Added IQPE FTQC demo example

/// iqpe_ftqc.cpp: Iterative quantum phase estimation

/// Compile:

/// $ qcor -qrt ftqc iqpe_ftqc.cpp

/// Execute: 

/// ./a.out

// Iterative Quantum Phase Estimation:

// Only use 2 qubits to achieve 4-bit accuracy (normally require 5 qubits)

// The oracle is a -5*pi/8 pHase rotation;

__qpu__ void oracle(qubit q) {

  auto angle = -5.0 * M_PI / 8.0;

  U1(q, angle);

}

using OracleCallable = KernelSignature<qubit>;

__qpu__ void phase_estimation(qreg q, OracleCallable oracle_fn) {

  X(q[1]);

  // Iterative phase estimation:

  H(q[0]);

  // C-U^8

  for (int i = 0; i < 8; i++) {

    oracle_fn.ctrl(q[0], q[1]);

  }

  H(q[0]);

  // Measure and reset

  // First bit:

  auto c0 = Measure(q[0]);

  Reset(q[0]);

  H(q[0]);

  // C-U^4

  for (int i = 0; i < 4; i++) {

    oracle_fn.ctrl(q[0], q[1]);

  }

  // Conditional phase correction based on previous results:

  if(c0) {

    Rz(q[0], -M_PI/2.0);

  }

  H(q[0]);

  // Second bit

  auto c1 = Measure(q[0]);

  Reset(q[0]);

  H(q[0]);

  // C-U^2

  for (int i = 0; i < 2; i++) {

    oracle_fn.ctrl(q[0], q[1]);

  }

  // Conditional phase correction based on previous results:

  if(c0) {

    Rz(q[0], -M_PI/4);

  }

  if(c1) {

    Rz(q[0], -M_PI/2);

  }

  H(q[0]);

  // 3rd bit:

  auto c2 = Measure(q[0]);

  Reset(q[0]);

  H(q[0]);

  // C-U^1

  oracle_fn.ctrl(q[0], q[1]);

  // Conditional phase correction based on previous results:

  if(c0) {

    Rz(q[0], -M_PI/8);

  }

  if(c1) {

    Rz(q[0], -M_PI/4);

  }

  if(c2) {

    Rz(q[0], -M_PI/2);

  }

  H(q[0]);

  // 4th bit:

  auto c3 = Measure(q[0]);

  // Print the result bit-string:

  print("Bit-string: ", c3, c2, c1, c0);

}

int main(int argc, char *argv[]) {

  qreg q = qalloc(2);

  // expected to get 4 bits (iteratively) of 1011 = 11(decimal):

  // phi_est = 11/16 (denom = 16 since we have 4 bits)

  // => phi = 2pi * 11/16 = 11pi/8 = 2pi - 5pi/8

  // i.e. we estimate the -5*pi/8 angle...

  phase_estimation(q, oracle);

  return 0;

}

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