gala-cookbook

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• SKILL.md

SKILL.md (first lines)

## Task

$ARGUMENTS

## Overview

Practical Gala patterns and recipes for common tasks. Copy-paste starting points for real programs.

## Recipe Index

1. [Bell Pair & Entanglement](#bell-pair--entanglement)
2. [Quantum Teleportation](#quantum-teleportation)
3. [Superdense Coding](#superdense-coding)
4. [Phase Estimation](#phase-estimation)
5. [Variational Classifier](#variational-classifier)
6. [QAOA for MaxCut](#qaoa-for-maxcut)
7. [VQE for Molecular Hamiltonian](#vqe-for-molecular-hamiltonian)
8. [Error Mitigation Wrapper](#error-mitigation-wrapper)
9. [Classical Pre/Post Processing](#classical-prepost-processing)
10. [Mid-Circuit Measurement Patterns](#mid-circuit-measurement-patterns)
11. [Ancilla Management](#ancilla-management)
12. [Parameter Sharing](#parameter-sharing)

---

## Bell Pair & Entanglement

```gala
fn bell_pair() -> Qubits<2> quantum {
    let a = qubit()
    let b = qubit()
    h(a)
    cx(a, b)
    (a, b)
}

// GHZ state (N-qubit entanglement)
fn ghz_state<const N: Int>() -> Qubits<N> quantum {
    let qs = qubits<N>()
    h(qs[0])
    for i in 1..N {
        cx(qs[0], qs[i])
    }
    qs
}

// W state (different entanglement)
fn w_state<const N: Int>() -> Qubits<N> quantum {
    let qs = qubits<N>()
    x(qs[0])  // Start with |100...0⟩
    for i in 1..N {
        // Controlled rotation to spread amplitude
        let theta = 2.0 * asin(1.0 / sqrt((N - i + 1) as Float))
        cry(qs[i-1], qs[i], theta)
    }
    qs
}
```

## Quantum Teleportation

```gala
fn teleport(msg: Qubit, alice: Qubit, bob: Qubit) -> (Qubit, Qubit, Measured<Bool>, Measured<Bool>) prob {
    // Alice prepares Bell pair with Bob
    h(alice)
    cx(alice, bob)
    
    // Alice measures msg + her half
    cx(msg, alice)
    h(msg)
    let m1 = measure(msg)
    let m2 = measure(alice)
    
    // Bob applies corrections (classical feedforward)
    if m2 { x(bob) }  // X correction
    if m1 { z(bob) }  // Z correction
    
    (bob, msg, m1, m2)  // bob now has msg state
}
```

## Superdense Coding

```gala
fn superdense_encode(alice: Qubit, bob: Qubit, bits: (Bool, Bool)) -> (Qubit, Qubit) quantum {
    // Pre-shared Bell pair
    h(alice)
    cx(alice, bob)
    
    // Alice encodes 2 classical bits
    match bits {
        (false, false) => {},           // |00⟩: I
        (true, false) => { x(alice) },  // |10⟩: X
        (false, true) => { z(alice) },  // |01⟩: Z
        (true, true) => { x(alice); z(alice) },  // |11⟩: XZ
    }
    (alice, bob)
}

fn superdense_decode(alice: Qubit, bob: Qubit) -> (Measured<Bool>, Measured<Bool>) prob {
    // Bob decodes
    cx(alice, bob)
    h(alice)
    let b1 = measure(alice)
    let b2 = measure(bob)
    (b1, b2)
}
```

## Phase Estimation

```gala
fn phase_estimation<const N: Int, const P: Int>(
    unitary: fn(Qubits<N>) -> Qubits<N> quantum,
    eigenstate: Qubits<N>
) -> (Qubits<P>, Qubits<N>) quantum {
    let eval = qubits<P>()
    let state = eigenstate

From gala-pl/gala, Apache-2.0.

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