added code, README and Makefile

[strong_simulation_gauss_sum_rank.git] / gausssums_multipleof3.c

diff --git a/gausssums_multipleof3.c b/gausssums_multipleof3.c
new file mode 100644 (file)
index 0000000..5cba378
--- /dev/null
+++ b/gausssums_multipleof3.c
@@ -0,0 +1,113 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <complex.h>
+#include <math.h>
+
+int readPaulicoeffs(int* alpha, int* beta, int* gamma, int* delta, int numqubits);
+complex double Gausssum1d(int quadraticcoeff, int linearcoeff);
+complex double Kroneck(int arg);
+  
+// order of matrix elements is [row][column]!!!
+
+int main()
+{
+
+  int i, x, y;
+  
+  int N;              // number of qubits
+  scanf("%d", &N);
+  if(N%3!=0) {
+    printf("Error: N must be a multiple of 3!\n");
+    return 1;
+  }
+
+  int alpha[N], beta[N], gamma[N], delta[N];
+
+  double complex summand, sum;
+
+  while(readPaulicoeffs(alpha, beta, gamma, delta, N)) {
+
+    /* for(i=0; i<N; i++) */
+    /*   printf("%d %d %d %d\n", alpha[i], beta[i], gamma[i], delta[i]); */
+
+    sum = 1.0+0.0*I;
+    for(i=0; i<N; i+=3) {
+      summand = 0.0*I;
+      for(y=0; y<=1; y++) {
+       //for(x=0;x<=(y*(gamma[i]+gamma[i+1])+(y+1)*(gamma[i]+delta[i+1]))%2; x++) {
+       for(x=y*(beta[i]+alpha[i+1]+beta[i+1])%2;x<=(y*(beta[i]+alpha[i+1]+beta[i+1])+y*(gamma[i]+gamma[i+1])+(y+1)*(gamma[i]+delta[i+1]))%2; x++) {
+         summand += 0.125*pow(2.0,1-y*pow(gamma[i]-gamma[i+1],2)-pow(y-1,2)*pow(gamma[i]-delta[i+1],2))*cexp(M_PI*I/2.0*((delta[i+1]-gamma[i])*pow(y+1,2)+2.0*(beta[i]+beta[i+1]+gamma[i]+delta[i+1])*x*pow(y+1,2)+2.0*(delta[i]+delta[i+1]+beta[i]+beta[i+1])*x*y+(2.0*beta[i]+3.0*delta[i]+delta[i+1])*y))*Gausssum1d(0.0,beta[i+2])*Kroneck(gamma[i]+delta[i]-gamma[i+1]-delta[i+1])*Kroneck(gamma[i+2]+delta[i+2]);
+         summand += 0.125*pow(2.0,1-y*pow(gamma[i]-gamma[i+1],2)-pow(y-1,2)*pow(gamma[i]-delta[i+1],2))*cexp(M_PI*I/2.0*((delta[i+1]-gamma[i])*pow(y+1,2)+2.0*(beta[i]+beta[i+1]+gamma[i]+delta[i+1])*x*pow(y+1,2)+2.0*(delta[i]+delta[i+1]+beta[i]+beta[i+1])*x*y+(2.0*beta[i]+3.0*delta[i]+delta[i+1])*y))*csqrt(-I)*Gausssum1d(gamma[i+2]+delta[i+2],0)*Kroneck(gamma[i]+delta[i]-gamma[i+1]-delta[i+1])*Kroneck(alpha[i+2]+beta[i+2]);
+         //summand += 0.125*pow(2.0,gamma[i]+delta[i]+x*y*(beta[i]+alpha[i])*alpha[i+1]+pow(x-1,2)*y*(alpha[i]+beta[i])*beta[i+1]-y*pow(gamma[i]-gamma[i+1],2)-pow(y-1,2)*pow(gamma[i]-delta[i+1],2))*cexp(M_PI*I/2.0*((delta[i+1]-gamma[i])*pow(y+1,2)+2.0*(beta[i]+beta[i+1]+gamma[i]+delta[i+1])*x*pow(y+1,2)+2.0*(delta[i]+delta[i+1]+beta[i]+beta[i+1])*x*y+(2.0*beta[i]+3.0*delta[i]+delta[i+1])*y))*Gausssum1d(0.0,beta[i+2])*Kroneck(gamma[i]+delta[i]-gamma[i+1]-delta[i+1])*Kroneck(gamma[i+2]+delta[i+2]);
+         //}
+       //for(x=((y+1)*(alpha[i]+beta[i]))%2;x<=((beta[i]+alpha[i])+y*(gamma[i]+gamma[i+1])+(y+1)*(gamma[i]+delta[i+1]))%2; x++) {              
+         //summand += 0.125*pow(2.0,gamma[i]+delta[i]+x*y*(beta[i]+alpha[i])*alpha[i+1]+pow(x-1,2)*y*(alpha[i]+beta[i])*beta[i+1]-y*pow(gamma[i]-gamma[i+1],2)-pow(y-1,2)*pow(gamma[i]-delta[i+1],2))*cexp(M_PI*I/2.0*((delta[i+1]-gamma[i])*pow(y+1,2)+2.0*(beta[i]+beta[i+1]+gamma[i]+delta[i+1])*x*pow(y+1,2)+2.0*(delta[i]+delta[i+1]+beta[i]+beta[i+1])*x*y+(2.0*beta[i]+3.0*delta[i]+delta[i+1])*y))*csqrt(-I)*Gausssum1d(gamma[i+2]+delta[i+2],0)*Kroneck(gamma[i]+delta[i]-gamma[i+1]-delta[i+1])*Kroneck(alpha[i+2]+beta[i+2]);         
+       }
+      }
+      for(y=0; y<=(1+alpha[i+2])%2; y++) {
+       for(x=0;x<=(1+beta[i+2])%2; x++) {
+         summand += 0.125*2.0*csqrt(-I)*cexp(M_PI*I/2.0*(2.0*beta[i+2]*y+pow(x+1,2)*(delta[i]+gamma[i+1]+2.0*beta[i+1])+x*(delta[i]+delta[i+1])))*Gausssum1d(1,beta[i]+beta[i+1]+delta[i]+(x+1)*gamma[i+1]+x*delta[i+1])*Kroneck(gamma[i]+delta[i]-gamma[i+1]-delta[i+1]+1)*Kroneck(gamma[i+2]+delta[i+2]);
+       }
+      }
+      for(y=0; y<=1; y++) {
+       for(x=(y*(delta[i]+delta[i+1]))%2;x<=(1+y*(gamma[i]+gamma[i+1]))%2; x++) {
+         summand += 0.125*pow(2.0,pow(y-1,2)*(pow(x,2)*(gamma[i]+delta[i+1])+pow(x-1,2)*(gamma[i+1]+delta[i])))*(-I)*cexp(M_PI*I/2.0*(y*(delta[i]+delta[i+1])+pow(y+1,2)*(delta[i]+gamma[i+1]+2*beta[i+1])+pow(x,2)+2*(beta[i]+beta[i+1]+delta[i]+gamma[i+1]*(y+1)+delta[i+1]*y)*x))*Gausssum1d(0,x+beta[i]+beta[i+1]+delta[i]+gamma[i+1]*(y+1)+delta[i+1]*y+gamma[i+2]+delta[i+2])*Kroneck(gamma[i]+delta[i]-gamma[i+1]-delta[i+1]+1)*Kroneck(alpha[i+2]+beta[i+2]);
+       }
+      }
+      sum *= summand;
+    }
+    //printf("%lf+%lfI\n", creal(sum), cimag(sum));
+    printf("%lf\n", cabs(creal(sum))); 
+
+
+  }
+
+  return 0;
+}
+
+complex double Kroneck(int arg)
+{
+  arg = (arg+1)%2; // output 1 if argument is 0 mod 2 and 0 otherwise
+  return ((complex double)arg);
+}
+
+complex double Gausssum1d(int quadraticcoeff, int linearcoeff)
+{
+  /*****************************************
+  /* NOTE! we assume coeffs are either 0 or 1
+  /* (So you cannot pass off a linear coeff as a quadratic coeff by multiplying it by a factor of 2 (and considering it as mod 4)!)
+  *****************************************/
+  
+  quadraticcoeff %= 2;
+  linearcoeff %= 2;
+    
+  if(quadraticcoeff == 0)
+    if(linearcoeff == 0)
+      return 2.0+0.0*I;
+    else
+      return 0.0*I;
+  else
+    if(linearcoeff == 0)
+      return 1.0+1.0*I;
+    else
+      return 1.0-1.0*I;
+
+}
+
+int readPaulicoeffs(int *alpha, int *beta, int *gamma, int *delta, int numqubits)
+{
+
+  int i;
+
+  if(scanf("%d %d %d %d", &alpha[0], &beta[0], &gamma[0], &delta[0]) != EOF) {
+    for(i=1; i<numqubits; i++) {
+      scanf("%d %d %d %d", &alpha[i], &beta[i], &gamma[i], &delta[i]);
+    }
+    return 1;
+  } else
+    return 0;
+
+}
+
+
+