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/* oaddn.c: Addition modulo an integer N
Copyright 2003 Bjoern Butscher, Hendrik Weimer
This file is part of libquantum
libquantum is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published
by the Free Software Foundation; either version 3 of the License,
or (at your option) any later version.
libquantum is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with libquantum; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "matrix.h"
#include "measure.h"
#include "defs.h"
#include "gates.h"
#include "qureg.h"
#include "config.h"
/* if bit "compare" - the global enable bit - is set, test_sums
checks, if the sum of the c-number and the q-number in register
add_sum is greater than n and sets the next lower bit to "compare" */
void
test_sum(int compare, int width, quantum_reg *reg)
{
int i;
if (compare & ((MAX_UNSIGNED) 1 << (width - 1)))
{
quantum_cnot(2*width-1, width-1, reg);
quantum_sigma_x(2*width-1, reg);
quantum_cnot(2*width-1, 0, reg);
}
else
{
quantum_sigma_x(2*width-1, reg);
quantum_cnot(2*width-1,width-1, reg);
}
for (i = (width-2);i>0;i--)
{
if (compare & (1<<i))
{//is bit i set in compare?
quantum_toffoli(i+1,width+i,i, reg);
quantum_sigma_x(width+i, reg);
quantum_toffoli(i+1,width+i,0, reg);
}
else
{
quantum_sigma_x(width+i, reg);
quantum_toffoli(i+1,width+i,i, reg);
}
}
if (compare & 1)
{
quantum_sigma_x(width, reg);
quantum_toffoli(width,1,0, reg);
}
quantum_toffoli(2*width+1,0,2*width, reg);//set output to 1 if enabled and b < compare
if (compare & 1)
{
quantum_toffoli(width,1,0, reg);
quantum_sigma_x(width, reg);
}
for (i = 1;i<=(width-2);i++)
{
if (compare & (1<<i))
{//is bit i set in compare?
quantum_toffoli(i+1,width+i,0, reg);
quantum_sigma_x(width+i, reg);
quantum_toffoli(i+1,width+i,i, reg);
}
else
{
quantum_toffoli(i+1,width+i,i, reg);
quantum_sigma_x(width+i, reg);
}
}
if (compare & (1<<(width-1)))
{
quantum_cnot(2*width-1,0, reg);
quantum_sigma_x(2*width-1, reg);
quantum_cnot(2*width-1,width-1, reg);
}
else
{
quantum_cnot(2*width-1,width-1, reg);
quantum_sigma_x(2*width-1, reg);
}
}
//This is a semi-quantum fulladder. It adds to b_in
//a c-number. Carry-in bit is c_in and carry_out is
//c_out. xlt-l and L are enablebits. See documentation
//for further information
void muxfa(int a, int b_in, int c_in, int c_out, int xlt_l,int L, int total,quantum_reg *reg){//a,
if(a==0){//00
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_cnot(b_in,c_in, reg);
}
if(a==3){//11
quantum_toffoli(L,c_in,c_out, reg);
quantum_cnot(L,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_cnot(b_in,c_in, reg);
}
if(a==1){//01
quantum_toffoli(L,xlt_l,b_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,b_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_cnot(b_in,c_in, reg);
}
if(a==2){//10
quantum_sigma_x(xlt_l, reg);
quantum_toffoli(L,xlt_l,b_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,b_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_cnot(b_in,c_in, reg);
quantum_sigma_x(xlt_l, reg);
}
}
//This is just the inverse operation of the semi-quantum fulladder
void muxfa_inv(int a,int b_in,int c_in,int c_out, int xlt_l,int L,int total,quantum_reg *reg){//a,
if(a==0){//00
quantum_cnot(b_in,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
}
if(a==3){//11
quantum_cnot(b_in,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_cnot(L,c_in, reg);
quantum_toffoli(L,c_in,c_out, reg);
}
if(a==1){//01
quantum_cnot(b_in,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,b_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,b_in, reg);
}
if(a==2){//10
quantum_sigma_x(xlt_l, reg);
quantum_cnot(b_in,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,c_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,b_in, reg);
quantum_toffoli(b_in,c_in,c_out, reg);
quantum_toffoli(L,xlt_l,b_in, reg);
quantum_sigma_x(xlt_l, reg);
}
}
//This is a semi-quantum halfadder. It adds to b_in
//a c-number. Carry-in bit is c_in and carry_out is
//not necessary. xlt-l and L are enablebits. See
//documentation for further information
void muxha(int a,int b_in,int c_in, int xlt_l, int L,int total,quantum_reg *reg){//a,
if(a==0){//00
quantum_cnot(b_in,c_in, reg);
}
if(a==3){//11
quantum_cnot(L,c_in, reg);
quantum_cnot(b_in,c_in, reg);
}
if(a==1){//01
quantum_toffoli(L,xlt_l,c_in, reg);
quantum_cnot(b_in,c_in, reg);
}
if(a==2){//10
quantum_sigma_x(xlt_l, reg);
quantum_toffoli(L,xlt_l,c_in, reg);
quantum_cnot(b_in,c_in, reg);
quantum_sigma_x(xlt_l, reg);
}
}
//just the inverse of the semi quantum-halfadder
void muxha_inv(int a,int b_in,int c_in, int xlt_l, int L, int total,quantum_reg *reg){//a,
if(a==0){//00
quantum_cnot(b_in,c_in, reg);
}
if(a==3){//11
quantum_cnot(b_in,c_in, reg);
quantum_cnot(L,c_in, reg);
}
if(a==1){//01
quantum_cnot(b_in,c_in, reg);
quantum_toffoli(L,xlt_l,c_in, reg);
}
if(a==2){//10
quantum_sigma_x(xlt_l, reg);
quantum_cnot(b_in,c_in, reg);
quantum_toffoli(L,xlt_l,c_in, reg);
quantum_sigma_x(xlt_l, reg);
}
}
//
void madd(int a,int a_inv,int width,quantum_reg *reg){
int i,j;
int total;
total = num_regs*width+2;
for (i = 0; i< width-1; i++){
if((1<<i) & a) j= 1<<1;
else j=0;
if((1<<i) & a_inv) j+=1;
muxfa(j,width+i,i,i+1,2*width,2*width+1, total, reg);
}
j=0;
if((1<<(width-1)) & a) j= 2;
if((1<<(width-1)) & a_inv) j+=1;
muxha(j,2*width-1,width-1,2*width,2*width+1, total, reg);
}
void madd_inv(int a,int a_inv,int width,quantum_reg *reg){
int i,j;
int total;
total = num_regs*width+2;
j=0;
if((1<<(width-1)) & a) j= 2;
if((1<<(width-1)) & a_inv) j+=1;
muxha_inv(j,width-1,2*width-1,2*width, 2*width+1, total, reg);
for (i = width-2; i>=0; i--){
if((1<<i) & a) j= 1<<1;
else j=0;
if((1<<i) & a_inv) j+=1;
muxfa_inv(j,i,width+i,width+1+i,2*width, 2*width+1, total, reg);
}
}
void addn(int N,int a,int width, quantum_reg *reg){//add a to register reg (mod N)
test_sum(N-a,width,reg); //xlt N-a
madd((1<<(width))+a-N,a,width,reg);//madd 2^K+a-N
}
void addn_inv(int N,int a,int width, quantum_reg *reg){//inverse of add a to register reg (mod N)
quantum_cnot(2*width+1,2*width,reg);//Attention! cnot gate instead of not, as in description
madd_inv((1<<(width))-a,N-a,width,reg);//madd 2^K+(N-a)-N = 2^K-a
quantum_swaptheleads(width,reg);
test_sum(a,width,reg);
}
void add_mod_n(int N,int a,int width, quantum_reg *reg){//add a to register reg (mod N) and clear the scratch bits
addn(N, a, width, reg);
addn_inv(N, a, width, reg);
}
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