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StabiliserVQE.c
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StabiliserVQE.c
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//------------------------------------------------------------------------------------------------------------------------
//----------------------------------------- Error-mitigated digital quantum simulation ----------------------------------
//------------------------------------------------------------------------------------------------------------------------
/*
* This program carries out the numerical simulations detailed in https://arxiv.org/abs/1807.02467.
* It computes the ground state energy of the di-hydrogen molecule, using the Hamiltonian averaging
* approach, along with a unitary coupled cluster ansatz. The circuit is subject to both stochastic
* depolarising noise, and temporally correlated over/under-rotations. These effects are mitigated
* using the stabiliser VQE technique, and linear extrapolation.
*/
#include <stdio.h>
# include <stdlib.h>
# include <time.h>
#include <sys/time.h>
# include <math.h>
# include <unistd.h>
# include <string.h>
# include <omp.h>
#include "QuEST.h"
const long double PI = 3.14159265358979323846264338327950288419716939937510;
int nParams = 3;
const int NUMTERMS = 15;
const int TERMLENGTH = 6;
const int CORRLEN = 6;
//// DATA FUNCTIONS ////////////////////////////////////////
void readData(double hamiltonianData[NUMTERMS][TERMLENGTH])
{
// Read in the Hamiltonian data.
FILE *fp;
fp = fopen("H2at075.txt", "r");
for(int i=0; i<NUMTERMS; i++)
{
for(int j=0; j<TERMLENGTH; j++)
{
fscanf(fp, "%lf ", &hamiltonianData[i][j]);
}
fscanf(fp, "\n");
}
fclose(fp);
}
//// CIRCUIT FUNCTIONS /////////////////////////////////////////
void oneQubitNoise(MultiQubit qReg, double gateNoise, int qubit, double errorArray[2])
{
// Adds depolarising noise after a single qubit gate.
double singleErrorProb = gateNoise/10;
double probNoError = 1 - singleErrorProb;
int noiseChanceInt = rand();
double noiseChance = (double)noiseChanceInt/(double)RAND_MAX;
if(noiseChance < probNoError)
{
// If the random number is below the error threshold, do nothing to the qubit.
}
else if(probNoError < noiseChance && noiseChance < (probNoError + singleErrorProb/3) )
{
sigmaX(qReg, qubit);
errorArray[0] = errorArray[0] + 1;
}
else if( (probNoError + singleErrorProb/3) < noiseChance && noiseChance < (probNoError + 2*singleErrorProb/3) )
{
sigmaY(qReg, qubit);
errorArray[0] = errorArray[0] + 1;
}
else
{
sigmaZ(qReg, qubit);
errorArray[0] = errorArray[0] + 1;
}
return;
}
void twoQubitNoise(MultiQubit qReg, double gateNoise, int qubit1, int qubit2, double errorArray[2])
{
// Adds depolarising noise after a two qubit gate.
double probNoError = 1 - gateNoise;
int noiseChanceInt = rand();
double noiseChance = (double)noiseChanceInt/(double)RAND_MAX;
if(noiseChance < probNoError)
{
// If the random number is below the error threshold, do nothing to the qubits.
}
else if(probNoError < noiseChance && noiseChance < (probNoError + 1*gateNoise/15) )
{
sigmaX(qReg, qubit1);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 1*gateNoise/15) < noiseChance && noiseChance < (probNoError + 2*gateNoise/15) )
{
sigmaY(qReg, qubit1);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 2*gateNoise/15) < noiseChance && noiseChance < (probNoError + 3*gateNoise/15) )
{
sigmaZ(qReg, qubit1);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 3*gateNoise/15) < noiseChance && noiseChance < (probNoError + 4*gateNoise/15) )
{
sigmaX(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 4*gateNoise/15) < noiseChance && noiseChance < (probNoError + 5*gateNoise/15) )
{
sigmaX(qReg, qubit1);
sigmaX(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 5*gateNoise/15) < noiseChance && noiseChance < (probNoError + 6*gateNoise/15) )
{
sigmaY(qReg, qubit1);
sigmaX(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 6*gateNoise/15) < noiseChance && noiseChance < (probNoError + 7*gateNoise/15) )
{
sigmaZ(qReg, qubit1);
sigmaX(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 7*gateNoise/15) < noiseChance && noiseChance < (probNoError + 8*gateNoise/15) )
{
sigmaY(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 8*gateNoise/15) < noiseChance && noiseChance < (probNoError + 9*gateNoise/15) )
{
sigmaX(qReg, qubit1);
sigmaY(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 9*gateNoise/15) < noiseChance && noiseChance < (probNoError + 10*gateNoise/15) )
{
sigmaY(qReg, qubit1);
sigmaY(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 10*gateNoise/15) < noiseChance && noiseChance < (probNoError + 11*gateNoise/15) )
{
sigmaZ(qReg, qubit1);
sigmaY(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 11*gateNoise/15) < noiseChance && noiseChance < (probNoError + 12*gateNoise/15) )
{
sigmaZ(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 12*gateNoise/15) < noiseChance && noiseChance < (probNoError + 13*gateNoise/15) )
{
sigmaX(qReg, qubit1);
sigmaZ(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else if((probNoError + 13*gateNoise/15) < noiseChance && noiseChance < (probNoError + 14*gateNoise/15) )
{
sigmaY(qReg, qubit1);
sigmaZ(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
else
{
sigmaZ(qReg, qubit1);
sigmaZ(qReg, qubit2);
errorArray[0] = errorArray[0] + 1;
}
return;
}
void fillCorrArray(double corrArray[CORRLEN], double corrBound)
{
// Fills the correlation array with a random seed between +corrBound and -corrBound.
for (int i=0; i<CORRLEN; i++)
{
double randRot = corrBound * ((double) rand() / (RAND_MAX));
double sign = ((double) rand() / (RAND_MAX));
if (sign < 0.5)
{
corrArray[i] = 1.0 - randRot;
}
else
{
corrArray[i] = 1.0 + randRot;
}
}
return;
}
void parametrisedCNOT(MultiQubit qReg, int controlQubit, int targetQubit, double correlationArray[CORRLEN])
{
// Performs a parametrised CNOT gate given by Control-(iRx(theta)).
double rotationAngle = correlationArray[targetQubit] * PI;
Complex r0c0 = {0, cos(rotationAngle/2)};
Complex r0c1 = {sin(rotationAngle/2), 0};
Complex r1c0 = {sin(rotationAngle/2), 0};
Complex r1c1 = {0, cos(rotationAngle/2)};
ComplexMatrix2 rotateMatrix = {r0c0, r0c1, r1c0, r1c1};
controlledUnitary(qReg, controlQubit, targetQubit, rotateMatrix);
return;
}
void parametrisedHadamard(MultiQubit qReg, int targetQubit, double correlationArray[CORRLEN])
{
// Performs a parametrised Hadamard gate.
double rotationAngle = (1.0 + ((correlationArray[targetQubit] - 1.0)/10.0)) * (PI/2);
Complex r0c0 = {cos(rotationAngle/2), 0};
Complex r0c1 = {sin(rotationAngle/2), 0};
Complex r1c0 = {sin(rotationAngle/2), 0};
Complex r1c1 = {-cos(rotationAngle/2), 0};
ComplexMatrix2 rotateMatrix = {r0c0, r0c1, r1c0, r1c1};
unitary(qReg, targetQubit, rotateMatrix);
return;
}
//// ANSATZ FUNCTIONS ////////////////////////////////////////////
void hydrogenUCCterm0a(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(i/2 X1 Y0) to the qubit register.
rotateX(qReg, 0, (PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
// Note - sign as exponent has + sign.
rotateZ(qReg, 1, -2*parameter * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 0, -(PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm0b(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(-i/2 Y1 X0) to the qubit register.
rotateX(qReg, 1, (PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
// Note + sign as exponent has - sign.
rotateZ(qReg, 1, 2*parameter * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
rotateX(qReg, 1, -(PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
return;
}
void hydrogenUCCterm1a(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(i/2 X3 Y2) to the qubit register.
rotateX(qReg, 2, (PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note - sign as exponent has + sign.
rotateZ(qReg, 3, -2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
rotateX(qReg, 2, -(PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
return;
}
void hydrogenUCCterm1b(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(-i/2 Y3 X2) to the qubit register.
rotateX(qReg, 3, (PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note + sign as exponent has - sign.
rotateZ(qReg, 3, 2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 3, -(PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
return;
}
void hydrogenUCCterm2a(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(i $\theta$ X3 X2 Y1 X0) to the qubit register.
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
rotateX(qReg, 1, (PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note - sign as exponent has + sign.
rotateZ(qReg, 3, -2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 1, -(PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm2b(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(i $\theta$ Y3 X2 X1 X0) to the qubit register.
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 3, (PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note - sign as exponent has + sign.
rotateZ(qReg, 3, -2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
rotateX(qReg, 3, -(PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm2c(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(i $\theta$ Y3 Y2 Y1 X0) to the qubit register.
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
rotateX(qReg, 1, (PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 2, (PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 3, (PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note - sign as exponent has + sign.
rotateZ(qReg, 3, -2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
rotateX(qReg, 3, -(PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
rotateX(qReg, 2, -(PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 1, -(PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm2d(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(i $\theta$ Y3 X2 Y1 Y0) to the qubit register.
rotateX(qReg, 0, (PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
rotateX(qReg, 1, (PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 3, (PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note - sign as exponent has + sign.
rotateZ(qReg, 3, -2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
rotateX(qReg, 3, -(PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 1, -(PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 0, -(PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm2e(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(-i $\theta$ X3 Y2 Y1 Y0) to the qubit register.
rotateX(qReg, 0, (PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
rotateX(qReg, 1, (PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 2, (PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note + sign as exponent has - sign.
rotateZ(qReg, 3, 2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
rotateX(qReg, 2, -(PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 1, -(PI/2) * (1.0 + ((corrArray[1] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 0, -(PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm2f(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(-i $\theta$ Y3 Y2 X1 Y0) to the qubit register.
rotateX(qReg, 0, (PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 2, (PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
rotateX(qReg, 3, (PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note + sign as exponent has - sign.
rotateZ(qReg, 3, 2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
rotateX(qReg, 3, -(PI/2) * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
rotateX(qReg, 2, -(PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 0, -(PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm2g(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(-i $\theta$ X3 Y2 X1 X0) to the qubit register.
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 2, (PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note + sign as exponent has - sign.
rotateZ(qReg, 3, 2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
rotateX(qReg, 2, -(PI/2) * (1.0 + ((corrArray[2] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 0, corrArray);
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void hydrogenUCCterm2h(double parameter, double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Applies the UCC term exp(-i $\theta$ X3 X2 X1 Y0) to the qubit register.
rotateX(qReg, 0, (PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Note + sign as exponent has - sign.
rotateZ(qReg, 3, 2*parameter * (1.0 + ((corrArray[3] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 1, 2, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 2, errorArray);
parametrisedCNOT(qReg, 0, 1, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 1, errorArray);
parametrisedHadamard(qReg, 3, corrArray);
oneQubitNoise(qReg, gateNoise, 3, errorArray);
parametrisedHadamard(qReg, 2, corrArray);
oneQubitNoise(qReg, gateNoise, 2, errorArray);
parametrisedHadamard(qReg, 1, corrArray);
oneQubitNoise(qReg, gateNoise, 1, errorArray);
rotateX(qReg, 0, -(PI/2) * (1.0 + ((corrArray[0] - 1.0)/10.0)));
oneQubitNoise(qReg, gateNoise, 0, errorArray);
return;
}
void makeAnsatz(double parameters[nParams], double gateNoise, MultiQubit qReg, double corrArray[CORRLEN], double errorArray[2])
{
// Creates the UCC ansatz applied to H2, starting from a HF state.
initStateZero(&qReg);
// Create Hartree-Fock state.
sigmaX(qReg, 0);
sigmaX(qReg, 2);
// Apply UCC circuit.
hydrogenUCCterm2a(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm2b(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm2c(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm2d(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm2e(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm2f(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm2g(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm2h(parameters[2], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm1a(parameters[1], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm1b(parameters[1], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm0a(parameters[0], gateNoise, qReg, corrArray, errorArray);
hydrogenUCCterm0b(parameters[0], gateNoise, qReg, corrArray, errorArray);
return;
}
//// MEASUREMENT FUNCTIONS ///////////////////////////////////////////////
void measureStateOnce(int numMeasured, double measuredReg[numMeasured], MultiQubit qReg)
{
// Measures the register such that it collapses to a single state in the computational basis.
for (int i=0; i<numMeasured; i++)
{
measuredReg[i] = measure(qReg, i);
}
return;
}
double getSubtermMeasurement(int numQubits, double parameters[nParams], double gateNoise,
MultiQubit qReg, double hamilTerm[TERMLENGTH], double errorArray[2], int numUp, int numParticles, double corrArray[CORRLEN])
{
// Performs a single measurement of one of the Pauli strings in the Hamiltonian.
int nRegister = numQubits - 2;
makeAnsatz(parameters, gateNoise, qReg, corrArray, errorArray);
// Parity check.
// First check spin up parity.
parametrisedCNOT(qReg, 1, 0, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 0, errorArray);
parametrisedCNOT(qReg, 0, 4, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 4, errorArray);
int parityUpMeasure = measure(qReg, 4);
double parityUpValue = pow(-1, parityUpMeasure);
parametrisedCNOT(qReg, 0, 4, corrArray);
twoQubitNoise(qReg, gateNoise, 0, 4, errorArray);
parametrisedCNOT(qReg, 1, 0, corrArray);
twoQubitNoise(qReg, gateNoise, 1, 0, errorArray);
// Check spin down parity.
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
parametrisedCNOT(qReg, 3, 5, corrArray);
twoQubitNoise(qReg, gateNoise, 3, 5, errorArray);
int parityDownMeasure = measure(qReg, 5);
double parityDownValue = pow(-1, parityDownMeasure);
parametrisedCNOT(qReg, 3, 5, corrArray);
twoQubitNoise(qReg, gateNoise, 3, 5, errorArray);
parametrisedCNOT(qReg, 2, 3, corrArray);
twoQubitNoise(qReg, gateNoise, 2, 3, errorArray);
// Check if parity has been violated. Return zero if so.
// If not, carry out the measurement of h_i.
int numDown = numParticles - numUp;
double parityUp = pow(-1, numUp);
double parityDown = pow(-1, numDown);
// Avoid comparing doubles in c.
double upDiff = fabs(parityUpValue - parityUp);
double downDiff = fabs(parityDownValue - parityDown);
if (upDiff > 0.1 || downDiff > 0.1)
// If either parity is not equal to true value, discard measurement.
{
return 0.0;
}
else
// Carry out the measurement of h_i.
{
// Change basis such that measuring Pauli term becomes equivalent to measuring in the computational basis.
for (int k=0; k<nRegister; k++)
{
double gate = hamilTerm[k+2];
if (gate > 0.98 && gate < 1.02)
{
hadamard(qReg, k);
}
else if (gate > 1.98 && gate < 2.02)
{
rotateX(qReg, k, PI/2);
}
else
{
// Do nothing for I or Z.
}
}
// Measure the main register in the Z basis.
double reg[nRegister];
measureStateOnce(nRegister, reg, qReg);
// Calculate the parity of relevant qubits in the term.
double paritySum = 0.0;
for (int l=0; l<nRegister; l++)
{
double gate = hamilTerm[l+2];
if (gate > 0.02)
{
paritySum = paritySum + reg[l];
}
}
double parityMeasurement = pow(-1, paritySum);
return parityMeasurement;
}
}
double getSubtermExpectation(int numQubits, double parameters[nParams], double gateNoise,
MultiQubit qReg, double hamilTerm[TERMLENGTH], int nRepeats, double errorArray[2], int numUp, int numParticles, double corrBound)
{
// Performs multiple state initialisations and measurements to measure the expectation value of a single Pauli term in the Hamiltonian.
int errorCounter = 0;
double expectationSum = 0.0;
double corrArray[CORRLEN];
for (int i=0; i<nRepeats; i++)
{
fillCorrArray(corrArray, corrBound);
double measuredValue = getSubtermMeasurement(numQubits, parameters, gateNoise, qReg, hamilTerm,
errorArray, numUp, numParticles, corrArray);
if (measuredValue < 0.01 && measuredValue > -0.01)
// Returned values are +/- 1 for no error detected, 0 for error detected, so a value between +/- 0.01 implies an error detection.
{
errorCounter = errorCounter + 1;
}
expectationSum = expectationSum + measuredValue;
}
double nTrials = nRepeats - errorCounter;
double expectation = expectationSum/nTrials;
errorArray[1] = errorArray[1] + errorCounter;
return expectation;
}
double getExtrapolatedExpectation(int numQubits, double parameters[nParams], double gateNoise, MultiQubit qReg,
double hamilTerm[TERMLENGTH], int nRepeats, double errorArray[2], int numUp, int numParticles, double corrBound)
{
// Performs linear error extrapolation of a single Hamiltonian term expectation value.
double stretchFactor = 1.0 + 0.0005/gateNoise;
double stretchOverRot = pow(stretchFactor, 0.5);
double expectationNormalError = getSubtermExpectation(numQubits, parameters, gateNoise, qReg,
hamilTerm, nRepeats/2, errorArray, numUp, numParticles, corrBound);
double expectationStretchedError = getSubtermExpectation(numQubits, parameters, stretchFactor*gateNoise, qReg,
hamilTerm, nRepeats/2, errorArray, numUp, numParticles, stretchOverRot*corrBound);
double gradient = (expectationStretchedError - expectationNormalError)/((stretchFactor - 1)*(gateNoise));
double extrapolatedValue = expectationNormalError - gradient*gateNoise;
return extrapolatedValue;
}
double getRepititionRatio(double desiredPrecision, double hamiltonian[NUMTERMS][TERMLENGTH])
{
// Calculates the repitition ratio required to achieve a specified precision in the final energy value.
// Find the max value in the Hamiltonian, and get the sum of the terms in the Hamiltonian.
double termSum = 0.0;
double maxValue = 0.0;
for (int i=1; i<NUMTERMS; i++)
{
if (fabs(hamiltonian[i][1]) > maxValue)
{
maxValue = fabs(hamiltonian[i][1]);
}
termSum = termSum + fabs(hamiltonian[i][1]);
}
// Get the repitition ratio, i.e. the maximum number of measurements any term gets, divided by the maximum Hamiltonian coefficient.
double maxReps = (maxValue*termSum)/(desiredPrecision*desiredPrecision);
double repititionRatio = maxReps/maxValue;
return repititionRatio;
}
double measureEnergy(int numQubits, double parameters[nParams], double gateNoise, MultiQubit qReg, double hamiltonian[NUMTERMS][TERMLENGTH], double precision,
double errorArray[2], int numUp, int numParticles,
int extrapolation, double corrBound)
{
// Measures the energy of the state defined by the parameters by performing many state initialisations and measurements.
double energy = 0.0;
double nuclearRepulsion = hamiltonian[0][1];
energy = energy + nuclearRepulsion;
double repRatio = getRepititionRatio(precision, hamiltonian);
for (int i=1; i<NUMTERMS; i++)
{
double termCoefficient = hamiltonian[i][1];
double termExpectation;
int termReps = floor(repRatio * fabs(termCoefficient));
if (extrapolation == 1)
{
termExpectation = getExtrapolatedExpectation(numQubits, parameters, gateNoise, qReg,
hamiltonian[i], termReps, errorArray, numUp, numParticles, corrBound);
// Stop over-extrapolation at points close to the boundaries.
if (termExpectation < -1.0)
{
termExpectation = -1.0;