--- /dev/null
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include <complex.h>
+#include "matrix.h"
+#include "exponentialsum.h"
+#include "shrink.h"
+#include "extend.h"
+#include "measurepauli.h"
+#include "innerproduct.h"
+
+int readPaulicoeffs(int *omega, int *alpha, int *beta, int *gamma, int *delta, int numqubits);
+
+// order of matrix elements is [row][column]!!!
+
+int main()
+{
+
+ int N; // number of qubits
+ scanf("%d", &N);
+
+ if(N%3 != 0) {
+ printf("'N' needs to be a multiple of 3 for a k=3 tensor factor decomposition!\n");
+ return 1;
+ }
+
+ int T; // number of T gate magic states (set to the first 'K' of the 'N' qubits -- the rest are set to the '0' computational basis state)
+ scanf("%d", &T);
+
+ int omega;
+ int alpha[N], beta[N], gamma[N], delta[N];
+ int Paulicounter = 0;
+
+ int i, j, k, l, m;
+
+ double complex coeffa = -0.25*(1.0-I)*(-1.0-I+sqrt(2.0))*csqrt(-I);
+ double complex coeffb = 0.25*(-1.0-I)*(1.0-I+sqrt(2.0))*csqrt(I);
+ double complex coeffc = 0.25*(-1.0-I)*(-1.0+I+sqrt(2.0))*csqrt(I);
+
+ int n1 = 3; int k1 = 1; int (*(G1[])) = { (int[]) {1, 1, 1}, (int[]) {0, 1, 0}, (int[]) {0, 0, 1}}; int (*(GBar1[])) = { (int[]) {1, 0, 0}, (int[]) {1, 1, 0}, (int[]) {1, 0, 1}}; int h1[] = {1, 1, 0}; int Q1 = 0; int D1[] = {2}; int (*(J1[])) = { (int[]) {4} };
+ int n2 = 3; int k2 = 3; int (*(G2[])) = { (int[]) {1, 0, 0}, (int[]) {0, 1, 0}, (int[]) {0, 0, 1} }; int (*(GBar2[])) = { (int[]) {1, 0, 0}, (int[]) {0, 1, 0}, (int[]) {0, 0, 1} }; int h2[] = {0, 0, 0}; int Q2 = 2; int D2[] = {2, 2, 0}; int (*(J2[])) = { (int[]) {4, 0, 0}, (int[]) {0, 4, 0}, (int[]) {0, 0, 0} };
+ int n3 = 3; int k3 = 3; int (*(G3[])) = { (int[]) {1, 0, 0}, (int[]) {0, 1, 0}, (int[]) {0, 0, 1} }; int (*(GBar3[])) = { (int[]) {1, 0, 0}, (int[]) {0, 1, 0}, (int[]) {0, 0, 1} }; int h3[] = {0, 0, 0}; int Q3 = 2; int D3[] = {6, 6, 0}; int (*(J3[])) = { (int[]) {4, 4, 4}, (int[]) {4, 4, 4}, (int[]) {4, 4, 0} };
+
+ int *K; int ***G; int ***GBar; int **h; int *Q; int **D; int ***J;
+ double complex Gamma[(int)pow(3,N/3)]; // prefactor in front of resultant state
+ G = calloc(pow(3,N/3),sizeof(int*)); GBar = calloc(pow(3,N/3),sizeof(int*));
+ h = calloc(pow(3,N/3),sizeof(int*));
+
+ J = calloc(pow(3,N/3),sizeof(int*)); D = calloc(pow(3,N/3),sizeof(int*)); Q = calloc(pow(3,N/3),sizeof(int));
+
+ K = calloc(pow(3,N/3), sizeof(int));
+
+ double complex origGamma[(int)pow(3,N/3)];
+ int *origK, *origQ, **origD, ***origJ;
+ int ***origG, ***origGBar, **origh;
+
+ origG = calloc(pow(3,N/3),sizeof(int*)); origGBar = calloc(pow(3,N/3),sizeof(int*));
+ origh = calloc(pow(3,N/3),sizeof(int*));
+
+ origJ = calloc(pow(3,N/3),sizeof(int*)); origD = calloc(pow(3,N/3),sizeof(int*)); origQ = calloc(pow(3,N/3),sizeof(int));
+
+ origK = calloc(pow(3,N/3), sizeof(int));
+
+ int combination; // a particular combination from the linear combo of stabilizer states making up the tensor factors multiplied together
+
+
+ for(j=0; j<pow(3,N/3); j++) { // there will be 3^(N/3) combinations when using k=3 tensor factors
+
+ combination = j;
+
+ K[j] = 0.0;
+
+ for(k=0; k<N/3; k++) {
+ K[j] += (((combination%3)==2)*k3 + ((combination%3)==1)*k2 + ((combination%3)==0)*k1);
+ combination /= 3;
+ }
+ combination = j;
+ origK[j] = K[j];
+
+ Gamma[j] = 1.0;
+
+ G[j] = calloc(N, sizeof(int*)); GBar[j] = calloc(N, sizeof(int*));
+ h[j] = calloc(N, sizeof(int));
+
+ if(K[j] > 0) {
+ J[j] = calloc(K[j], sizeof(int*)); D[j] = calloc(K[j], sizeof(int));
+ for(k=0; k<K[j]; k++)
+ J[j][k] = calloc(K[j], sizeof(int));
+ }
+
+ origG[j] = calloc(N, sizeof(int*)); origGBar[j] = calloc(N, sizeof(int*));
+ origh[j] = calloc(N, sizeof(int));
+
+ if(K[j] > 0) {
+ origJ[j] = calloc(K[j], sizeof(int*)); origD[j] = calloc(K[j], sizeof(int));
+ for(k=0; k<K[j]; k++)
+ origJ[j][k] = calloc(K[j], sizeof(int));
+ }
+
+ for(k=0; k<N; k++) {
+ G[j][k] = calloc(N, sizeof(int)); GBar[j][k] = calloc(N, sizeof(int));
+ origG[j][k] = calloc(N, sizeof(int)); origGBar[j][k] = calloc(N, sizeof(int));
+ }
+
+ int Kcounter = 0; // Kcounter keeps track of the K<=N that we have added already to the G rows etc. for each combination that is indexed by the digits (base 3) of 'j' in that we go through with 'k'
+ int Kcombo; // Kcombo stores the k<(n1=n2=n3) dimension of the member of the combination that we are currently adding
+ for(k=0; k<N/3; k++) {
+
+ Q[j] += ((combination%3)==2)*Q3 + ((combination%3)==1)*Q2 + ((combination%3)==0)*Q1;
+
+ Gamma[j] *= (((combination%3)==2)*coeffc + ((combination%3)==1)*coeffb + ((combination%3)==0)*coeffa);
+
+ Kcombo = (((combination%3)==2)*k3 + ((combination%3)==1)*k2 + ((combination%3)==0)*k1);
+ for(l=0; l<Kcombo; l++) {
+ // D1 has a different number of rows 'l' than D2 and D3 so you need to use something like 'switch' to check combination%3 without going out of bound of J1
+ switch(combination%3) {
+ case 0:
+ D[j][Kcounter+l] = D1[l];
+ break;
+ case 1:
+ D[j][Kcounter+l] = D2[l];
+ break;
+ case 2:
+ D[j][Kcounter+l] = D3[l];
+ break;
+ default:
+ printf("error");
+ return 1;
+ }
+ for(m=0; m<Kcombo; m++) {
+ // J1 has a different number of rows 'l' than J2 and J3 so you need to use something like 'switch' to check combination%3 without going out of bound of J1
+ switch(combination%3) {
+ case 0:
+ J[j][Kcounter+l][Kcounter+m] = J1[l][m];
+ break;
+ case 1:
+ J[j][Kcounter+l][Kcounter+m] = J2[l][m];
+ break;
+ case 2:
+ J[j][Kcounter+l][Kcounter+m] = J3[l][m];
+ break;
+ default:
+ printf("error");
+ return 1;
+ }
+ }
+ }
+
+ for(l=0; l<n1; l++) { // assuming n1=n2=n3
+ h[j][k*n1+l] = ((combination%3)==2)*h3[l] + ((combination%3)==1)*h2[l] + ((combination%3)==0)*h1[l];
+ }
+ // only filling the K[j] first rows of G and GBar here corresponding to the basis for D and J
+ for(l=0; l<Kcombo; l++) {
+ for(m=0; m<n1; m++) { // assuming n1=n2=n3
+ G[j][Kcounter+l][k*n1+m] = ((combination%3)==2)*G3[l][m] + ((combination%3)==1)*G2[l][m] + ((combination%3)==0)*G1[l][m];
+ GBar[j][Kcounter+l][k*n1+m] = ((combination%3)==2)*GBar3[l][m] + ((combination%3)==1)*GBar2[l][m] + ((combination%3)==0)*GBar1[l][m];
+ }
+ }
+ Kcounter = Kcounter + Kcombo;
+
+ /* printf("intermediate G[%d]:\n", j); */
+ /* printMatrix(G[j], N, N); */
+ /* printf("intermediate GBar[%d]:\n", j); */
+ /* printMatrix(GBar[j], N, N); */
+ //memcpy(origG[j][k], G[j][k], N*sizeof(int)); memcpy(origGBar[j][k], GBar[j][k], N*sizeof(int));
+
+ //memcpy(origJ[j][k], J[j][k], K[j]*sizeof(int));
+
+ combination /= 3; // shift to the right by one (in base-3 arithmetic)
+ }
+ //printf("!\n");
+
+ // now need to fill the N-Kcounter remaining rows of G and GBar that are outside the spanning basis states of D and J
+ combination = j;
+ for(k=0; k<(N/3); k++) {
+ Kcombo = (((combination%3)==2)*k3 + ((combination%3)==1)*k2 + ((combination%3)==0)*k1);
+ //printf("Kcounter=%d\n", Kcounter);
+ // G and GBar rows that are outside the first 'k' spanning basis states
+ for(l=Kcombo; l<n1; l++) { // assuming n1=n2=n3
+ //printf("l=%d\n", l);
+ for(m=0; m<n1; m++) { // assuming n1=n2=n3
+ /* printf("m=%d\n", m); */
+ /* printf("Kcounter+l=%d\n", Kcounter+l); */
+ /* printf("k*n1+m=%d\n", k*n1+m); */
+ G[j][Kcounter+l-Kcombo][k*n1+m] = ((combination%3)==2)*G3[l][m] + ((combination%3)==1)*G2[l][m] + ((combination%3)==0)*G1[l][m];
+ GBar[j][Kcounter+l-Kcombo][k*n1+m] = ((combination%3)==2)*GBar3[l][m] + ((combination%3)==1)*GBar2[l][m] + ((combination%3)==0)*GBar1[l][m];
+ }
+ }
+ Kcounter = Kcounter + (n1-Kcombo);
+
+ /* printf("intermediate G[%d]:\n", j); */
+ /* printMatrix(G[j], N, N); */
+ /* printf("intermediate GBar[%d]:\n", j); */
+ /* printMatrix(GBar[j], N, N); */
+
+ combination /= 3;
+ }
+ for(k=0; k<N; k++) {
+ memcpy(origG[j][k], G[j][k], N*sizeof(int)); memcpy(origGBar[j][k], GBar[j][k], N*sizeof(int));
+ }
+ for(k=0; k<K[j]; k++) {
+ memcpy(origJ[j][k], J[j][k], K[j]*sizeof(int));
+ }
+
+ memcpy(origh[j], h[j], N*sizeof(int));
+ memcpy(origD[j], D[j], K[j]*sizeof(int));
+
+ }
+ //exit(0);
+ memcpy(origGamma, Gamma, pow(3,N/3)*sizeof(double complex));
+
+ memcpy(origQ, Q, pow(3,N/3)*sizeof(int));
+
+ while(readPaulicoeffs(&omega, alpha, beta, gamma, delta, N)) {
+
+ Paulicounter++;
+ if(Paulicounter > N) {
+ printf("Error: Number of Paulis is greater than N!\n");
+ return 1;
+ }
+
+ // Let's break up the Ys into Xs and Zs in the order Z X, as required to pass to measurepauli()
+ // Y_i = -I*Z*X
+ for(i=0; i<N; i++) {
+ if(delta[i]){
+ omega += 3; // -I = I^3
+ beta[i] = delta[i];
+ gamma[i] = delta[i];
+ }
+ }
+
+
+ for(j=0; j<pow(3,N/3); j++) { // the kets
+
+ Gamma[j] *= measurepauli(N, &K[j], h[j], G[j], GBar[j], &Q[j], &D[j], &J[j], omega, gamma, beta);
+
+ }
+
+ }
+
+ double complex amplitude = 0.0 + 0.0*I;
+ for(i=0; i<pow(3,N/3); i++) { // the bras
+ for(j=0; j<pow(3,N/3); j++) {
+ double complex newamplitude = innerproduct(N, K[j], h[j], G[j], GBar[j], Q[j], D[j], J[j], N, origK[i], origh[i], origG[i], origGBar[i], origQ[i], origD[i], origJ[i]);
+ amplitude = amplitude + conj(origGamma[i])*Gamma[j]*newamplitude;
+ }
+ }
+
+ printf("amplitude:\n");
+ if(creal(amplitude+0.00000001)>0)
+ printf("%lf %c %lf I\n", cabs(creal(amplitude)), cimag(amplitude+0.00000001)>0?'+':'-' , cabs(cimag(amplitude)));
+ else
+ printf("%lf %c %lf I\n", creal(amplitude), cimag(amplitude+0.00000001)>0?'+':'-' , cabs(cimag(amplitude)));
+ //printf("%lf %c %lf I\n", creal(amplitude), cimag(amplitude)>0?'+':'-' , cabs(cimag(amplitude)));
+
+ return 0;
+
+}
+
+
+
+int readPaulicoeffs(int *omega, int *alpha, int *beta, int *gamma, int *delta, int numqubits)
+{
+
+ int newomega, newalpha, newbeta, newgamma, newdelta;
+ int i;
+
+ if(scanf("%d", &newomega) != EOF) {
+ *omega = newomega;
+ for(i=0; i<numqubits; i++) {
+ if(scanf("%d %d %d %d", &newalpha, &newbeta, &newgamma, &newdelta) == EOF) {
+ printf("Error: Too few input coeffs!\n");
+ exit(0);
+ }
+ if(newalpha+newbeta+newgamma+newdelta > 1) {
+ printf("Error: Too many coefficients are non-zero at Pauli %d!\n", i);
+ exit(0);
+ }
+ alpha[i] = newalpha; beta[i] = newbeta; gamma[i] = newgamma; delta[i] = newdelta;
+ }
+ return 1;
+ } else
+ return 0;
+
+}
projects / strong_simulation_stabilizer_rank.git / blobdiff