R/cntrld.R

In QuantumOps: Performs Common Linear Algebra Operations Used in Quantum Computing and Implements Quantum Algorithms

#make controlled version of input gate
#' @export
cntrld <- function(gate,n,...){
	qbitlist <- as.integer(list(...))				#list of qubits
	CQubits <- qbitlist[-length(qbitlist)]			#control qubits are all but last
	nCQubits <- length(CQubits)						#number of control qubits
	tQubit <- qbitlist[length(qbitlist)]			#target qubit is last

	d <- dim(gate)[1]		#side length of input gate
	D <- 2^n	#side length of controlled version
	g <- diag(1,D,D)		#create diagonal matrix

	v <- seq(0,D-1,by=1)			#binary indices
	b <- matrix(rep(0,D*log(D,base=2)),nrow=D)
	for(j in log(D,base=2):1){				#create matrix of binary values 
		b[,j] <- v %% 2			# of all possible values
		v <- floor(v/2)
	}


	CQubits <- CQubits + 1	#R indexes from 1
	tQubit <- tQubit + 1

	#Build the operator, which is gate applied just to target Qubit
	if(d == 2){							#If it is a single qubit gate, proceed as normal, fully general (gate can be applied to any qubit in ket)
		if(tQubit == 1){				#if target is first qubit
			operator <- gate			#it is gate, tensored with I for all other qubits
			for(j in 2:n)
				operator <- tensor(operator,I())
		} else{
			operator <- I()				#otherwise, first qubit gets I
			if(tQubit != 2){			#and all others up to target qubit
				for(j in 2:(tQubit-1))
					operator <- tensor(operator,I())
			}
			operator <- tensor(operator,gate)	#target qubit gets gate
			if(tQubit != n)
				for(j in (tQubit+1):n)			#I for all remaining qubits
					operator <- tensor(operator,I())
		}
	} else{		#Gate is NOT a single qubit gate, in this case it is restricted to being applied to the last qubits in ket (loss of generality)
		CQubits <- c(CQubits,tQubit)		#in this case, the list of qubits are ALL control qubits (last is not the target as target is predefined)
		operator <- repeatTensor(I(),n-log(d,base=2))
		operator <- tensor(operator,gate)
	}

	#For each basis state
	for(j in 0:(D-1)){
			if( all(b[j+1,CQubits] == 1) ){			#if all control qubits are 1
				g[j+1,] <- operator %*% intket(j,n)	#that column is operator applied to it (gate applied to just target qubit)
			}										#otherwise, it is the 1 on the diagonal (already)
	}
	g		#return the gate
}