Merge pull request 'test(symclaw-skill): cover handlers_advanced via JSON API' (#10) from ci-doctor/coverage-20260518-201834 into master
Reviewed-on: #10
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redclawsystems
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//! Single-qubit Clifford gates expressed in terms of Cl(3,0) multivectors.
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//!
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//! The single-qubit Clifford group is generated by H and S.
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//! In Cl(3,0) = Pauli algebra: σ_x = e1, σ_y = e2, σ_z = e3.
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//! A unitary U acts on a Pauli P as: P → UPU†
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use num_rational::Rational64;
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use serde::{Deserialize, Serialize};
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use symclaw_core::clifford::{BasisBlade, Multivector, Signature};
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/// The Clifford group signature: Cl(3,0).
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pub fn pauli_sig() -> Signature {
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Signature::euclidean(3)
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}
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fn r(n: i64, d: i64) -> Rational64 {
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Rational64::new(n, d)
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}
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/// Single-qubit gate as a Cl(3,0) multivector U (acting as U·P·U†).
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///
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/// We encode:
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/// H → (1/√2)(e1 + e3) — approximate with rational 1/1 since Clifford uses exact algebra
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/// S → (1+e12)/√2 — similarly
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///
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/// Since Cl(3,0) uses rational coefficients but Clifford gate matrices have √2 denominators,
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/// we instead represent gates via their *action* on the Pauli basis elements rather than
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/// the multivectors themselves.
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#[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
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pub enum CliffordGate1Q {
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Identity,
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H,
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X,
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Y,
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Z,
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S,
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Sdg,
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T, // non-Clifford but useful to track
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Tdg,
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}
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impl CliffordGate1Q {
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/// Action on Pauli X: returns (phase, new_pauli_index) where 0=X, 1=Y, 2=Z.
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/// Represents the conjugation U·σ·U†.
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#[must_use]
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pub fn conjugate_x(&self) -> (i8, usize) {
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match self {
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Self::Identity => (1, 0), // X → X
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Self::H => (1, 2), // X → Z
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Self::X => (1, 0), // X → X
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Self::Y => (-1, 0), // X → -X
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Self::Z => (-1, 0), // X → -X
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Self::S => (1, 1), // X → Y (S·X·S† = Y)
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Self::Sdg => (-1, 1), // X → -Y
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Self::T => (1, 0), // (approximate for tracking)
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Self::Tdg => (1, 0),
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}
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}
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/// Action on Pauli Z: U·Z·U†.
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#[must_use]
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pub fn conjugate_z(&self) -> (i8, usize) {
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match self {
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Self::Identity => (1, 2), // Z → Z
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Self::H => (1, 0), // Z → X
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Self::X => (-1, 2), // Z → -Z
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Self::Y => (-1, 2), // Z → -Z
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Self::Z => (1, 2), // Z → Z
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Self::S => (1, 2), // Z → Z
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Self::Sdg => (1, 2), // Z → Z
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Self::T => (1, 2),
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Self::Tdg => (1, 2),
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}
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}
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/// True if this gate is Clifford (preserves the Pauli group under conjugation).
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#[must_use]
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pub fn is_clifford(&self) -> bool {
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!matches!(self, Self::T | Self::Tdg)
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}
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/// Compose two gates: `self` then `other`.
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/// Uses the table of Clifford group elements (order 24).
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#[must_use]
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pub fn compose(&self, other: &Self) -> Vec<Self> {
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// For simplicity, just list both — full Clifford table composition would be a 24×24 table
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// We represent composition as a sequence (circuit model).
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vec![self.clone(), other.clone()]
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}
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/// Adjoint (dagger) of the gate.
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#[must_use]
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pub fn dagger(&self) -> Self {
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match self {
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Self::S => Self::Sdg,
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Self::Sdg => Self::S,
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Self::T => Self::Tdg,
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Self::Tdg => Self::T,
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other => other.clone(), // H, X, Y, Z, I are self-adjoint
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}
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}
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/// Represent this gate as a Cl(3,0) element using the embedding σ_x=e1, σ_y=e2, σ_z=e3.
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/// Returns a Multivector whose grade-1 parts give the Pauli basis transformation.
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///
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/// Note: since √2 is irrational, we represent gates symbolically by their Pauli action
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/// rather than as exact Clifford algebra elements with rational coefficients.
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/// This method returns the pure-vector part of the transformation matrix.
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#[must_use]
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pub fn pauli_action_vector(&self) -> Multivector {
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let sig = pauli_sig();
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// Returns the vector U·e1·U† (i.e., the image of e1 = σ_x)
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let (sgn, idx) = self.conjugate_x();
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let coeff = r(sgn as i64, 1);
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let blade = BasisBlade::vector(idx as u8);
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Multivector::from_terms(std::iter::once((blade, coeff)), sig)
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}
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}
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impl std::fmt::Display for CliffordGate1Q {
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fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
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write!(
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f,
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"{}",
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match self {
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Self::Identity => "I",
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Self::H => "H",
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Self::X => "X",
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Self::Y => "Y",
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Self::Z => "Z",
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Self::S => "S",
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Self::Sdg => "S†",
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Self::T => "T",
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Self::Tdg => "T†",
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}
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)
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use num_traits::One;
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#[test]
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fn h_maps_x_to_z() {
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let (sign, idx) = CliffordGate1Q::H.conjugate_x();
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assert_eq!(sign, 1);
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assert_eq!(idx, 2, "H maps X to Z");
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}
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#[test]
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fn h_maps_z_to_x() {
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let (sign, idx) = CliffordGate1Q::H.conjugate_z();
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assert_eq!(sign, 1);
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assert_eq!(idx, 0, "H maps Z to X");
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}
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#[test]
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fn s_maps_x_to_y() {
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let (sign, idx) = CliffordGate1Q::S.conjugate_x();
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assert_eq!(sign, 1);
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assert_eq!(idx, 1, "S maps X to Y");
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}
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#[test]
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fn identity_is_clifford() {
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assert!(CliffordGate1Q::Identity.is_clifford());
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assert!(CliffordGate1Q::H.is_clifford());
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assert!(!CliffordGate1Q::T.is_clifford());
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}
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#[test]
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fn dagger_h_is_h() {
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assert_eq!(CliffordGate1Q::H.dagger(), CliffordGate1Q::H);
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}
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#[test]
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fn dagger_s_is_sdg() {
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assert_eq!(CliffordGate1Q::S.dagger(), CliffordGate1Q::Sdg);
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assert_eq!(CliffordGate1Q::Sdg.dagger(), CliffordGate1Q::S);
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}
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#[test]
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fn pauli_action_h_on_x() {
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let mv = CliffordGate1Q::H.pauli_action_vector();
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// H maps X → Z, so the vector part should be e3 (index 2 = Z)
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assert_eq!(mv.coeff(BasisBlade::vector(2)), Rational64::one());
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}
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#[test]
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fn x_gate_is_clifford() {
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assert!(CliffordGate1Q::X.is_clifford());
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}
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}
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