Inverse QFT

Based on the last QFT , I tried the inverse QFT.

I got the result of  [640, 654, 573, 666, 615, 601, 635, 654, 616, 603, 646, 602, 629, 605, 593, 668].
This means that the initial state of QFFT is recovered by iQFFT.

The codes of QFT and iQFT are as follows (as far as I understand).

namespace QFT_naive {

open Microsoft.Quantum.Canon;

open Microsoft.Quantum.Intrinsic;

open Microsoft.Quantum.Convert;

open Microsoft.Quantum.Arrays;

open Microsoft.Quantum.Measurement;

open Microsoft.Quantum.Math;

@EntryPoint()

operation SayHello() : Unit {

let nQubit = 4;

let maxNum = PowI(2,nQubit);

mutable counts = new Int[maxNum];

mutable theta = new Double[maxNum];

mutable revSeq = new Int[nQubit];

for iQubit in 0..(nQubit-1){

set theta w/= iQubit <- calcTheta(IntAsDouble(iQubit+1));

}

for iQubit in 0..(nQubit-1){

set revSeq w/= iQubit <- nQubit-1-iQubit;

}

for trial in 1..10000 {

use input = Qubit[nQubit] {

// 1/sqrt(8) (|000> + |001> + ,,, + |111>)

for iQubit in 0..(nQubit-1){

H(input[iQubit]);

}

// Star QFT

for iQubit in 0..(nQubit-1){

H(input[iQubit]);

for jQubit in 1..(nQubit-1-iQubit){

(Controlled R1)([input[jQubit+iQubit]],(theta[jQubit],input[iQubit]));

}

}

let numLoopSwap = Floor(IntAsDouble(nQubit)*0.5);

for iQubit in 0..(numLoopSwap-1) {

SWAP(input[iQubit],input[nQubit-1-iQubit]);

}

// Start Inverse QFFT

for iQubit in 0..(numLoopSwap-1) {

SWAP(input[iQubit],input[nQubit-1-iQubit]);

}

for iQubit in revSeq{

for jQubit in 0..(nQubit-1)-iQubit-1{

let kQubit = revSeq[(nQubit-1)-jQubit];

let controlQubit = nQubit-kQubit-1;

let rotationIndex= nQubit-(kQubit+iQubit)-1;

(Controlled R1)([input[controlQubit]],(-1.0*theta[rotationIndex],input[iQubit]));

}

H(input[iQubit]);

}

let res = MultiM(input);

let bit = ResultArrayAsInt(res);

set counts w/= bit <- counts[bit]+ 1;

ResetAll(input);

}

}

for j in 0..(maxNum-1) {

Message(IntAsString(counts[j]));

}

}

function calcTheta(l : Double) : Double {

return 2.0*PI()/(PowD(2.0,l));

}

}