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chapter_6.f90
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! Source codes for Numerical Recipes in Quantum Information Theory and Quantum Computing:
!An Adventure in FORTRAN 90 -by M. S. Ramkarthik and Payal D. Solanki
!This file contains all the source codes for chapter 6.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHAPTER 6!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.1.1
subroutine XHAM(s,B,HB)
implicit none
integer::s,t(0:s-1),y(0:s-1),i,j,d,w
real*8::B(0:s-1),h,e
real*8::HB(0:2**s-1,0:2**s-1)
HB=0.0d0
do i=0,2**s-1,1
do j=i,2**s-1,1
call DTOB(j,y,s)
e=0
t=y
do d=0,s-1
t(d)=1-t(d)
call BTOD(t,w,s)
if(w==i) then
h=B(d)
else
h=0
end if
e=e+h
t=y
end do
HB(i,j)=e
HB(j,i)=HB(i,j)
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.1.2
subroutine YHAM(s,B,HB)
implicit none
integer::s,t(0:s-1),y(0:s-1),i,j,d,w
real*8::B(0:s-1)
complex*16::HB(0:2**s-1,0:2**s-1),phase,h,e
HB=0.0d0
do i=0,2**s-1,1
do j=i,2**s-1,1
call DTOB(j,y,s)
e=0
t=y
do d=0,s-1
if(t(d)==0) then
t(d)=1
phase=dcmplx(0,1)
else
t(d)=0
phase=dcmplx(0,-1)
end if
call BTOD(t,w,s)
if(w==i) then
h=phase*B(d)
else
h=0
end if
e=e+h
t=y
end do
HB(i,j)=e
HB(j,i)=conjg(HB(i,j))
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.1.3
subroutine ZHAM(s,B,HB)
implicit none
integer::s,i,j,v,x(0:s-1)
real*8::B(0:s-1)
real*8::HB(0:2**s-1,0:2**s-1),m1
HB=0.0d0
do i=0,2**s-1,1
do j=i,2**s-1,1
call DTOB(i,x,s)
if (i==j) then
do v=0,s-1
m1=(1-2*x(v))*B(v)
HB(i,j)=HB(i,j)+m1
end do
else
HB(i,j)=0
end if
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.2.1
subroutine ISINGXHAM(s,r,BC,Jr,HI)
implicit none
integer::s,r,t(0:s-1),y(0:s-1),i,j,d,w
real*8::HI(0:2**s-1,0:2**s-1),e,e1
real*8::h,Jr(0:s-1)
character*1::BC
if (r>s) then
print*, 'r should be less than s'
stop
end if
HI=0.0d0
do i=0,2**s-1,1
do j=i,2**s-1,1
call DTOB(j,y,s)
e=0
e1=0
t=y
do d=0,s-1
if(d.le.s-r-1) then
t(d)=1-t(d)
t(d+r)=1-t(d+r)
call BTOD(t,w,s)
if(w==i) then
h=Jr(d)
else
h=0
end if
e=e+h
t=y
else
if (BC=='y' ) then
t(d)=1-t(d)
t(d+r-s)=1-t(d+r-s)
call BTOD(t,w,s)
if(w==i) then
h=Jr(d)
else
h=0
end if
e1=e1+h
t=y
end if
end if
end do
HI(i,j)=e+e1
HI(j,i)=HI(i,j)
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.2.2
subroutine ISINGYHAM(s,r,BC,Jr,HI)
implicit none
integer*4::s,r,t(0:s-1),y(0:s-1),d,w,i,j
real*8::HI(0:2**s-1,0:2**s-1),e,e1,Jr(0:s-1)
complex*16::i2,p1,p2,p3,p4,h
character*1::BC
if (r>s) then
print*, 'r should be less than s'
stop
end if
HI=0.0d0
i2=dcmplx(0,1)
do i=0,2**s-1,1
do j=i,2**s-1,1
call DTOB(j,y,s)
e=0
e1=0
t=y
do d=0,s-1
if(d.le.s-r-1) then
p1=i2*((-1)**(t(d)))
p2=i2*((-1)**(t(d+r)))
t(d)=1-t(d)
t(d+r)=1-t(d+r)
call BTOD(t,w,s)
if(w==i) then
h=p1*p2*Jr(d)
else
h=0
end if
e=e+real(h)
t=y
else
if (BC=='y') then
p3=i2*((-1)**(t(d)))
p4=i2*((-1)**(t(d+r-s)))
t(d)=1-t(d)
t(d+r-s)=1-t(d+r-s)
call BTOD(t,w,s)
if(w==i) then
h=p3*p4*Jr(d)
else
h=0
end if
e1=e1+real(h)
t=y
end if
end if
end do
HI(i,j)=e+e1
HI(j,i)=HI(i,j)
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.2.3
subroutine ISINGZHAM(s,r,BC,Jr,HI)
implicit none
integer*4::s,r,i,j,v,x(0:s-1)
real*8::HI(0:2**s-1,0:2**s-1),m1,Jr(0:s-1)
character*1::BC
if (r>s) then
print*, 'r should be less than s'
stop
end if
HI=0.0d0
do i=0,2**s-1,1
do j=i,2**s-1,1
HI(i,j)=0.0d0
call DTOB(j,x,s)
if (i==j) then
do v=0,s-1
if(v.le.s-r-1) then
m1=(1-2*x(v))*(1-2*x(v+r))*Jr(v)
HI(i,j)=HI(i,j)+m1
else
if (BC=='y') then
m1=(1-2*x(v))*(1-2*x(v+r-s))*Jr(v)
HI(i,j)=HI(i,j)+m1
end if
end if
end do
end if
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.3
subroutine HEIHAM(s,r,BC,Jr,H)
implicit none
integer::s,r,i,j,y(0:s-1),z(0:s-1),o,w,temp
real*8,dimension(0:2**s-1,0:2**s-1)::H
real*8::c,h1,h2,h3,h4,h5
character*1::BC
real*8::Jr(0:s-1),summ
summ=0.0d0
if (BC=='y') then
do i=0,s-1
summ=summ+Jr(i)
end do
end if
if (BC=='n') then
do i=0,s-r-1
summ=summ+Jr(i)
end do
end if
do i=0,2**s-1,1
do j=i,2**s-1,1
call DTOB(j,y,s)
h1=0
h2=0
h3=0
h4=0
do o=0,s-1,1
z=y
if(o.le.s-r-1) then
temp=z(o)
z(o)=z(o+r)
z(o+r)=temp
call BTOD(z,w,s)
if(w==i) then
c=Jr(o)
else
c=0
end if
h1=h1+c
else
if (BC=='y') then
temp=z(o)
z(o)=z(o+r-s)
z(o+r-s)=temp
call BTOD(z,w,s)
if(w==i) then
c=Jr(o)
else
c=0
end if
h2=h2+c
end if
end if
end do
if(i==j)then
h3=summ
else
h3=0
end if
h4=h1+h2
H(i,j)=4.0d0*(h4/2.0d0-h3/4.0d0)
H(j,i)=H(i,j)
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.4.1
subroutine DMHAMX(s,r,BC,Dr,HDM)
implicit none
integer::s,r
integer::x,i,j,t(0:s-1),y(0:s-1),w1
real*8::Dr(0:s-1),m
character*1::BC
complex*16::i2,phase,h,HDM(0:2**s-1,0:2**s-1),e,e1,h1,h2,e2,e3
i2=dcmplx(0,1)
do i=0,2**s-1
do j=i,2**s-1
call DTOB(j,y,s)
e=0
e1=0
t=y
e2=0
e3=0
do x=0,s-1
if(x.le.s-r-1) then
phase=i2*((-1)**(t(x)))
t(x)=1-t(x)
m=1-2*t(x+r)
call BTOD(t,w1,s)
if(w1==i) then
h=m*phase*Dr(x)
else
h=0
end if
e=e+h
t=y
else
if (BC=='y') then
phase=i2*((-1.0)**(t(x)))
t(x)=1-t(x)
m=1-2*t(x+r-s)
call BTOD(t,w1,s)
if(w1==i) then
h=m*phase*Dr(x)
else
h=0
end if
e1=e1+h
t=y
end if
end if
end do
h1=e+e1
do x=0,s-1
if(x.le.s-r-1) then
phase=i2*((-1.0)**(t(x+r)))
m=1-2*t(x)
t(x+r)=1-t(x+r)
call BTOD(t,w1,s)
if(w1==i) then
h=m*phase*Dr(x)
else
h=0
end if
e2=e2+h
t=y
else
if (BC=='y') then
phase=i2*((-1)**(t(x+r-s)))
t(x+r-s)=1-t(x+r-s)
m=1-2*t(x)
call BTOD(t,w1,s)
if(w1==i) then
h=m*phase*Dr(x)
else
h=0
end if
e3=e3+h
t=y
end if
end if
end do
h2=e2+e3
HDM(i,j)=h1-h2
HDM(j,i)=conjg(HDM(i,j))
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.4.2
subroutine DMHAMY(s,r,BC,Dr,HDM)
implicit none
integer::s,r
integer::x,i,j,t(0:s-1),y(0:s-1),w1
real*8::Dr(0:s-1),m
character*1::BC
real*8::i2,h,HDM(0:2**s-1,0:2**s-1),e,e1,h1,h2,e2,e3
do i=0,2**s-1
do j=i,2**s-1
call DTOB(j,y,s)
e=0
e1=0
t=y
e2=0
e3=0
do x=0,s-1
if(x.le.s-r-1) then
t(x)=1-t(x)
m=1-2*t(x+r)
call BTOD(t,w1,s)
if(w1==i) then
h=m*Dr(x)
else
h=0
end if
e=e+h
t=y
else
if (BC=='y') then
t(x)=1-t(x)
m=1-2*t(x+r-s)
call BTOD(t,w1,s)
if(w1==i) then
h=m*Dr(x)
else
h=0
end if
e1=e1+h
t=y
end if
end if
end do
h1=e+e1
do x=0,s-1
if(x.le.s-r-1) then
m=1-2*t(x)
t(x+r)=1-t(x+r)
call BTOD(t,w1,s)
if(w1==i) then
h=m*Dr(x)
else
h=0
end if
e2=e2+h
t=y
else
if (BC=='y') then
t(x+r-s)=1-t(x+r-s)
m=1-2*t(x)
call BTOD(t,w1,s)
if(w1==i) then
h=m*Dr(x)
else
h=0
end if
e3=e3+h
t=y
end if
end if
end do
h2=e2+e3
HDM(i,j)=(h2-h1)
HDM(j,i)=HDM(i,j)
end do
end do
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!6.4.3
subroutine DMHAMZ(s,r,BC,Dr,HDM)
implicit none
integer::s,r
integer::x,i,j,t(0:s-1),y(0:s-1),w1
real*8::Dr(0:s-1),m
character*1::BC
complex*16::i2,phase,h,HDM(0:2**s-1,0:2**s-1),e,e1,h1,h2,e2,e3
i2=dcmplx(0,1)
do i=0,2**s-1
do j=i,2**s-1
call DTOB(j,y,s)
e=0
e1=0
t=y
e2=0
e3=0
do x=0,s-1
if(x.le.s-r-1) then
phase=i2*((-1)**(t(x+r)))
t(x)=1-t(x)
t(x+r)=1-t(x+r)
call BTOD(t,w1,s)
if(w1==i) then
h=phase*Dr(x)
else
h=0
end if
e=e+h
t=y
else
if (BC=='y') then
phase=i2*((-1.0)**(t(x+r-s)))
t(x)=1-t(x)
t(x+r-s)=1-t(x+r-s)
call BTOD(t,w1,s)
if(w1==i) then
h=phase*Dr(x)
else
h=0
end if
e1=e1+h
t=y
end if
end if
end do
h1=e+e1
do x=0,s-1
if(x.le.s-r-1) then
phase=i2*((-1.0)**(t(x)))
t(x)=1-t(x)
t(x+r)=1-t(x+r)
call BTOD(t,w1,s)
if(w1==i) then
h=phase*Dr(x)
else
h=0
end if
e2=e2+h
t=y
else
if (BC=='y') then
phase=i2*((-1)**(t(x)))
t(x+r-s)=1-t(x+r-s)
t(x)=1-t(x)
call BTOD(t,w1,s)
if(w1==i) then
h=phase*Dr(x)
else
h=0
end if
e3=e3+h
t=y
end if
end if
end do
h2=e2+e3
HDM(i,j)=(h1-h2)
HDM(j,i)=conjg(HDM(i,j))
end do
end do
end subroutine