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QuEST_cpu.c
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QuEST_cpu.c
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// Distributed under MIT licence. See https://github.com/QuEST-Kit/QuEST/blob/master/LICENCE.txt for details
/** @file
* The core of the CPU backend functionality. The CPU/MPI implementations of the pure state functions in
* ../QuEST_ops_pure.h are in QuEST_cpu_local.c and QuEST_cpu_distributed.c which mostly wrap the core
* functions defined here. Some additional hardware-agnostic functions are defined here
*
* @author Ania Brown
* @author Tyson Jones
* @author Balint Koczor
*/
# include "QuEST.h"
# include "QuEST_internal.h"
# include "QuEST_precision.h"
# include "QuEST_validation.h"
# include "mt19937ar.h"
# include "QuEST_cpu_internal.h"
# include <math.h>
# include <stdio.h>
# include <stdlib.h>
# include <stdint.h>
# include <assert.h>
# ifdef _OPENMP
# include <omp.h>
# endif
/* to support MSVC, we must remove the use of VLA in multiQubtUnitary.
* We'll instead create stack arrays use _malloca
*/
#ifdef _WIN32
#include <malloc.h>
#endif
/*
* overloads for consistent API with GPU
*/
void copyStateToGPU(Qureg qureg) {
}
void copyStateFromGPU(Qureg qureg) {
}
void statevec_copySubstateToGPU(Qureg qureg, long long int startInd, long long int numAmps) {
}
void statevec_copySubstateFromGPU(Qureg qureg, long long int startInd, long long int numAmps) {
}
/*
* state vector and density matrix operations
*/
void densmatr_oneQubitDegradeOffDiagonal(Qureg qureg, int targetQubit, qreal retain){
long long int numTasks = qureg.numAmpsPerChunk;
long long int innerMask = 1LL << targetQubit;
long long int outerMask = 1LL << (targetQubit + (qureg.numQubitsRepresented));
long long int thisTask;
long long int thisPattern;
long long int totMask = innerMask|outerMask;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (innerMask,outerMask,totMask,qureg,retain,numTasks, targetQubit) \
private (thisTask,thisPattern)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (thisTask=0; thisTask<numTasks; thisTask++){
thisPattern = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMask;
if ((thisPattern==innerMask) || (thisPattern==outerMask)){
// do dephase
// the lines below will degrade the off-diagonal terms |..0..><..1..| and |..1..><..0..|
qureg.stateVec.real[thisTask] = retain*qureg.stateVec.real[thisTask];
qureg.stateVec.imag[thisTask] = retain*qureg.stateVec.imag[thisTask];
}
}
}
}
void densmatr_mixDephasing(Qureg qureg, int targetQubit, qreal dephase) {
qreal retain=1-dephase;
densmatr_oneQubitDegradeOffDiagonal(qureg, targetQubit, retain);
}
void densmatr_mixTwoQubitDephasing(Qureg qureg, int qubit1, int qubit2, qreal dephase) {
qreal retain=1-dephase;
long long int numTasks = qureg.numAmpsPerChunk;
long long int innerMaskQubit1 = 1LL << qubit1;
long long int outerMaskQubit1 = 1LL << (qubit1 + (qureg.numQubitsRepresented));
long long int innerMaskQubit2 = 1LL << qubit2;
long long int outerMaskQubit2 = 1LL << (qubit2 + (qureg.numQubitsRepresented));
long long int totMaskQubit1 = innerMaskQubit1|outerMaskQubit1;
long long int totMaskQubit2 = innerMaskQubit2|outerMaskQubit2;
long long int thisTask;
long long int thisPatternQubit1, thisPatternQubit2;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (innerMaskQubit1,outerMaskQubit1,totMaskQubit1,innerMaskQubit2,outerMaskQubit2, \
totMaskQubit2,qureg,retain,numTasks) \
private (thisTask,thisPatternQubit1,thisPatternQubit2)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (thisTask=0; thisTask<numTasks; thisTask++){
thisPatternQubit1 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit1;
thisPatternQubit2 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit2;
// any mismatch |...0...><...1...| etc
if ( (thisPatternQubit1==innerMaskQubit1) || (thisPatternQubit1==outerMaskQubit1) ||
(thisPatternQubit2==innerMaskQubit2) || (thisPatternQubit2==outerMaskQubit2) ){
// do dephase
// the lines below will degrade the off-diagonal terms |..0..><..1..| and |..1..><..0..|
qureg.stateVec.real[thisTask] = retain*qureg.stateVec.real[thisTask];
qureg.stateVec.imag[thisTask] = retain*qureg.stateVec.imag[thisTask];
}
}
}
}
void densmatr_mixDepolarisingLocal(Qureg qureg, int targetQubit, qreal depolLevel) {
qreal retain=1-depolLevel;
long long int numTasks = qureg.numAmpsPerChunk;
long long int innerMask = 1LL << targetQubit;
long long int outerMask = 1LL << (targetQubit + (qureg.numQubitsRepresented));
long long int totMask = innerMask|outerMask;
long long int thisTask;
long long int partner;
long long int thisPattern;
qreal realAv, imagAv;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (innerMask,outerMask,totMask,qureg,retain,depolLevel,numTasks) \
private (thisTask,partner,thisPattern,realAv,imagAv)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (thisTask=0; thisTask<numTasks; thisTask++){
thisPattern = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMask;
if ((thisPattern==innerMask) || (thisPattern==outerMask)){
// do dephase
// the lines below will degrade the off-diagonal terms |..0..><..1..| and |..1..><..0..|
qureg.stateVec.real[thisTask] = retain*qureg.stateVec.real[thisTask];
qureg.stateVec.imag[thisTask] = retain*qureg.stateVec.imag[thisTask];
} else {
if ((thisTask&totMask)==0){ //this element relates to targetQubit in state 0
// do depolarise
partner = thisTask | totMask;
realAv = (qureg.stateVec.real[thisTask] + qureg.stateVec.real[partner]) /2 ;
imagAv = (qureg.stateVec.imag[thisTask] + qureg.stateVec.imag[partner]) /2 ;
qureg.stateVec.real[thisTask] = retain*qureg.stateVec.real[thisTask] + depolLevel*realAv;
qureg.stateVec.imag[thisTask] = retain*qureg.stateVec.imag[thisTask] + depolLevel*imagAv;
qureg.stateVec.real[partner] = retain*qureg.stateVec.real[partner] + depolLevel*realAv;
qureg.stateVec.imag[partner] = retain*qureg.stateVec.imag[partner] + depolLevel*imagAv;
}
}
}
}
}
void densmatr_mixDampingLocal(Qureg qureg, int targetQubit, qreal damping) {
qreal retain=1-damping;
qreal dephase=sqrt(retain);
long long int numTasks = qureg.numAmpsPerChunk;
long long int innerMask = 1LL << targetQubit;
long long int outerMask = 1LL << (targetQubit + (qureg.numQubitsRepresented));
long long int totMask = innerMask|outerMask;
long long int thisTask;
long long int partner;
long long int thisPattern;
//qreal realAv, imagAv;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (innerMask,outerMask,totMask,qureg,retain,damping,dephase,numTasks) \
private (thisTask,partner,thisPattern)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (thisTask=0; thisTask<numTasks; thisTask++){
thisPattern = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMask;
if ((thisPattern==innerMask) || (thisPattern==outerMask)){
// do dephase
// the lines below will degrade the off-diagonal terms |..0..><..1..| and |..1..><..0..|
qureg.stateVec.real[thisTask] = dephase*qureg.stateVec.real[thisTask];
qureg.stateVec.imag[thisTask] = dephase*qureg.stateVec.imag[thisTask];
} else {
if ((thisTask&totMask)==0){ //this element relates to targetQubit in state 0
// do depolarise
partner = thisTask | totMask;
//realAv = (qureg.stateVec.real[thisTask] + qureg.stateVec.real[partner]) /2 ;
//imagAv = (qureg.stateVec.imag[thisTask] + qureg.stateVec.imag[partner]) /2 ;
qureg.stateVec.real[thisTask] = qureg.stateVec.real[thisTask] + damping*qureg.stateVec.real[partner];
qureg.stateVec.imag[thisTask] = qureg.stateVec.imag[thisTask] + damping*qureg.stateVec.imag[partner];
qureg.stateVec.real[partner] = retain*qureg.stateVec.real[partner];
qureg.stateVec.imag[partner] = retain*qureg.stateVec.imag[partner];
}
}
}
}
}
void densmatr_mixDepolarisingDistributed(Qureg qureg, int targetQubit, qreal depolLevel) {
// first do dephase part.
// TODO -- this might be more efficient to do at the same time as the depolarise if we move to
// iterating over all elements in the state vector for the purpose of vectorisation
// TODO -- if we keep this split, move this function to densmatr_mixDepolarising()
densmatr_mixDephasing(qureg, targetQubit, depolLevel);
long long int sizeInnerBlock, sizeInnerHalfBlock;
long long int sizeOuterColumn, sizeOuterHalfColumn;
long long int thisInnerBlock, // current block
thisOuterColumn, // current column in density matrix
thisIndex, // current index in (density matrix representation) state vector
thisIndexInOuterColumn,
thisIndexInInnerBlock;
int outerBit;
long long int thisTask;
long long int numTasks=qureg.numAmpsPerChunk>>1;
// set dimensions
sizeInnerHalfBlock = 1LL << targetQubit;
sizeInnerBlock = 2LL * sizeInnerHalfBlock;
sizeOuterColumn = 1LL << qureg.numQubitsRepresented;
sizeOuterHalfColumn = sizeOuterColumn >> 1;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (sizeInnerBlock,sizeInnerHalfBlock,sizeOuterColumn,sizeOuterHalfColumn, \
qureg,depolLevel,numTasks,targetQubit) \
private (thisTask,thisInnerBlock,thisOuterColumn,thisIndex,thisIndexInOuterColumn, \
thisIndexInInnerBlock,outerBit)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
// thisTask iterates over half the elements in this process' chunk of the density matrix
// treat this as iterating over all columns, then iterating over half the values
// within one column.
// If this function has been called, this process' chunk contains half an
// outer block or less
for (thisTask=0; thisTask<numTasks; thisTask++) {
// we want to process all columns in the density matrix,
// updating the values for half of each column (one half of each inner block)
thisOuterColumn = thisTask / sizeOuterHalfColumn;
thisIndexInOuterColumn = thisTask&(sizeOuterHalfColumn-1); // thisTask % sizeOuterHalfColumn
thisInnerBlock = thisIndexInOuterColumn/sizeInnerHalfBlock;
// get index in state vector corresponding to upper inner block
thisIndexInInnerBlock = thisTask&(sizeInnerHalfBlock-1); // thisTask % sizeInnerHalfBlock
thisIndex = thisOuterColumn*sizeOuterColumn + thisInnerBlock*sizeInnerBlock
+ thisIndexInInnerBlock;
// check if we are in the upper or lower half of an outer block
outerBit = extractBit(targetQubit, (thisIndex+qureg.numAmpsPerChunk*qureg.chunkId)>>qureg.numQubitsRepresented);
// if we are in the lower half of an outer block, shift to be in the lower half
// of the inner block as well (we want to dephase |0><0| and |1><1| only)
thisIndex += outerBit*(sizeInnerHalfBlock);
// NOTE: at this point thisIndex should be the index of the element we want to
// dephase in the chunk of the state vector on this process, in the
// density matrix representation.
// thisTask is the index of the pair element in pairStateVec
// state[thisIndex] = (1-depolLevel)*state[thisIndex] + depolLevel*(state[thisIndex]
// + pair[thisTask])/2
qureg.stateVec.real[thisIndex] = (1-depolLevel)*qureg.stateVec.real[thisIndex] +
depolLevel*(qureg.stateVec.real[thisIndex] + qureg.pairStateVec.real[thisTask])/2;
qureg.stateVec.imag[thisIndex] = (1-depolLevel)*qureg.stateVec.imag[thisIndex] +
depolLevel*(qureg.stateVec.imag[thisIndex] + qureg.pairStateVec.imag[thisTask])/2;
}
}
}
void densmatr_mixDampingDistributed(Qureg qureg, int targetQubit, qreal damping) {
qreal retain=1-damping;
qreal dephase=sqrt(1-damping);
// multiply the off-diagonal (|0><1| and |1><0|) terms by sqrt(1-damping)
densmatr_oneQubitDegradeOffDiagonal(qureg, targetQubit, dephase);
// below, we modify the diagonals terms which require |1><1| to |0><0| communication
long long int sizeInnerBlock, sizeInnerHalfBlock;
long long int sizeOuterColumn, sizeOuterHalfColumn;
long long int thisInnerBlock, // current block
thisOuterColumn, // current column in density matrix
thisIndex, // current index in (density matrix representation) state vector
thisIndexInOuterColumn,
thisIndexInInnerBlock;
int outerBit;
int stateBit;
long long int thisTask;
long long int numTasks=qureg.numAmpsPerChunk>>1;
// set dimensions
sizeInnerHalfBlock = 1LL << targetQubit;
sizeInnerBlock = 2LL * sizeInnerHalfBlock;
sizeOuterColumn = 1LL << qureg.numQubitsRepresented;
sizeOuterHalfColumn = sizeOuterColumn >> 1;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (sizeInnerBlock,sizeInnerHalfBlock,sizeOuterColumn,sizeOuterHalfColumn, \
qureg,damping, retain, dephase, numTasks,targetQubit) \
private (thisTask,thisInnerBlock,thisOuterColumn,thisIndex,thisIndexInOuterColumn, \
thisIndexInInnerBlock,outerBit, stateBit)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
// thisTask iterates over half the elements in this process' chunk of the density matrix
// treat this as iterating over all columns, then iterating over half the values
// within one column.
// If this function has been called, this process' chunk contains half an
// outer block or less
for (thisTask=0; thisTask<numTasks; thisTask++) {
// we want to process all columns in the density matrix,
// updating the values for half of each column (one half of each inner block)
thisOuterColumn = thisTask / sizeOuterHalfColumn;
thisIndexInOuterColumn = thisTask&(sizeOuterHalfColumn-1); // thisTask % sizeOuterHalfColumn
thisInnerBlock = thisIndexInOuterColumn/sizeInnerHalfBlock;
// get index in state vector corresponding to upper inner block
thisIndexInInnerBlock = thisTask&(sizeInnerHalfBlock-1); // thisTask % sizeInnerHalfBlock
thisIndex = thisOuterColumn*sizeOuterColumn + thisInnerBlock*sizeInnerBlock
+ thisIndexInInnerBlock;
// check if we are in the upper or lower half of an outer block
outerBit = extractBit(targetQubit, (thisIndex+qureg.numAmpsPerChunk*qureg.chunkId)>>qureg.numQubitsRepresented);
// if we are in the lower half of an outer block, shift to be in the lower half
// of the inner block as well (we want to dephase |0><0| and |1><1| only)
thisIndex += outerBit*(sizeInnerHalfBlock);
// NOTE: at this point thisIndex should be the index of the element we want to
// dephase in the chunk of the state vector on this process, in the
// density matrix representation.
// thisTask is the index of the pair element in pairStateVec
// Extract state bit, is 0 if thisIndex corresponds to a state with 0 in the target qubit
// and is 1 if thisIndex corresponds to a state with 1 in the target qubit
stateBit = extractBit(targetQubit, (thisIndex+qureg.numAmpsPerChunk*qureg.chunkId));
// state[thisIndex] = (1-depolLevel)*state[thisIndex] + depolLevel*(state[thisIndex]
// + pair[thisTask])/2
if(stateBit == 0){
qureg.stateVec.real[thisIndex] = qureg.stateVec.real[thisIndex] +
damping*( qureg.pairStateVec.real[thisTask]);
qureg.stateVec.imag[thisIndex] = qureg.stateVec.imag[thisIndex] +
damping*( qureg.pairStateVec.imag[thisTask]);
} else{
qureg.stateVec.real[thisIndex] = retain*qureg.stateVec.real[thisIndex];
qureg.stateVec.imag[thisIndex] = retain*qureg.stateVec.imag[thisIndex];
}
}
}
}
void densmatr_mixTwoQubitDepolarisingLocal(Qureg qureg, int qubit1, int qubit2, qreal delta, qreal gamma) {
long long int numTasks = qureg.numAmpsPerChunk;
long long int innerMaskQubit1 = 1LL << qubit1;
long long int outerMaskQubit1= 1LL << (qubit1 + qureg.numQubitsRepresented);
long long int totMaskQubit1 = innerMaskQubit1 | outerMaskQubit1;
long long int innerMaskQubit2 = 1LL << qubit2;
long long int outerMaskQubit2 = 1LL << (qubit2 + qureg.numQubitsRepresented);
long long int totMaskQubit2 = innerMaskQubit2 | outerMaskQubit2;
long long int thisTask;
long long int partner;
long long int thisPatternQubit1, thisPatternQubit2;
qreal real00, imag00;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (totMaskQubit1,totMaskQubit2,qureg,delta,gamma,numTasks) \
private (thisTask,partner,thisPatternQubit1,thisPatternQubit2,real00,imag00)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
//--------------------------------------- STEP ONE ---------------------
for (thisTask=0; thisTask<numTasks; thisTask++){
thisPatternQubit1 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit1;
thisPatternQubit2 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit2;
if ((thisPatternQubit1==0) && ((thisPatternQubit2==0)
|| (thisPatternQubit2==totMaskQubit2))){
//this element of form |...X...0...><...X...0...| for X either 0 or 1.
partner = thisTask | totMaskQubit1;
real00 = qureg.stateVec.real[thisTask];
imag00 = qureg.stateVec.imag[thisTask];
qureg.stateVec.real[thisTask] = qureg.stateVec.real[thisTask]
+ delta*qureg.stateVec.real[partner];
qureg.stateVec.imag[thisTask] = qureg.stateVec.imag[thisTask]
+ delta*qureg.stateVec.imag[partner];
qureg.stateVec.real[partner] = qureg.stateVec.real[partner] + delta*real00;
qureg.stateVec.imag[partner] = qureg.stateVec.imag[partner] + delta*imag00;
}
}
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
//--------------------------------------- STEP TWO ---------------------
for (thisTask=0; thisTask<numTasks; thisTask++){
thisPatternQubit1 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit1;
thisPatternQubit2 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit2;
if ((thisPatternQubit2==0) && ((thisPatternQubit1==0)
|| (thisPatternQubit1==totMaskQubit1))){
//this element of form |...0...X...><...0...X...| for X either 0 or 1.
partner = thisTask | totMaskQubit2;
real00 = qureg.stateVec.real[thisTask];
imag00 = qureg.stateVec.imag[thisTask];
qureg.stateVec.real[thisTask] = qureg.stateVec.real[thisTask]
+ delta*qureg.stateVec.real[partner];
qureg.stateVec.imag[thisTask] = qureg.stateVec.imag[thisTask]
+ delta*qureg.stateVec.imag[partner];
qureg.stateVec.real[partner] = qureg.stateVec.real[partner] + delta*real00;
qureg.stateVec.imag[partner] = qureg.stateVec.imag[partner] + delta*imag00;
}
}
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
//--------------------------------------- STEP THREE ---------------------
for (thisTask=0; thisTask<numTasks; thisTask++){
thisPatternQubit1 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit1;
thisPatternQubit2 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit2;
if ((thisPatternQubit2==0) && ((thisPatternQubit1==0)
|| (thisPatternQubit1==totMaskQubit1))){
//this element of form |...0...X...><...0...X...| for X either 0 or 1.
partner = thisTask | totMaskQubit2;
partner = partner ^ totMaskQubit1;
real00 = qureg.stateVec.real[thisTask];
imag00 = qureg.stateVec.imag[thisTask];
qureg.stateVec.real[thisTask] = gamma * (qureg.stateVec.real[thisTask]
+ delta*qureg.stateVec.real[partner]);
qureg.stateVec.imag[thisTask] = gamma * (qureg.stateVec.imag[thisTask]
+ delta*qureg.stateVec.imag[partner]);
qureg.stateVec.real[partner] = gamma * (qureg.stateVec.real[partner]
+ delta*real00);
qureg.stateVec.imag[partner] = gamma * (qureg.stateVec.imag[partner]
+ delta*imag00);
}
}
}
}
void densmatr_mixTwoQubitDepolarisingLocalPart1(Qureg qureg, int qubit1, int qubit2, qreal delta) {
long long int numTasks = qureg.numAmpsPerChunk;
long long int innerMaskQubit1 = 1LL << qubit1;
long long int outerMaskQubit1= 1LL << (qubit1 + qureg.numQubitsRepresented);
long long int totMaskQubit1 = innerMaskQubit1 | outerMaskQubit1;
long long int innerMaskQubit2 = 1LL << qubit2;
long long int outerMaskQubit2 = 1LL << (qubit2 + qureg.numQubitsRepresented);
long long int totMaskQubit2 = innerMaskQubit2 | outerMaskQubit2;
// correct for being in a particular chunk
//totMaskQubit2 = totMaskQubit2&(qureg.numAmpsPerChunk-1); // totMaskQubit2 % numAmpsPerChunk
long long int thisTask;
long long int partner;
long long int thisPatternQubit1, thisPatternQubit2;
qreal real00, imag00;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (totMaskQubit1,totMaskQubit2,qureg,delta,numTasks) \
private (thisTask,partner,thisPatternQubit1,thisPatternQubit2,real00,imag00)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
//--------------------------------------- STEP ONE ---------------------
for (thisTask=0; thisTask<numTasks; thisTask ++){
thisPatternQubit1 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit1;
thisPatternQubit2 = (thisTask+qureg.numAmpsPerChunk*qureg.chunkId)&totMaskQubit2;
if ((thisPatternQubit1==0) && ((thisPatternQubit2==0)
|| (thisPatternQubit2==totMaskQubit2))){
//this element of form |...X...0...><...X...0...| for X either 0 or 1.
partner = thisTask | totMaskQubit1;
real00 = qureg.stateVec.real[thisTask];
imag00 = qureg.stateVec.imag[thisTask];
qureg.stateVec.real[thisTask] = qureg.stateVec.real[thisTask]
+ delta*qureg.stateVec.real[partner];
qureg.stateVec.imag[thisTask] = qureg.stateVec.imag[thisTask]
+ delta*qureg.stateVec.imag[partner];
qureg.stateVec.real[partner] = qureg.stateVec.real[partner] + delta*real00;
qureg.stateVec.imag[partner] = qureg.stateVec.imag[partner] + delta*imag00;
}
}
}
}
void densmatr_mixTwoQubitDepolarisingDistributed(Qureg qureg, int targetQubit,
int qubit2, qreal delta, qreal gamma) {
long long int sizeInnerBlockQ1, sizeInnerHalfBlockQ1;
long long int sizeInnerBlockQ2, sizeInnerHalfBlockQ2, sizeInnerQuarterBlockQ2;
long long int sizeOuterColumn, sizeOuterQuarterColumn;
long long int thisInnerBlockQ2,
thisOuterColumn, // current column in density matrix
thisIndex, // current index in (density matrix representation) state vector
thisIndexInOuterColumn,
thisIndexInInnerBlockQ1,
thisIndexInInnerBlockQ2,
thisInnerBlockQ1InInnerBlockQ2;
int outerBitQ1, outerBitQ2;
long long int thisTask;
long long int numTasks=qureg.numAmpsPerChunk>>2;
// set dimensions
sizeInnerHalfBlockQ1 = 1LL << targetQubit;
sizeInnerHalfBlockQ2 = 1LL << qubit2;
sizeInnerQuarterBlockQ2 = sizeInnerHalfBlockQ2 >> 1;
sizeInnerBlockQ2 = sizeInnerHalfBlockQ2 << 1;
sizeInnerBlockQ1 = 2LL * sizeInnerHalfBlockQ1;
sizeOuterColumn = 1LL << qureg.numQubitsRepresented;
sizeOuterQuarterColumn = sizeOuterColumn >> 2;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (sizeInnerBlockQ1,sizeInnerHalfBlockQ1,sizeInnerBlockQ2,sizeInnerHalfBlockQ2,sizeInnerQuarterBlockQ2,\
sizeOuterColumn,sizeOuterQuarterColumn,qureg,delta,gamma,numTasks,targetQubit,qubit2) \
private (thisTask,thisInnerBlockQ2,thisInnerBlockQ1InInnerBlockQ2, \
thisOuterColumn,thisIndex,thisIndexInOuterColumn, \
thisIndexInInnerBlockQ1,thisIndexInInnerBlockQ2,outerBitQ1,outerBitQ2)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
// thisTask iterates over half the elements in this process' chunk of the density matrix
// treat this as iterating over all columns, then iterating over half the values
// within one column.
// If this function has been called, this process' chunk contains half an
// outer block or less
for (thisTask=0; thisTask<numTasks; thisTask++) {
// we want to process all columns in the density matrix,
// updating the values for half of each column (one half of each inner block)
thisOuterColumn = thisTask / sizeOuterQuarterColumn;
// thisTask % sizeOuterQuarterColumn
thisIndexInOuterColumn = thisTask&(sizeOuterQuarterColumn-1);
thisInnerBlockQ2 = thisIndexInOuterColumn / sizeInnerQuarterBlockQ2;
// thisTask % sizeInnerQuarterBlockQ2;
thisIndexInInnerBlockQ2 = thisTask&(sizeInnerQuarterBlockQ2-1);
thisInnerBlockQ1InInnerBlockQ2 = thisIndexInInnerBlockQ2 / sizeInnerHalfBlockQ1;
// thisTask % sizeInnerHalfBlockQ1;
thisIndexInInnerBlockQ1 = thisTask&(sizeInnerHalfBlockQ1-1);
// get index in state vector corresponding to upper inner block
thisIndex = thisOuterColumn*sizeOuterColumn + thisInnerBlockQ2*sizeInnerBlockQ2
+ thisInnerBlockQ1InInnerBlockQ2*sizeInnerBlockQ1 + thisIndexInInnerBlockQ1;
// check if we are in the upper or lower half of an outer block for Q1
outerBitQ1 = extractBit(targetQubit, (thisIndex+qureg.numAmpsPerChunk*qureg.chunkId)>>qureg.numQubitsRepresented);
// if we are in the lower half of an outer block, shift to be in the lower half
// of the inner block as well (we want to dephase |0><0| and |1><1| only)
thisIndex += outerBitQ1*(sizeInnerHalfBlockQ1);
// check if we are in the upper or lower half of an outer block for Q2
outerBitQ2 = extractBit(qubit2, (thisIndex+qureg.numAmpsPerChunk*qureg.chunkId)>>qureg.numQubitsRepresented);
// if we are in the lower half of an outer block, shift to be in the lower half
// of the inner block as well (we want to dephase |0><0| and |1><1| only)
thisIndex += outerBitQ2*(sizeInnerQuarterBlockQ2<<1);
// NOTE: at this point thisIndex should be the index of the element we want to
// dephase in the chunk of the state vector on this process, in the
// density matrix representation.
// thisTask is the index of the pair element in pairStateVec
// state[thisIndex] = (1-depolLevel)*state[thisIndex] + depolLevel*(state[thisIndex]
// + pair[thisTask])/2
// NOTE: must set gamma=1 if using this function for steps 1 or 2
qureg.stateVec.real[thisIndex] = gamma*(qureg.stateVec.real[thisIndex] +
delta*qureg.pairStateVec.real[thisTask]);
qureg.stateVec.imag[thisIndex] = gamma*(qureg.stateVec.imag[thisIndex] +
delta*qureg.pairStateVec.imag[thisTask]);
}
}
}
void densmatr_mixTwoQubitDepolarisingQ1LocalQ2DistributedPart3(Qureg qureg, int targetQubit,
int qubit2, qreal delta, qreal gamma) {
long long int sizeInnerBlockQ1, sizeInnerHalfBlockQ1;
long long int sizeInnerBlockQ2, sizeInnerHalfBlockQ2, sizeInnerQuarterBlockQ2;
long long int sizeOuterColumn, sizeOuterQuarterColumn;
long long int thisInnerBlockQ2,
thisOuterColumn, // current column in density matrix
thisIndex, // current index in (density matrix representation) state vector
thisIndexInPairVector,
thisIndexInOuterColumn,
thisIndexInInnerBlockQ1,
thisIndexInInnerBlockQ2,
thisInnerBlockQ1InInnerBlockQ2;
int outerBitQ1, outerBitQ2;
long long int thisTask;
long long int numTasks=qureg.numAmpsPerChunk>>2;
// set dimensions
sizeInnerHalfBlockQ1 = 1LL << targetQubit;
sizeInnerHalfBlockQ2 = 1LL << qubit2;
sizeInnerQuarterBlockQ2 = sizeInnerHalfBlockQ2 >> 1;
sizeInnerBlockQ2 = sizeInnerHalfBlockQ2 << 1;
sizeInnerBlockQ1 = 2LL * sizeInnerHalfBlockQ1;
sizeOuterColumn = 1LL << qureg.numQubitsRepresented;
sizeOuterQuarterColumn = sizeOuterColumn >> 2;
//# if 0
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (sizeInnerBlockQ1,sizeInnerHalfBlockQ1,sizeInnerBlockQ2,sizeInnerHalfBlockQ2,sizeInnerQuarterBlockQ2,\
sizeOuterColumn,sizeOuterQuarterColumn,qureg,delta,gamma, numTasks,targetQubit,qubit2) \
private (thisTask,thisInnerBlockQ2,thisInnerBlockQ1InInnerBlockQ2, \
thisOuterColumn,thisIndex,thisIndexInPairVector,thisIndexInOuterColumn, \
thisIndexInInnerBlockQ1,thisIndexInInnerBlockQ2,outerBitQ1,outerBitQ2)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
//# endif
// thisTask iterates over half the elements in this process' chunk of the density matrix
// treat this as iterating over all columns, then iterating over half the values
// within one column.
// If this function has been called, this process' chunk contains half an
// outer block or less
for (thisTask=0; thisTask<numTasks; thisTask++) {
// we want to process all columns in the density matrix,
// updating the values for half of each column (one half of each inner block)
thisOuterColumn = thisTask / sizeOuterQuarterColumn;
// thisTask % sizeOuterQuarterColumn
thisIndexInOuterColumn = thisTask&(sizeOuterQuarterColumn-1);
thisInnerBlockQ2 = thisIndexInOuterColumn / sizeInnerQuarterBlockQ2;
// thisTask % sizeInnerQuarterBlockQ2;
thisIndexInInnerBlockQ2 = thisTask&(sizeInnerQuarterBlockQ2-1);
thisInnerBlockQ1InInnerBlockQ2 = thisIndexInInnerBlockQ2 / sizeInnerHalfBlockQ1;
// thisTask % sizeInnerHalfBlockQ1;
thisIndexInInnerBlockQ1 = thisTask&(sizeInnerHalfBlockQ1-1);
// get index in state vector corresponding to upper inner block
thisIndex = thisOuterColumn*sizeOuterColumn + thisInnerBlockQ2*sizeInnerBlockQ2
+ thisInnerBlockQ1InInnerBlockQ2*sizeInnerBlockQ1 + thisIndexInInnerBlockQ1;
// check if we are in the upper or lower half of an outer block for Q1
outerBitQ1 = extractBit(targetQubit, (thisIndex+qureg.numAmpsPerChunk*qureg.chunkId)>>qureg.numQubitsRepresented);
// if we are in the lower half of an outer block, shift to be in the lower half
// of the inner block as well (we want to dephase |0><0| and |1><1| only)
thisIndex += outerBitQ1*(sizeInnerHalfBlockQ1);
// For part 3 we need to match elements such that (my Q1 != pair Q1) AND (my Q2 != pair Q2)
// Find correct index in pairStateVector
thisIndexInPairVector = thisTask + (1-outerBitQ1)*sizeInnerHalfBlockQ1*sizeOuterQuarterColumn -
outerBitQ1*sizeInnerHalfBlockQ1*sizeOuterQuarterColumn;
// check if we are in the upper or lower half of an outer block for Q2
outerBitQ2 = extractBit(qubit2, (thisIndex+qureg.numAmpsPerChunk*qureg.chunkId)>>qureg.numQubitsRepresented);
// if we are in the lower half of an outer block, shift to be in the lower half
// of the inner block as well (we want to dephase |0><0| and |1><1| only)
thisIndex += outerBitQ2*(sizeInnerQuarterBlockQ2<<1);
// NOTE: at this point thisIndex should be the index of the element we want to
// dephase in the chunk of the state vector on this process, in the
// density matrix representation.
// state[thisIndex] = (1-depolLevel)*state[thisIndex] + depolLevel*(state[thisIndex]
// + pair[thisIndexInPairVector])/2
qureg.stateVec.real[thisIndex] = gamma*(qureg.stateVec.real[thisIndex] +
delta*qureg.pairStateVec.real[thisIndexInPairVector]);
qureg.stateVec.imag[thisIndex] = gamma*(qureg.stateVec.imag[thisIndex] +
delta*qureg.pairStateVec.imag[thisIndexInPairVector]);
}
}
}
/* Without nested parallelisation, only the outer most loops which call below are parallelised */
void zeroSomeAmps(Qureg qureg, long long int startInd, long long int numAmps) {
long long int i;
# ifdef _OPENMP
# pragma omp parallel for schedule (static)
# endif
for (i=startInd; i < startInd+numAmps; i++) {
qureg.stateVec.real[i] = 0;
qureg.stateVec.imag[i] = 0;
}
}
void normaliseSomeAmps(Qureg qureg, qreal norm, long long int startInd, long long int numAmps) {
long long int i;
# ifdef _OPENMP
# pragma omp parallel for schedule (static)
# endif
for (i=startInd; i < startInd+numAmps; i++) {
qureg.stateVec.real[i] /= norm;
qureg.stateVec.imag[i] /= norm;
}
}
void alternateNormZeroingSomeAmpBlocks(
Qureg qureg, qreal norm, int normFirst,
long long int startAmpInd, long long int numAmps, long long int blockSize
) {
long long int numDubBlocks = numAmps / (2*blockSize);
long long int blockStartInd;
if (normFirst) {
long long int dubBlockInd;
# ifdef _OPENMP
# pragma omp parallel for schedule (static) private (blockStartInd)
# endif
for (dubBlockInd=0; dubBlockInd < numDubBlocks; dubBlockInd++) {
blockStartInd = startAmpInd + dubBlockInd*2*blockSize;
normaliseSomeAmps(qureg, norm, blockStartInd, blockSize); // |0><0|
zeroSomeAmps( qureg, blockStartInd + blockSize, blockSize);
}
} else {
long long int dubBlockInd;
# ifdef _OPENMP
# pragma omp parallel for schedule (static) private (blockStartInd)
# endif
for (dubBlockInd=0; dubBlockInd < numDubBlocks; dubBlockInd++) {
blockStartInd = startAmpInd + dubBlockInd*2*blockSize;
zeroSomeAmps( qureg, blockStartInd, blockSize);
normaliseSomeAmps(qureg, norm, blockStartInd + blockSize, blockSize); // |1><1|
}
}
}
/** Renorms (/prob) every | * outcome * >< * outcome * | state, setting all others to zero */
void densmatr_collapseToKnownProbOutcome(Qureg qureg, int measureQubit, int outcome, qreal totalStateProb) {
// only (global) indices (as bit sequence): '* outcome *(n+q) outcome *q are spared
// where n = measureQubit, q = qureg.numQubitsRepresented.
// We can thus step in blocks of 2^q+n, killing every second, and inside the others,
// stepping in sub-blocks of 2^q, killing every second.
// When outcome=1, we offset the start of these blocks by their size.
long long int innerBlockSize = (1LL << measureQubit);
long long int outerBlockSize = (1LL << (measureQubit + qureg.numQubitsRepresented));
// Because there are 2^a number of nodes(/chunks), each node will contain 2^b number of blocks,
// or each block will span 2^c number of nodes. Similarly for the innerblocks.
long long int locNumAmps = qureg.numAmpsPerChunk;
long long int globalStartInd = qureg.chunkId * locNumAmps;
int innerBit = extractBit(measureQubit, globalStartInd);
int outerBit = extractBit(measureQubit + qureg.numQubitsRepresented, globalStartInd);
// If this chunk's amps are entirely inside an outer block
if (locNumAmps <= outerBlockSize) {
// if this is an undesired outer block, kill all elems
if (outerBit != outcome) {
zeroSomeAmps(qureg, 0, qureg.numAmpsPerChunk);
return;
}
// othwerwise, if this is a desired outer block, and also entirely an inner block
if (locNumAmps <= innerBlockSize) {
// and that inner block is undesired, kill all elems
if (innerBit != outcome)
zeroSomeAmps(qureg, 0, qureg.numAmpsPerChunk);
// otherwise normalise all elems
else
normaliseSomeAmps(qureg, totalStateProb, 0, qureg.numAmpsPerChunk);
return;
}
// otherwise this is a desired outer block which contains 2^a inner blocks; kill/renorm every second inner block
alternateNormZeroingSomeAmpBlocks(
qureg, totalStateProb, innerBit==outcome, 0, qureg.numAmpsPerChunk, innerBlockSize);
return;
}
// Otherwise, this chunk's amps contain multiple outer blocks (and hence multiple inner blocks)
long long int numOuterDoubleBlocks = locNumAmps / (2*outerBlockSize);
long long int firstBlockInd;
// alternate norming* and zeroing the outer blocks (with order based on the desired outcome)
// These loops aren't parallelised, since they could have 1 or 2 iterations and will prevent
// inner parallelisation
if (outerBit == outcome) {
for (long long int outerDubBlockInd = 0; outerDubBlockInd < numOuterDoubleBlocks; outerDubBlockInd++) {
firstBlockInd = outerDubBlockInd*2*outerBlockSize;
// *norm only the desired inner blocks in the desired outer block
alternateNormZeroingSomeAmpBlocks(
qureg, totalStateProb, innerBit==outcome,
firstBlockInd, outerBlockSize, innerBlockSize);
// zero the undesired outer block
zeroSomeAmps(qureg, firstBlockInd + outerBlockSize, outerBlockSize);
}
} else {
for (long long int outerDubBlockInd = 0; outerDubBlockInd < numOuterDoubleBlocks; outerDubBlockInd++) {
firstBlockInd = outerDubBlockInd*2*outerBlockSize;
// same thing but undesired outer blocks come first
zeroSomeAmps(qureg, firstBlockInd, outerBlockSize);
alternateNormZeroingSomeAmpBlocks(
qureg, totalStateProb, innerBit==outcome,
firstBlockInd + outerBlockSize, outerBlockSize, innerBlockSize);
}
}
}
qreal densmatr_calcPurityLocal(Qureg qureg) {
/* sum of qureg^2, which is sum_i |qureg[i]|^2 */
long long int index;
long long int numAmps = qureg.numAmpsPerChunk;
qreal trace = 0;
qreal *vecRe = qureg.stateVec.real;
qreal *vecIm = qureg.stateVec.imag;
# ifdef _OPENMP
# pragma omp parallel \
shared (vecRe, vecIm, numAmps) \
private (index) \
reduction ( +:trace )
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (index=0LL; index<numAmps; index++) {
trace += vecRe[index]*vecRe[index] + vecIm[index]*vecIm[index];
}
}
return trace;
}
void densmatr_mixDensityMatrix(Qureg combineQureg, qreal otherProb, Qureg otherQureg) {
/* corresponding amplitudes live on the same node (same dimensions) */
// unpack vars for OpenMP
qreal* combineVecRe = combineQureg.stateVec.real;
qreal* combineVecIm = combineQureg.stateVec.imag;
qreal* otherVecRe = otherQureg.stateVec.real;
qreal* otherVecIm = otherQureg.stateVec.imag;
long long int numAmps = combineQureg.numAmpsPerChunk;
long long int index;
# ifdef _OPENMP
# pragma omp parallel \
default (none) \
shared (combineVecRe,combineVecIm,otherVecRe,otherVecIm, otherProb, numAmps) \
private (index)
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (index=0; index < numAmps; index++) {
combineVecRe[index] *= 1-otherProb;
combineVecIm[index] *= 1-otherProb;
combineVecRe[index] += otherProb * otherVecRe[index];
combineVecIm[index] += otherProb * otherVecIm[index];
}
}
}
/** computes Tr((a-b) conjTrans(a-b)) = sum of abs values of (a-b) */
qreal densmatr_calcHilbertSchmidtDistanceSquaredLocal(Qureg a, Qureg b) {
long long int index;
long long int numAmps = a.numAmpsPerChunk;
qreal *aRe = a.stateVec.real;
qreal *aIm = a.stateVec.imag;
qreal *bRe = b.stateVec.real;
qreal *bIm = b.stateVec.imag;
qreal trace = 0;
qreal difRe, difIm;
# ifdef _OPENMP
# pragma omp parallel \
shared (aRe,aIm, bRe,bIm, numAmps) \
private (index,difRe,difIm) \
reduction ( +:trace )
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (index=0LL; index<numAmps; index++) {
difRe = aRe[index] - bRe[index];
difIm = aIm[index] - bIm[index];
trace += difRe*difRe + difIm*difIm;
}
}
return trace;
}
/** computes Tr(conjTrans(a) b) = sum of (a_ij^* b_ij) */
qreal densmatr_calcInnerProductLocal(Qureg a, Qureg b) {
long long int index;
long long int numAmps = a.numAmpsPerChunk;
qreal *aRe = a.stateVec.real;
qreal *aIm = a.stateVec.imag;
qreal *bRe = b.stateVec.real;
qreal *bIm = b.stateVec.imag;
qreal trace = 0;
# ifdef _OPENMP
# pragma omp parallel \
shared (aRe,aIm, bRe,bIm, numAmps) \
private (index) \
reduction ( +:trace )
# endif
{
# ifdef _OPENMP
# pragma omp for schedule (static)
# endif
for (index=0LL; index<numAmps; index++) {
trace += aRe[index]*bRe[index] + aIm[index]*bIm[index];
}
}