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Annoyingcutie feature/sk decompose #85

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merged 6 commits into from
Mar 8, 2024
Merged

Annoyingcutie feature/sk decompose #85

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b975a38
Update tensor.hpp
annoyingcutie Mar 6, 2024
8b0d78d
Update tensor.hpp
annoyingcutie Mar 6, 2024
791f195
Update tensor.hpp
annoyingcutie Mar 6, 2024
d106796
Replace tensordot by tensor_multiply
annoyingcutie Mar 7, 2024
2ec8b18
🔀 Merge branch 'feature/SK-decompose' of https://github.com/annoyingc…
chinyi0523 Mar 8, 2024
c77bfbf
:art: Rename functions
chinyi0523 Mar 8, 2024
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104 changes: 69 additions & 35 deletions src/tensor/tensor.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -148,7 +148,7 @@ class Tensor {

Tensor<DT> SK(const std::vector<Tensor<DT>>& gate_list, Tensor<DT> u ,size_t n );

void SK_decompose();
void solovay_kitaev_decompose();

bool tensor_read(std::string const&);
bool tensor_write(std::string const&);
Expand Down Expand Up @@ -316,6 +316,7 @@ Tensor<DT> Tensor<DT>::transpose(TensorAxisList const& perm) const {

template <typename DT>
void Tensor<DT>::adjoint() {
//std::cout << dimension() << std::endl;
assert(dimension() == 2);
_tensor = xt::conj(xt::transpose(_tensor, {1, 0}));
}
Expand Down Expand Up @@ -432,9 +433,9 @@ Tensor<DT> Tensor<DT>::random_u(double x,double y, double z){
std::complex<double> img(0, 1);
std::complex<double> neg(-1, 0);

std::complex<double> X(2 * PI * x, 0);
std::complex<double> Y(2 * PI * y, 0);
std::complex<double> Z(2 * PI * z, 0);
std::complex<double> X(2 * M_PI * x, 0);
std::complex<double> Y(2 * M_PI * y, 0);
std::complex<double> Z(2 * M_PI * z, 0);

Tensor<DT> _X = {{cos(X / 2.0), img*sin(X / 2.0)*neg},{img*sin(X / 2.0*neg), cos(X / 2.0)}};
Tensor<DT> _Y = {{cos(Y / 2.0), neg*sin(Y / 2.0)},{sin(Y / 2.0), cos(Y / 2.0)}};
Expand Down Expand Up @@ -509,12 +510,14 @@ auto Tensor<DT>::eigen() {
}

template <typename DT>
Tensor<DT> Tensor<DT>::diagonalize(const Tensor<DT> u) {
Tensor<DT> Tensor<DT>::diagonalize(Tensor<DT> u) {
// Check if the matrix is 2x2
std::complex<double> neg(-1, 0);
std::tuple b = u->eigen();
std::tuple b = u.eigen();
Tensor<DT> value = std::get<0>(b);
Tensor<DT> vector = std::get<1>(b);
return vector;
/*
auto eigenvectors = vector._tensor;

if (abs(eigenvectors(0,0).real())< abs(eigenvectors(0,1).real()))
Expand All @@ -534,6 +537,7 @@ Tensor<DT> Tensor<DT>::diagonalize(const Tensor<DT> u) {

vector._tensor = eigenvectors;
return vector;
*/
}


Expand All @@ -547,7 +551,7 @@ Tensor<DT> Tensor<DT>::to_su2(Tensor<DT> &u) {
template <typename DT>
bool Tensor<DT>::create_gate_list(size_t length) {
std::complex<double> sqrt2(std::sqrt(2),0);
std::complex<double> t(0,PI/4);
std::complex<double> t(0,M_PI/4);
Tensor<DT> H = {{1./sqrt2,1./sqrt2},{1./sqrt2,-1./sqrt2}};
Tensor<DT> T = {{1,0},{0,pow(M_E,t)}};
std::vector<Tensor<DT>> base = {to_su2(H), to_su2(T)};
Expand All @@ -567,7 +571,8 @@ bool Tensor<DT>::create_gate_list(size_t length) {
{
char bit = bits[j];
int index = int(bit) - 48; // Convert char to int (assuming ASCII)
u = tensordot(u , base[index]);
Tensor<DT> temp = base[index];
u = tensor_multiply(u , temp);
}
gate_list.push_back(u);
//std::cout<< u << std::endl;
Expand Down Expand Up @@ -648,41 +653,62 @@ std::vector<Tensor<DT>> Tensor<DT>::read_gate_list(std::string const& filepath)

template <typename DT>
Tensor<DT> Tensor<DT>::find_closest_u(const std::vector<Tensor<DT>>& gate_list, Tensor<DT> u){

double min_dist = 10;
Tensor<DT> min_u = {{1,0},{0,1}};
for (int i = 0; i<gate_list.size(); i++)

std::complex<double> one(1,0);
std::complex<double> zero(0,0);
Tensor<DT> min_u = {{one,zero},{zero,one}};

int s = gate_list.size();
for (int i = 0; i<s; i++)
{
double tr_dist = (trace_distance(gate_list[i],u));
Tensor<DT> temp = gate_list[i];
double tr_dist = (trace_distance(temp,u));
if (min_dist - tr_dist > pow(10,-12))
{
min_dist = tr_dist;
min_u = gate_list[i];
min_u = temp;
}
}
return min_u;
}

template <typename DT>
std::vector<Tensor<DT>> Tensor<DT>::gc_decomp(Tensor<DT> u){
assert(dimension() == 2);
std::vector<std::complex<double>> axis = u_to_bloch(u);
std::complex<double> result(0, 1);
std::complex<double> neg(-1, 0);
// The angle phi calculation
std::complex<double> phi = 2.0 * asin(std::sqrt(std::sqrt(0.5 - 0.5 * cos(axis[3] / 2.0))));
Tensor<DT> v = {{ cos(phi / 2.0),neg*result*sin(phi / 2.0) }, { neg*result*sin(phi / 2.0), cos(phi / 2.0)}} ;
Tensor<DT> w = {{ 0.,0. }, { 0.,0. }} ;
std::complex<double> zero(0, 0);
Tensor<DT> w = {{ zero,zero }, { zero,zero }} ;
if(axis[2].real() > 0){
w = {{cos((2 * PI - phi) / 2.0), neg*sin( (2 * PI - phi) / 2.0)} , {sin( (2 * PI - phi) / 2.0), cos( (2 * PI - phi) / 2.0)}};
w = {{cos((2 * M_PI - phi) / 2.0), neg*sin( (2 * M_PI - phi) / 2.0)} , {sin( (2 * M_PI - phi) / 2.0), cos( (2 * M_PI - phi) / 2.0)}};
}
else{
w = {{cos(phi / 2.0), neg*sin(phi / 2.0)} , {sin(phi / 2.0), cos(phi / 2.0)}};
}
Tensor<DT> ud = (diagonalize(u));
Tensor<DT> vwvdwd = (diagonalize(tensordot(v ,tensordot(w, tensordot(v._tensor->adjoint(), w._tensor->adjoint() )))));
Tensor<DT> s = tensordot(ud, vwvdwd._tensor->adjoint());
Tensor<DT> v_hat = tensordot(s, tensordot(v, s._tensor->adjoint()));
Tensor<DT> w_hat = tensordot(s, tensordot(w, s._tensor->adjoint()));
v.adjoint();
//std::cout<<"v.adjoint()" <<std::endl;
w.adjoint();
//std::cout<<"w.adjoint()" <<std::endl;
Tensor<DT> vwvdwd = (diagonalize(tensor_multiply(v ,tensor_multiply(w, tensor_multiply(v, w)))));
vwvdwd.adjoint();
//std::cout<<"vwvdwd.adjoint()" <<std::endl;

Tensor<DT> s = tensor_multiply(ud, vwvdwd);

//std::cout<<"S = " << s <<std::endl;
//std::cout<<"ud = " << ud <<std::endl;
//std::cout<<"vwvdwd = " << vwvdwd <<std::endl;

s.adjoint();
// std::cout<<"s.adjoint()" <<std::endl;
Tensor<DT> v_hat = tensor_multiply(s,tensor_multiply(v, s));
Tensor<DT> w_hat = tensor_multiply(s, tensor_multiply(w, s));
std::vector<Tensor<DT>> vw = {v_hat,w_hat};

return vw;
Expand All @@ -693,36 +719,44 @@ Tensor<DT> Tensor<DT>::SK(const std::vector<Tensor<DT>>& gate_list, Tensor<DT> u
{
if(n == 0){
Tensor<DT> re = find_closest_u(gate_list, u);
std::cout << "distance of recurrsion" << n << " : " << trace_distance(re, u) << std::endl;
return re;
}
else{
Tensor<DT> u_p = SK(gate_list, u , n-1);
std::vector<Tensor<DT>> vw = gc_decomp( tensordot(u,u_p._tensor->adjoint()));
u_p.adjoint();
//std::cout<<"u_p.adjoint()" <<std::endl;
std::vector<Tensor<DT>> vw = gc_decomp(tensor_multiply(u,u_p));
Tensor<DT> v = vw[0];
Tensor<DT> w = vw[1];
Tensor<DT> v_p = sk_algo(gate_list ,v , n-1);
Tensor<DT> w_p = sk_algo(gate_list ,w , n-1);
Tensor<DT> re = tensordot(v_p, tensordot(w_p, tensordot(v_p._tensor->adjoint(), tensordot(w_p._tensor->adjoint(),u_p)) ));
Tensor<DT> v_p = SK(gate_list ,v , n-1);
Tensor<DT> w_p = SK(gate_list ,w , n-1);
v_p.adjoint();
//std::cout<<"v_p.adjoint()" <<std::endl;
w_p.adjoint();
//std::cout<<"w_p.adjoint()" <<std::endl;
Tensor<DT> re =tensor_multiply(v_p,tensor_multiply(w_p, tensor_multiply(v_p, tensor_multiply(w_p,u_p)) ));
std::cout << "distance of recurrsion" << n << " : " << trace_distance(re, u) << std::endl;
return re;}
}


template <typename DT>
void Tensor<DT>::SK_decompose() {
void Tensor<DT>::solovay_kitaev_decompose() {
assert(dimension() == 2);
// TODO - Move your code here, you may also create new files src/tensor/

Tensor<DT> a = to_su2(*this);

std::cout <<create_gate_list(14) << std::endl;

std::vector<Tensor<DT>> gate_list = read_gate_list("gate_list_14.csv");
//Tensor<DT> a = to_su2(*this);
Tensor<DT> a =*this;
std::cout <<create_gate_list(7) << std::endl;
std::cout <<"read_gate_list" << std::endl ;
std::vector<Tensor<DT>> gate_list = read_gate_list("gate_list_7.csv");
//for(int i = 0; i<10 ; i++ ){std::cout << gate_list[i] << std::endl;}
std::cout <<"SKing" << std::endl ;
Tensor<DT> re = SK(gate_list , a , 8);
double tr_dist = (trace_distance(a , re));

// Tensor<DT> re = SK(gate_list , a , 8);
// double tr_dist = (trace_distance(a , re));

// std::cout <<"distance : " << tr_dist << std::endl ;
std::cout <<"distance : " << tr_dist << std::endl ;
}


Expand Down Expand Up @@ -813,8 +847,8 @@ template <typename DT>
double Tensor<DT>::trace_distance(Tensor<DT>& t1, Tensor<DT>& t2) {
// TODO
Tensor<DT> t1_t2 = t1 - t2;
t1_t2._tensor->adjoint();
t1_t2._tensor->sqrt();
t1_t2.adjoint();
t1_t2.sqrt();
std::complex<double> t(0.5,0);
return (0.5 * t1_t2.trace()).real();
}
Expand Down