The Standard Gate Set¶
Below is a summary of the key gates used in tweedledum
Name(s) |
Symbol |
tweedledum symbol |
Matrix |
|
---|---|---|---|---|
Identity |
I |
|
\(\pmatrix{1&0 \\ 0&1}\) |
|
Hadamard |
H |
|
\(\frac{1}{\sqrt{2}}\pmatrix{1&1 \\ 1&-1}\) |
|
Arbitrary rotations |
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X Rotation |
Rx |
|
\(\pmatrix{\cos\frac\theta2 & -\mathrm{i}\sin\frac\theta2 \\ -\mathrm{i}\sin\frac\theta2 & \cos\frac\theta2}\) |
|
Y Rotation |
Ry |
|
||
Z Rotation |
Rz |
|
\(\pmatrix{e^{-\mathrm{i}\theta}&0 \\ 0&e^{\mathrm{i}\theta}}\) |
|
Named Rotations |
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Pauli X, NOT |
X |
|
\(\pmatrix{0&1 \\ 1&0}\) |
|
T |
T |
|
\(\pmatrix{1&0 \\ 0&e^{\mathrm{i}\frac\pi4}}\) |
|
T dagger |
T† |
|
||
Phase |
S |
|
\(\pmatrix{1&0 \\ 0&\mathrm{i}}\) |
|
Phase dagger |
S† |
|
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Pauli Z, Phase flip |
Z |
|
\(\pmatrix{1&0 \\ 0&-1}\) |
|
Controlled gates |
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Control NOT |
CNOT |
|
\(\pmatrix{1&0&0&0 \\ 0&1&0&0 \\ 0&0&0&1 \\ 0&0&1&0}\) |
|
Control Z |
CZ |
|
\(\pmatrix{1&0&0&0 \\ 0&1&0&0 \\ 0&0&1&0 \\ 0&0&0&-1}\) |
|
Multiple Control NOT, Toffoli |
|
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Multiple Control Z |
|