# R/sqgate.R In qsimulatR: A Quantum Computer Simulator

#### Documented in HIdRxsqgate

```check_sqgate  <- function(object) {
stopifnot(length(object@bit) == 1)
stopifnot(object@bit > 0)
stopifnot(all(dim(object@M) == c(2,2)))
## check unitarity
X <- as.vector(object@M %*% t(Conj(object@M)))
stopifnot(all(Re(X- c(1,0,0,1)) < 1.e-12))
stopifnot(all(Im(X- c(1,0,0,1)) < 1.e-12))
}

#' A single qubit gate
#'
#' This class represents a generic single qubit gate
#'
#' @slot bit Integer. The single bit to act on.
#' @slot M complex valued array. The 2x2 matrix representing the
#' gate
#' @slot type a character vector representing the type of gate
#'
#' @details
#' The qubits are counted from 1 to \code{nbits} starting with the least
#' significant bit.
#'
#' @include state.R
#'
#' @examples
#' x <- qstate(nbits=2)
#' ## application of the X (NOT) gate to bit 1
#' z <- sqgate(bit=1L, M=array(as.complex(c(0,1,1,0)), dim=c(2,2))) * x
#' z
#'
#' @name sqgate
#' @rdname sqgate
#' @aliases sqgate-class
#' @exportClass sqgate
setClass("sqgate",
representation(bit="integer",
M="array",
type="character"),
prototype(bit=c(1L),
M=array(as.complex(c(1,0,0,1)), dim=c(2,2)),
type="Id"),
validity=check_sqgate)

#' @export
sqgate <- function(bit=1L, M=array(as.complex(c(1,0,0,1)), dim=c(2,2)), type="Id") {
return(methods::new("sqgate", bit=as.integer(bit), M=M, type=type))
}

#' times-sqgate-qstate
#'
#' Applies a single qubit gate to a quantum state.
#'
#' @param e1 object of S4 class 'sqgate'
#' @param e2 object of S4 class 'qstate'
#' @return
#' An object of S4 class 'qstate'
#'
setMethod("*", c("sqgate", "qstate"),
function(e1, e2) {
stopifnot(e1@bit > 0 && e1@bit <= e2@nbits)
bit <- e1@bit
nbits <- e2@nbits
res <- c()
al <- 0:(2^e2@nbits-1)
ii <- is.bitset(al, bit=bit)
kk <- !ii
res[kk] <- e1@M[1,1]*e2@coefs[kk] + e1@M[1,2]*e2@coefs[ii]
res[ii] <- e1@M[2,1]*e2@coefs[kk] + e1@M[2,2]*e2@coefs[ii]
## the gatelist needs to be extended for plotting
circuit <- e2@circuit
ngates <- length(circuit\$gatelist)
circuit\$gatelist[[ngates+1]] <- list(type=e1@type, bits=c(e1@bit, NA, NA))
if(e1@type == "Rx" || e1@type == "Ry" || e1@type == "Rz" || grepl("^R[0-9]+", e1@type))
circuit\$gatelist[[ngates+1]]\$angle <- Arg(e1@M[2,2])
circuit\$gatelist[[ngates+1]]\$controlled <- FALSE
return(qstate(nbits=nbits, coefs=as.complex(res), basis=e2@basis, circuit=circuit))
}
)

#'
#' @param bit integer. The bit to which to apply the gate
#'
#' @examples
#' x <- qstate(nbits=2)
#' z <- H(1) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
H <- function(bit) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(1,1,1,-1)), dim=c(2,2))/sqrt(2), type="H"))
}
#' The identity gate
#'
#' @param bit integer. The bit to which to apply the gate
#'
#' @examples
#' x <- qstate(nbits=2)
#' z <- Id(1) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
Id <- function(bit) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(1,0,0,1)), dim=c(2,2)), type="Id"))
}
#' The Rx gate
#'
#' @param bit integer. The bit to which to apply the gate
#' @param theta numeric. angle
#'
#' @examples
#' x <- qstate(nbits=2)
#' z <- Rx(1, pi/4) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
Rx <- function(bit, theta=0.) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(cos(theta/2), -1i*sin(theta/2), -1i*sin(theta/2), cos(theta/2))), dim=c(2,2)), type="Rx"))
}
#' The Ry gate
#'
#' @param bit integer. The bit to which to apply the gate
#' @param theta numeric. angle
#'
#' @examples
#' x <- qstate(nbits=2)
#' z <- Ry(1, pi/4) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
Ry <- function(bit, theta=0.) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(cos(theta/2), sin(theta/2), -sin(theta/2), cos(theta/2))), dim=c(2,2)), type="Ry"))
}
#' The Rz gate
#'
#' @param bit integer. The bit to which to apply the gate
#' @param theta numeric. angle
#'
#' @examples
#' x <- qstate(nbits=2)
#' z <- Rz(1, pi/4) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
Rz <- function(bit, theta=0.) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(exp(-1i*theta/2), 0, 0, exp(1i*theta/2))), dim=c(2,2)), type="Rz"))
}

#' The Ri gate
#'
#' @param bit integer. The bit to which to apply the gate
#' @param i integer
#'
#' @examples
#' x <- X(1) * qstate(nbits=2)
#' z <- Ri(1, i=2) * x
#' z
#'
#' @details
#' Implements the gate
#' ( 1   0                )
#' ( 0   exp(+-2*pi*1i/2^i) )
#'
#' If 'sign < 0', the inverse of the exponential is used.
#' This gate is up to global phase identical with the 'Rz'
#' gate with specific values of the angle.
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
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))
}
#' The S gate
#'
#' @param bit integer. The bit to which to apply the gate
#'
#' @examples
#' x <- X(1) * qstate(nbits=2)
#' z <- S(1) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
S <- function(bit) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(1,0,0,1i)), dim=c(2,2)), type="S"))
}
#' The Tgate gate
#'
#' @param bit integer. The bit to which to apply the gate
#'
#' @examples
#' x <- X(1)*qstate(nbits=2)
#' z <- Tgate(1) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
Tgate <- 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="T"))
}
#' The X gate
#'
#' @param bit integer. The bit to which to apply the gate
#'
#' @examples
#' x <- qstate(nbits=2)
#' z <- X(1) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
X <- function(bit) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(0., 1., 1., 0.)), dim=c(2,2)), type="X"))
}
#' The Y gate
#'
#' @param bit integer. The bit to which to apply the gate
#'
#' @examples
#' x <- qstate(nbits=2)
#' z <- Y(1) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
Y <- function(bit) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(0., -1i, 1i, 0.)), dim=c(2,2)), type="Y"))
}
#' The Z gate
#'
#' @param bit integer. The bit to which to apply the gate
#'
#' @examples
#' x <- X(1) * qstate(nbits=2)
#' z <- Z(1) * x
#' z
#'
#' @return
#' An S4 class 'sqgate' object is returned
#' @export
Z <- function(bit) {
return(methods::new("sqgate", bit=as.integer(bit), M=array(as.complex(c(1., 0., 0., -1.)), dim=c(2,2)), type="Z"))
}
```

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qsimulatR documentation built on Jan. 13, 2021, 3:13 p.m.