Gates

Gates in yao-rs are represented by the Gate enum, covering standard qubit gates, parameterized rotations, and custom matrices.

#![allow(unused)]
fn main() {
pub enum Gate {
    X, Y, Z, H, S, T, SWAP,
    Phase(f64),
    Rx(f64), Ry(f64), Rz(f64),
    Custom { matrix: Array2<Complex64>, is_diagonal: bool },
}
}

Named Qubit Gates

Gate	Matrix	Diagonal
`X`	`[[0, 1], [1, 0]]`	No
`Y`	`[[0, -i], [i, 0]]`	No
`Z`	`[[1, 0], [0, -1]]`	Yes
`H`	`1/sqrt(2) [[1, 1], [1, -1]]`	No
`S`	`[[1, 0], [0, i]]`	Yes
`T`	`[[1, 0], [0, e^(i*pi/4)]]`	Yes

SWAP Gate

The 2-qubit Gate::SWAP acts on 2 sites. Its 4x4 matrix swaps the |01> and |10> basis states.

Rotation Gates

Rx(theta): [[cos(theta/2), -i*sin(theta/2)], [-i*sin(theta/2), cos(theta/2)]]
Ry(theta): [[cos(theta/2), -sin(theta/2)], [sin(theta/2), cos(theta/2)]]
Rz(theta): [[e^(-i*theta/2), 0], [0, e^(i*theta/2)]] – diagonal

Phase Gate

Gate::Phase(theta) represents diag(1, e^(i*theta)). This is equivalent to Yao.jl’s shift(theta).

Special cases:

Phase(pi) = Z
Phase(pi/2) = S
Phase(pi/4) = T

The Phase gate is diagonal.

Custom Gates

#![allow(unused)]
fn main() {
Gate::Custom {
    matrix: Array2<Complex64>,
    is_diagonal: bool,
}
}

Provide an arbitrary unitary matrix. The is_diagonal flag tells the tensor network exporter to use the diagonal optimization (shared legs instead of separate input/output legs).

The matrix dimension determines how many sites the gate acts on: a d^n x d^n matrix acts on n sites of dimension d.

Diagonal Gate Optimization

In tensor networks, diagonal gates have one shared leg per site instead of separate input and output legs. This reduces the tensor rank and can improve contraction efficiency.

Gates that are diagonal: Z, S, T, Phase(theta), Rz(theta), and any Custom gate with is_diagonal: true.

Getting the Matrix

#![allow(unused)]
fn main() {
let mat = Gate::H.matrix(2);  // d=2 for qubits
}

Named gates require d=2 (will panic otherwise). Custom gates work with any dimension.

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