example.cpp

Demonstrates the process of creating a Net and using it to return approximations

#include <iostream>

#include "Net.h"
#include "Exception.h"

using namespace std;
typedef complex<double> cdouble;

int main(void)
{
    // Square root of -1
    cdouble I = cdouble(0,1);

    // Set up the labels array
    char labels[] = {'H', 'T'};

    // And set up the 2D array of matrices correspnding to these labels
    cdouble gates[][4] =
    {
      { I/SQRT2, I/SQRT2, I/SQRT2, -1.0*I/SQRT2 },  
      { cdouble(cos(PI/8),-sin(PI/8)) ,0, 0, cdouble(cos(PI/8),sin(PI/8)) } 
    };

    // Construct a Net with the HT gate set and a tile width of 0.14
    Net enet(0.18);
    cout << "... generating net ..." << endl;
    enet.generate(labels,gates,2,14);
    
    // Optionally save the net into a file
    // enet.save("ht14.net"); 
    // Which can be loaded next time as follows
    // Net enet("lps7.net");

    cout << enet << endl;

    // Generate a random 4D unit vector
    srand(time(0));
    double a[4];
    double norm = 0;
    for (int i=0;i<4;i++) {a[i] = (float)rand()/RAND_MAX; norm += a[i]*a[i]; }
    norm = sqrtf(norm);
    for (int i=0;i<4;i++) { a[i] /= norm; }

    // and construct a matrix from this unit vector
    Matrix<cdouble> A(2,2);
    su2::cart4_to_mat(a,A);

    cout << "A = " << A << endl;

    try {
    
    cout << "calling Solovay-Kitaev() to depth 5" << endl;
    Net::knot ska = enet.solovay_kitaev(A,5);

    cout << "got a sequence of length " << ska.l << endl;

    cout << "A ~ " << ska.M << endl;
    cout << "accuracy " << su2::proj_trace_dist(A,ska.M) << endl;

    // Confirm this sequence is what it's supposed to be
    // Matrix<cdouble> B = enet.evaluate(ska.word);
    // cout << "0 = " << su2::proj_trace_dist(ska.M,B) << endl;
    
    // catch any exceptions
    }
    catch (Exception& E) { cout << "*** ERROR: " << E.msg << endl; }
}

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