- or d-dependent gates

The expression language (js/gate-math.js) has + - * / ^, parentheses, juxtaposition as multiplication (2 pi t, i sin(x)), the constants pi, e, i, and sqrt exp cos sin tan acos asin atan ln. The first qubit is the most significant bit. Gates whose size depends on n or d (QFT, MCX, the qudit gates) give a small instance and say so in matrix_note.

npm run check verifies every matrix is unitary, that each Quirk circuit reproduces its matrix, and that the Weyl coordinates agree with the matrix via Makhlin's invariants. It runs in CI on every push.

JSON API

The built site publishes the same data as JSON:

• /api/gates.json — every gate, in the order of the table on the home page
• /api/gates/<slug>.json — one gate, for example /api/gates/cnot.json
• /api/groups.json — the groups and their members

Records are deliberately lean: slug, title, symbol (LaTeX), aliases, notations (LaTeX), description, qubit count and dimension, the parameters (label, default and range in units of π), the matrix as expressions (and matrix_note for the instance shown), groups, properties and the page URL. Evaluate the matrix with js/gate-math.js or any CAS; a parameter name inside an entry is the angle in radians.

Quirk links

Gate pages link to the gate in Quirk when the front matter has a quirk entry. Either list Quirk's gates per circuit column (the top wire is the page's first qubit), or give the unitary as a Quirk matrix string (Quirk's wires are little-endian, so the first qubit of the page's matrix is the last index). Parameterised circuits reference the gate's params from Quirk's formula gates (Rxft, Ryft, Rzft, Z^ft) with param and an optional mul; rotation gates read the value in radians, Z^ft as an exponent. spin gives each parameter's rate in Quirk's clock t (0 to 1, repeating): the link substitutes spin × t, so the gate spins through its family and loops seamlessly, and the unitary panel's play button follows the same path. Constant angles use arg with a Quirk formula. note (LaTeX) overrides the generated description; phase records a global phase the page's matrix carries and the circuit cannot.

quirk:
  cols: [["•", "X"]]                            # CNOT from Quirk's own gates

quirk:
  spin: {theta: 4}                              # theta = 4πt in the link
  cols:
    - ["•", {id: Rxft, param: theta}]           # or {id: Rzft, param: theta, mul: -0.5}

quirk:
  matrix: "{{1,0,0,0},{0,0,i,0},{0,i,0,0},{0,0,0,1}}"
  name: iSWAP                                   # label drawn on the gate in Quirk
  controls: 1                                   # optional control wires in front of the gate

Weyl chamber coordinates

Two-qubit gate pages show where the gate sits in the Weyl chamber. The data lives in each gate's front matter, in units of π, using the convention of the canonical gate: U ≃ exp(i(a XX + b YY + c ZZ)) up to single-qubit gates, reduced to π/4 ≥ a ≥ b ≥ |c| (the canonical form Qiskit and Cirq use as well).

Fixed gates give the point directly:

weyl: [1/4, 0, 0]   # CNOT

Parameterised gates give the raw exponent coefficients as expressions in the gate's params (see "Gate definitions"); the Weyl panel's sliders are the same parameters as the matrix panel's, and the two stay in step:

params:
  theta: { label: \theta, default: 1/2, range: [0, 2] }
weyl:
  coords: [-theta/2, 0, 0]   # R_xx(θ) = exp(-iθ/2 X⊗X); here theta is in units of π

The page reduces the raw coefficients to the chamber itself, so write whatever falls out of the gate's definition. Only signed fractions of a single parameter are understood (-phi/4, 3/16, a). The drawing is done by js/weyl.js.