// Phase estimation of p(3π/4), whose eigenvalue on |1⟩ is e^{2πi·3/8}, with
// three counting qubits: `ctrl @ pow(2**j) @` on a gate the program defines,
// and the inverse of its own QFT with `inv @`. 3/8 is three bits exactly, so
// every shot reads 3: k[0] and k[1] are 1, k[2] is 0.
OPENQASM 3.1;
include "stdgates.inc";
gate u_phase a { p(3 * pi / 4) a; }
gate qft3 a, b, c {
  h a;
  cp(pi / 2) b, a;
  cp(pi / 4) c, a;
  h b;
  cp(pi / 2) c, b;
  h c;
  swap a, c;
}
qubit[3] k;
qubit t;
bit[3] r;
x t;
h k;
for uint j in [0:2] {
  ctrl @ pow(2 ** j) @ u_phase k[j], t;
}
inv @ qft3 k[2], k[1], k[0];
r = measure k;