-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <math.h>
-#include <complex.h>
-#include <time.h>
-#include "matrix.h"
-#include "exponentialsum.h"
-#include "shrinkstar.h"
-#include "extend.h"
-#include "measurepauli.h"
-#include "innerproduct.h"
-#include "randomstabilizerstate.h"
-
-#define ZEROTHRESHOLD (0.00000001)
-
-int readPaulicoeffs(int *omega, int *alpha, int *beta, int *gamma, int *delta, int numqubits);
-
-// order of matrix elements is [row][column]!!!
-
-int main(int argc, char *argv[])
-{
-
- if(argc != 2) {
- printf("strongsim3_rellerr argument: \"number of stabilizer state samples\"\n");
- exit(0);
- }
-
- int NUMSTABSTATESAMPLES = atoi(argv[1]); // number of stabilizer state samples
-
- 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[N]; // max of N measurements
- int alpha[N][N], beta[N][N], gamma[N][N], delta[N][N]; // max of N measurements of N Paulis
- int Paulicounter = 0;
-
- int i, j, k, l, m;
-
- FILE *fp;
- char buff[255];
-
- srand((unsigned)time(NULL)); // seeding the random number generator for randomstabilizerstate()
-
- fp = fopen("Pd.txt", "r");
-
- if(fscanf(fp, "%s", buff) == EOF) {
- printf("Error: Pd.txt should start with the number N of P(d) of values tabulated.");
- return 1;
- }
-
- double** Pd;
-
- int PdN = atoi(buff);
-
- Pd = calloc(PdN, sizeof(double*));
- for(i=0; i<PdN; i++)
- Pd[i] = calloc(PdN+1, sizeof(double));
-
- double tmp;
-
- for(i=1; i<PdN; i++) {
- tmp = 0.0;
- for(j=0; j<=i; j++) {
- if(fscanf(fp, "%s", buff) == EOF) {
- printf("Error: expected more values tabulated for P(d) for N=%d", PdN);
- return 1;
- }
- Pd[i][j] = atof(buff);
- //printf("%e ", Pd[i][j]);
- tmp += Pd[i][j];
- }
- //printf("\n");
- //printf("total=%f\n", tmp);
- }
-
-
- 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));
-
- int origK, origQ, *origD;
- int **origJ;
- int **origG, **origGBar;
- int *origh;
- double complex origGamma;
-
- 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=12 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;
-
- 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));
- }
-
- for(k=0; k<N; k++) {
- G[j][k] = calloc(N, sizeof(int)); GBar[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-7 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;
- }
-
- /*printf("G[%d]:\n", j);
- printMatrix(G[j], N, N);
- printf("GBar[%d]:\n", j);
- printMatrix(GBar[j], N, N);
-
- printf("h[%d]:\n", j);
- printVector(h[j], N);
-
- printf("J[%d]:\n", j);
- printMatrix(J[j], K[j], K[j]);
-
- printf("D[%d]:\n", j);
- printVector(D[j], K[j]);
-
- printf("Q[%d]=%d\n", j, Q[j]);*/
-
- }
- //exit(0);
-
- while(readPaulicoeffs(&omega[Paulicounter], alpha[Paulicounter], beta[Paulicounter], gamma[Paulicounter], delta[Paulicounter], N)) {
-
- if((Paulicounter+1) > 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[Paulicounter][i]){
- omega[Paulicounter] += 3; // -I = I^3
- beta[Paulicounter][i] = delta[Paulicounter][i];
- gamma[Paulicounter][i] = delta[Paulicounter][i];
- }
- }
-
- /*printf("*******\n");
- printf("*******\n");
- printf("omega=%d\n", omega);
- printf("X:\n");
- printVector(gamma, N);
- printf("Z:\n");
- printVector(beta, N);
- printf("*******\n");
- printf("*******\n");*/
-
- //for(j=0; j<pow(3,N/3); j++) { // the kets
-
- /*printf("========\n");
- printf("before:\n");
- printf("K=%d\n", K[j]);
- printf("h:\n");
- printVector(h[j], N);
- printf("Gamma[%d]=%lf+%lf\n", j, creal(Gamma[j]), cimag(Gamma[j]));
- printf("G:\n");
- printMatrix(G[j], N, N);
- printf("GBar:\n");
- printMatrix(GBar[j], N, N);
- printf("Q=%d\n", Q[j]);
- printf("D:\n");
- printVector(D[j], K[j]);
- printf("J:\n");
- printMatrix(J[j], K[j], K[j]);*/
- //Gamma[j] *= measurepauli(N, &K[j], h[j], G[j], GBar[j], &Q[j], &D[j], &J[j], omega, gamma, beta);
- /*printf("\nafter:\n");
- printf("K=%d\n", K[j]);
- printf("h:\n");
- printVector(h[j], N);
- printf("Gamma[%d]=%lf+%lf\n", j, creal(Gamma[j]), cimag(Gamma[j]));
- printf("G:\n");
- printMatrix(G[j], N, N);
- printf("GBar:\n");
- printMatrix(GBar[j], N, N);
- printf("Q=%d\n", Q[j]);
- printf("D:\n");
- printVector(D[j], K[j]);
- printf("J:\n");
- printMatrix(J[j], K[j], K[j]);*/
-
- //}
-
- Paulicounter++;
- }
-
- double complex amplitude = 0.0 + 0.0*I;
- for(i=0; i<NUMSTABSTATESAMPLES; i++) { // the bras
- //printf("i=%d\n", i);
-
- randomstabilizerstate(N, &origK, &origh, &origG, &origGBar, &origQ, &origD, &origJ, Pd);
-
- origGamma = 1.0 + 0.0*I;
-
- for(k=0; k<Paulicounter; k++) {
- origGamma *= measurepauli(N, &origK, origh, origG, origGBar, &origQ, &origD, &origJ, omega[k], gamma[k], beta[k]);
- //printf("k=%d\n", k);
- }
- /*printf("origK=%d\n", origK);
- printf("origG:\n");
- printMatrix(origG, N, N);
- printf("origGBar:\n");
- printMatrix(origGBar, N, N);
- printf("origh:\n");
- printVector(origh, N);*/
-
- double complex stabstateaverage = 0.0 + 0.0*I;
-
- for(j=0; j<pow(3,N/3); j++) {
- //printf("j=%d\n", j);
- double complex newamplitude = innerproduct(N, K[j], h[j], G[j], GBar[j], Q[j], D[j], J[j], N, origK, origh, origG, origGBar, origQ, origD, origJ);
- stabstateaverage = stabstateaverage + origGamma*Gamma[j]*newamplitude;
- }
- amplitude = amplitude + conj(stabstateaverage)*stabstateaverage/((double)(NUMSTABSTATESAMPLES))*pow(2.0,T);
-
- deallocate_mem(&origG, N);
- deallocate_mem(&origGBar, N);
- free(origh);
- deallocate_mem(&origJ, origK);
- free(origD);
- }
-
- printf("amplitude:\n");
- if(creal(amplitude+ZEROTHRESHOLD)>0)
- printf("%.10lf %c %.10lf I\n", cabs(creal(amplitude)), cimag(amplitude+ZEROTHRESHOLD)>0?'+':'-' , cabs(cimag(amplitude)));
- else
- printf("%.10lf %c %.10lf I\n", creal(amplitude), cimag(amplitude+ZEROTHRESHOLD)>0?'+':'-' , cabs(cimag(amplitude)));
-
-
-
- for(i=0; i<PdN; i++)
- free(Pd[i]);
- free(Pd);
-
- 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 / commitdiff