/*
 * Iterative phase estimation
 */
include "stdgates.inc";

const int[32] n = 10;          // number of iterations
const float[32] theta = 3 * pi / 8;  // phase angle on target qubit

qubit q;    // phase estimation qubit
qubit r;    // target qubit for the controlled-unitary gate
angle[n] c; // phase estimation bits

// initialize
reset q;
reset r;

// prepare uniform superposition of eigenvectors of phase
h r;

// iterative phase estimation loop
uint[n] power = 1;
for uint i in [0: n - 1] {  // implicitly cast val to int
  reset q;
  h q;
  ctrl @ pow(power) @ phase(theta) q, r;
  inv @ phase(c) q;
  h q;
  measure q -> c[0];
  // newest measurement outcome is associated to a pi/2 phase shift
  // in the next iteration, so shift all bits of c left
  c <<= 1;
  power <<= 1;
}

// Now c contains the n-bit estimate of phi in the
// eigenvalue e^{i*phi} and qreg r is projected to an
// approximate eigenstate of the phase gate.