136 lines
No EOL
3.4 KiB
Markdown
136 lines
No EOL
3.4 KiB
Markdown
# Gates
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Here is the list of all the main gates in quantum algorithm available in the library. In the following formulas, `i` represents the complex number.
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## H(q: QuBit) -> None
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`Hadamard's gate`.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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\frac {1} {\sqrt 2} & \frac {1} {\sqrt 2}\\
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\frac {1} {\sqrt 2} & -\frac {1} {\sqrt 2}
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\end{pmatrix}$
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## X(q: QuBit) -> None
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`Pauli-X gate` or `NOT gate`. Inplementes a rotation aroud the x-axis of $\pi$ radians.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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0 & 1\\
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1 & 0
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\end{pmatrix}$
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## Y(q: QuBit) -> None
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`Pauli-Y gate`. Inplementes a rotation aroud the y-axis of $\pi$ radians.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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0 & -i\\
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i & 0
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\end{pmatrix}$
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## Z(q: QuBit) -> None
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`Pauli-Z gate`. Inplementes a rotation aroud z-axis of $\pi$ radians.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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1 & 0\\
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0 & -1
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\end{pmatrix}$
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## S(q: QuBit) -> None
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`NOT gate`. Invert the state |0> and |1> of the QuiBit q.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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1 & 0\\
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0 & i
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\end{pmatrix}$
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## T(q: QuBit) -> None
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`NOT gate`. Invert the state |0> and |1> of the QuiBit q.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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1 & 0\\
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0 & e^{i\frac\pi4}
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\end{pmatrix}$
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## Rx(q: QuBit, phi: float) -> None
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`NOT gate`. Inplementes a rotation aroud x-axis of $\phi$ radians.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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\cos(\frac\phi2) & -\sin(\frac\phi2)\\
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\sin(\frac\phi2) & \cos(\frac\phi2)
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\end{pmatrix}$
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## Ry(q: QuBit, phi: float) -> None
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`NOT gate`. Inplementes a rotation aroud y-axis of $\pi$ radians.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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e^{-i\frac\phi2} & 0\\
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0 & e^{i\frac\phi2}
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\end{pmatrix}$
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## R1(q: QuBit, phi: float) -> None
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`NOT gate`. Invert the state |0> and |1> of the QuiBit q.
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- q: the qubit manipulated by the gate. This function is in-place.
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- matrix: $\begin{pmatrix}
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1 & 0\\
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0 & e^{i\frac\phi2}
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\end{pmatrix}$
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## CNOT(q: MuBit, n1: int, n2: int) -> None
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`X-controlled gate`. Invert the state |0> and |1> of the QuiBit in n2 if the state of the QuBit in n1 is 1.
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- q: the qubit manipulated by the gate. This function is in-place.
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- n1: the first QuBit to manipualte.
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- n2: the second QuBit to manipulate
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- matrix: $\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & 0 & 1\\
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0 & 0 & 1 & 0
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\end{pmatrix}$
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## SWAP(q: MuBit, n1: int, n2: int) -> None
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`NOT gate`. Invert the state |0> and |1> of the QuiBit q.
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- q: the qubit manipulated by the gate. This function is in-place.
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- n1: the first QuBit to manipualte.
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- n2: the second QuBit to manipulate
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- matrix: $\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 0 & 1 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & 0 & 1
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\end{pmatrix}$
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## Cu(q: MuBit, u: list[list[float]], n1: int, n2: int) -> None
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`controlled-u gate`. Applies the gate u to the QuBit in n2 if the Qubit in n1 is 1.
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- q: the qubit manipulated by the gate. This function is in-place.
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- the list respresentation of a matrix of the size 2 by 2.
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- n1: the first QuBit to manipualte.
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- n2: the second QuBit to manipulate
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- matrix: $\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & u_{00} & u_{01}\\
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0 & 0 & u_{10} & u_{11}
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\end{pmatrix}$ |