Nothing
## ----echo=FALSE---------------------------------------------------------------
library(knitr)
library(qsimulatR)
knitr::opts_chunk$set(fig.align='center',
comment='')
## -----------------------------------------------------------------------------
N <- 3
v <- seq(1:2^N)
v <- v/sqrt(sum(v^2))
w <- fft(v, inverse=TRUE)/sqrt(length(v))
## -----------------------------------------------------------------------------
x <- qstate(N, coefs=as.complex(v))
x <- H(3) * x
x <- cqgate(bits=c(2, 3), gate=S(3)) * x
x <- cqgate(bits=c(1, 3), gate=Tgate(3)) * x
x <- H(2) * x
x <- cqgate(bits=c(1, 2), gate=S(2)) * x
x <- H(1) * x
x <- SWAP(c(1,3)) * x
## -----------------------------------------------------------------------------
plot(x)
## -----------------------------------------------------------------------------
sum(x@coefs*Conj(x@coefs))
## -----------------------------------------------------------------------------
sqrt(sum((w - x@coefs)*Conj(w - x@coefs)))
## -----------------------------------------------------------------------------
Tdagger <- function(bit) {
return(methods::new("sqgate",
bit=as.integer(bit),
M=array(as.complex(c(1., 0, 0, exp(-1i*pi/4))), dim=c(2,2)),
type="Tdag"))
}
Sdagger <- function(bit) {
return(methods::new("sqgate",
bit=as.integer(bit),
M=array(as.complex(c(1,0,0,-1i)), dim=c(2,2)),
type="Sdag"))
}
## -----------------------------------------------------------------------------
z <- qstate(N, coefs=x@coefs)
z <- SWAP(c(1,3)) * z
z <- H(1) * z
z <- cqgate(bits=c(1, 2), gate=Sdagger(2)) * z
z <- H(2) * z
z <- cqgate(bits=c(1, 3), gate=Tdagger(2)) * z
z <- cqgate(bits=c(2, 3), gate=Sdagger(2)) * z
z <- H(3) * z
## -----------------------------------------------------------------------------
plot(z)
## -----------------------------------------------------------------------------
sqrt(sum((v - z@coefs)*Conj(v - z@coefs)))
## -----------------------------------------------------------------------------
y <- qstate(N, coefs=x@coefs)
y <- H(3) * y
y <- cqgate(bits=c(2, 3), gate=Sdagger(3)) * y
y <- cqgate(bits=c(1, 3), gate=Tdagger(3)) * y
y <- H(2) * y
y <- cqgate(bits=c(1, 2), gate=Sdagger(2)) * y
y <- H(1) * y
y <- SWAP(c(1,3)) * y
plot(y)
## -----------------------------------------------------------------------------
sqrt(sum((v - y@coefs)*Conj(v - y@coefs)))
## -----------------------------------------------------------------------------
Ri <- function(bit, i, sign=+1) {
type <- paste0("R", i)
if(sign < 0) {
type <- paste0("R", i, "dag")
}
return(methods::new("sqgate",
bit=as.integer(bit),
M=array(as.complex(c(1,0,0,exp(sign*2*pi*1i/2^i))),
dim=c(2,2)), type=type))
}
## ---- eval=FALSE--------------------------------------------------------------
# qft <- function(x, inverse=FALSE) {
# n <- x@nbits
# y <- x
# sign <- +1
# if(inverse) sign <- -1
# for(bit in c(n:1)) {
# y <- H(bit) * y
# if(bit > 1) {
# for(i in c((bit-1):1)) {
# y <- cqgate(bits=c(i, bit), gate=Ri(bit, bit-(i-1), sign=sign)) * y
# }
# }
# }
# ## reverse order
# for(k in c(1:floor(n/2))) {
# y <- SWAP(c(k, n-(k-1))) * y
# }
# return(invisible(y))
# }
## -----------------------------------------------------------------------------
y <- qstate(N, coefs=x@coefs)
y <- qft(y, inverse=TRUE)
plot(y)
sqrt(sum((v - y@coefs)*Conj(v - y@coefs)))
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