Triangle QAOA MaxCut | Turn lessons into working experiments

Starter code

module triangle_qaoa;
@seed(23);
param gamma: Angle = 0.7;
param beta: Angle = 0.4;
fn main() {
  let q = qreg[3];
  H(q[0]);
  H(q[1]);
  H(q[2]);
  RZZ(q[0], q[1], gamma);
  RZZ(q[1], q[2], gamma);
  RZZ(q[0], q[2], gamma);
  Rx(q[0], beta);
  Rx(q[1], beta);
  Rx(q[2], beta);
  let cut = expect -0.5 Z(q[0]) Z(q[1]) -0.5 Z(q[1]) Z(q[2]) -0.5 Z(q[0]) Z(q[2]);
  // The expected triangle cut is 1.5 + cut, so maximize this observable.
  train {
    objective: maximize cut;
    optimizer: adam(lr = 0.15);
    steps: 50;
  }
  return cut;
}

Expected output

Three qubits encode graph nodes

RZZ gates encode all three edges

The train block optimizes gamma and beta

The exact triangle max cut is 2

Debugging checklist

Run the triangle source

Inspect gamma and beta history

Identify all RZZ edge terms

Compare the best bitstring with maxCut=2

Extension challenge

Build a four-cycle with p=2 and target an approximation ratio of at least 0.9.