QComp.js Specification Sheet

GitLab Repo:
https://gitlab.com/EngineersBox/qcompjs

GitHub Repo (pushed from GitLab):
https://github.com/EngineersBox/qcompjs

JavaScript Version: ECMAscript 6

Dependancies: Math.js

CONSTANTS

Constant	Matrix Representation	Description	Code Representation
one	$one = \begin{bmatrix}0\\1\end{bmatrix}$	2-dimensional Hilbert space vector representation of qubit value of 1	`const one = [0,1];`
zero	$zero = \begin{bmatrix}1\\0\end{bmatrix}$	2-dimensional Hilbert space vector representation of qubit value of 0	`const zero = [1,0];`
posi	$posi = 0+1i$	Complex number with positive complex value of 1	`const posi = math.complex("0+1i");`
negi	$negi = 0-1i$	Complex number with negative complex value of 1	`const negi = math.complex("0-1i");`

FUNCTIONS

Function	Matrix Representation	Description	Usage
QC(args)	None	Instantiate a new quantum register with values as arguments.	`const qc = new QC("\|01101>");` or `const qc = new QC("01101");`
log()	None	Display arguments in console	`log("Example");` Result: Example
#.getValues()	None	Return a formatted string of this.values of a QC instantiation	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.getValues(); Result: [[0,1],[1,0],[1,0],[0,1]]
format.evalBraKet(args)	None	Return an array of matrix-vector formatted 1's and 0's given via arguments	`format.evalBraKet("\|1001>");` Result: [[0,1],[1,0],[1,0],[0,1]]
format.convetResultToString(args)	None	Return a format retainted string of the argument	`format.convetResultToString([[0,1],[1,0]]);` Result: [[0,1],[1,0]]
#.X(args)	$X = \begin{bmatrix}0&1\\1&0\end{bmatrix}$	Return Pauli-X matrix multiplied by vectors in this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.X([0,1]]); Result: [[1,0],[0,1],[1,0],[0,1]]
#.Y(args)	$Y = \begin{bmatrix}0&-i\\i&0\end{bmatrix}$	Return Pauli-Y matrix multiplied by vectors in this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.Y([0,1]]); Result: [[1+0i, 0+0i],[0+0i, -1+0i],[1,0],[0,1]]
#.Z(args)	$X = \begin{bmatrix}1&0\\0&-1\end{bmatrix}$	Return Pauli-Z matrix multiplied by vectors in this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.Z([0,1]]); Result: [[0,-1],[1,0],[1,0],[0,1]]
#.S(args)	$S = \begin{bmatrix}1&0\\0&i\end{bmatrix}$	Rotate bits in this.values specified by argument list by 90 degrees on the z-axis	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.S([0,1]]); Result: [[0,1+0i],[1,0+0i],[1,0],[0,1]]
#.Sdagger(args)	$S^{\dagger} = \begin{bmatrix}1&0\\0&-i\end{bmatrix}$	Conjugate transpose of the S gate	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.Sdagger([0,1]]); Result: [[0+0i,-1+0i],[1+0i,0+0i],[1,0],[0,1]]
#.sqrtx(args)	$\sqrt x = 0.5\times\begin{bmatrix}i&-i\\-i&i\end{bmatrix}$	Return square root of x matrix multiplied by vectors in this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.sqrtx([0,1]]); Result: [[-0.5+0i,0.5+0i],[0.5+0i, -0.5+0i],[1,0],[0,1]]
#.phase(theta, args)	$phase = \begin{bmatrix}1&0\\0&e^{i\theta}\end{bmatrix}$	Return a phase rotation by theta radians to this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.phase(math.pi/3,[0,1]); Result: [[0,2.849653908226361],[1,0],[1,0],[0,1]]
#.T(args)	$T = \begin{bmatrix}1&0\\0&e^{i\frac{\pi}{4}}\end{bmatrix}$	Return a rotation by ^π⁄₄ radians to this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.T([0,1]); Result: [[0,2.1932800507380152],[1,0],[1,0],[0,1]]
#.Tdagger(args)	$T^{\dagger} = \begin{bmatrix}1&0\\0&e^{-i\frac{\pi}{4}}\end{bmatrix}$	Conjugate transpose of the T gate	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.Tdagger([0,1]); Result: [[0,0.45593812776599624+0i],[1,0+0i],[1,0],[0,1]]
#.H(args)	$H= \frac{1}{\sqrt 2}\times\begin{bmatrix}1&1\\1&-1\end{bmatrix}$	Return a superposition given via qubit state to this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.H([0,1]); Result: [[0.7071067811865475,-0.7071067811865475],[0.7071067811865475,0.7071067811865475],[1,0],[0,1]]
#.swap(firstBit, secondBit)	$swap= \begin{bmatrix}1&0&0&0\\0&0&1&0\\0&1&0&0\\0&0&0&1\end{bmatrix}$	Swap the values of the bits denoted by indexes in arguments as firstBit and secondBit	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.swap(0,1); Result: [[1,0],[0,1],[1,0],[0,1]]
#.cnot(controlBits, targetBits)	$cnot = \begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{bmatrix}$	Apply a Pauli-X gate to the targetBits if and only if the controlBits are 1's	//this.values = [[0,1],[0,1],[1,0],[0,1]] qc.cnot([0,1],[2,3]); Result: [[0,1],[0,1],[0,1],[1,0]]
#.cswap(controlBits, targetBits)	$cswap= \begin{bmatrix}1&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0\\0&0&1&0&0&0&0&0\\0&0&0&1&0&0&0&0\\0&0&0&0&1&0&0&0\\0&0&0&0&0&0&1&0\\0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&1\end{bmatrix}$	Swap the values of the targetBits (targetBits must be of length 2) if and only if the controlBits are 1's	//this.values = [[0,1],[0,1],[1,0],[0,1]] qc.cwap([0,1],[2,3]); Result: [[0,1],[0,1],[0,1],[1,0]]
#.rx(theta, args)	$Rx_\theta = \begin{bmatrix}cos(\frac{\theta}{2})&-isin(\frac{\theta}{2})\\-isin(\frac{\theta}{2})&cos(\frac{\theta}{2})\end{bmatrix}$	Return a rotation on the x-axis by theta radians to this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.rx(math.pi/5,[0,1]); Result: [[-0.3090169943749474+0i, 0.9510565162951535,+0i],[0.9510565162951535+0i,-0.3090169943749474+0i],[1,0],[0,1]]
#.ry(theta, args)	$Ry_\theta = \begin{bmatrix}cos(\frac{\theta}{2})&-sin(\frac{\theta}{2})\\sin(\frac{\theta}{2})&cos(\frac{\theta}{2})\end{bmatrix}$	Return a rotation on the y-axis by theta radians to this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.ry(math.pi/5,[0,1]); Result: [[0.5+0i,0.8660254037844387+0i],[0.8660254037844387+0i, -0.5+0i],[1,0],[0,1]]
#.rz(theta, args)	$Rz_\theta = \begin{bmatrix}e^{-i\frac{\theta}{2}}&0\\0&e^{i\frac{\theta}{2}}\end{bmatrix}$	Return a rotation on the z-axis by theta radians to this.values specified by argument array	//this.values = [[0,1],[1,0],[1,0],[0,1]] qc.rz(math.pi/5,[0,1]); Result: [[0+0i, 0.9510565162951535+0.3090169943749474i],[0.9510565162951535-0.3090169943749474i,0+0i],[1,0],[0,1]]