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Add Gate::to_axis_angle and Gate::to_euler_angles
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- Add Bloch Rotation (Euler angles) to gate doc
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@Strilanc
Strilanc committed Nov 18, 2023
1 parent fdc9462 commit 8387240
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197 changes: 166 additions & 31 deletions doc/gates.md
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Expand Up @@ -113,11 +113,20 @@ Stabilizer Generators:
X -> X
Z -> Z

Bloch Rotation:
Bloch Rotation (axis angle):

Axis:
Angle: 0 degrees
Axis: +X
Angle: 0°

Bloch Rotation (Euler angles):

theta = 0°
phi = 0°
lambda = 0°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(0°) * RotZ(0°)
unitary = I * I * I

Unitary Matrix:

[+1 , ]
Expand Down Expand Up @@ -154,11 +163,20 @@ Stabilizer Generators:
X -> X
Z -> -Z

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +X
Angle: 180 degrees
Angle: 180°

Bloch Rotation (Euler angles):

theta = 180°
phi = 0°
lambda = 180°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(180°) * RotZ(180°)
unitary = I * Y * Z

Unitary Matrix:

[ , +1 ]
Expand Down Expand Up @@ -197,11 +215,20 @@ Stabilizer Generators:
X -> -X
Z -> -Z

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +Y
Angle: 180 degrees
Angle: 180°

Bloch Rotation (Euler angles):

theta = 180°
phi = 0°
lambda = 0°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(180°) * RotZ(0°)
unitary = I * Y * I

Unitary Matrix:

[ , -i]
Expand Down Expand Up @@ -243,11 +270,20 @@ Stabilizer Generators:
X -> -X
Z -> Z

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +Z
Angle: 180 degrees
Angle: 180°

Bloch Rotation (Euler angles):

theta = 0°
phi = 0°
lambda = 180°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(0°) * RotZ(180°)
unitary = I * I * Z

Unitary Matrix:

[+1 , ]
Expand Down Expand Up @@ -286,11 +322,20 @@ Stabilizer Generators:
X -> Y
Z -> X

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +X+Y+Z
Angle: 120 degrees
Angle: 120°

Bloch Rotation (Euler angles):

theta = 90°
phi = 0°
lambda = 90°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(90°) * RotZ(90°)
unitary = I * SQRT_Y * S

Unitary Matrix:

[+1-i, -1-i]
Expand Down Expand Up @@ -329,11 +374,20 @@ Stabilizer Generators:
X -> Z
Z -> Y

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +X+Y+Z
Angle: -120 degrees
Angle: -120°

Bloch Rotation (Euler angles):

theta = 90°
phi = 90°
lambda = 180°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(90°) * RotY(90°) * RotZ(180°)
unitary = S * SQRT_Y * Z

Unitary Matrix:

[+1+i, +1+i]
Expand Down Expand Up @@ -373,11 +427,20 @@ Stabilizer Generators:
X -> Z
Z -> X

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +X+Z
Angle: 180 degrees
Angle: 180°

Bloch Rotation (Euler angles):

theta = 90°
phi = 0°
lambda = 180°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(90°) * RotZ(180°)
unitary = I * SQRT_Y * Z

Unitary Matrix:

[+1 , +1 ]
Expand Down Expand Up @@ -415,11 +478,20 @@ Stabilizer Generators:
X -> Y
Z -> -Z

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +X+Y
Angle: 180 degrees
Angle: 180°

Bloch Rotation (Euler angles):

theta = 180°
phi = 0°
lambda = 90°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(180°) * RotZ(90°)
unitary = I * Y * S

Unitary Matrix:

[ , +1-i]
Expand Down Expand Up @@ -459,11 +531,20 @@ Stabilizer Generators:
X -> -X
Z -> Y

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +Y+Z
Angle: 180 degrees
Angle: 180°

Bloch Rotation (Euler angles):

theta = 90°
phi = 90°
lambda = 90°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(90°) * RotY(90°) * RotZ(90°)
unitary = S * SQRT_Y * S

Unitary Matrix:

[+1 , -i]
Expand Down Expand Up @@ -506,11 +587,20 @@ Stabilizer Generators:
X -> Y
Z -> Z

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +Z
Angle: 90 degrees
Angle: 90°

Bloch Rotation (Euler angles):

theta = 0°
phi = 0°
lambda = 90°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(0°) * RotZ(90°)
unitary = I * I * S

Unitary Matrix:

[+1 , ]
Expand Down Expand Up @@ -549,11 +639,20 @@ Stabilizer Generators:
X -> X
Z -> -Y

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +X
Angle: 90 degrees
Angle: 90°

Bloch Rotation (Euler angles):

theta = 90°
phi = -90°
lambda = 90°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(-90°) * RotY(90°) * RotZ(90°)
unitary = S_DAG * SQRT_Y * S

Unitary Matrix:

[+1+i, +1-i]
Expand Down Expand Up @@ -592,11 +691,20 @@ Stabilizer Generators:
X -> X
Z -> Y

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +X
Angle: -90 degrees
Angle: -90°

Bloch Rotation (Euler angles):

theta = 90°
phi = 90°
lambda = -90°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(90°) * RotY(90°) * RotZ(-90°)
unitary = S * SQRT_Y * S_DAG

Unitary Matrix:

[+1-i, +1+i]
Expand Down Expand Up @@ -635,11 +743,20 @@ Stabilizer Generators:
X -> -Z
Z -> X

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +Y
Angle: 90 degrees
Angle: 90°

Bloch Rotation (Euler angles):

theta = 90°
phi = 0°
lambda = 0°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(90°) * RotZ(0°)
unitary = I * SQRT_Y * I

Unitary Matrix:

[+1+i, -1-i]
Expand Down Expand Up @@ -678,11 +795,20 @@ Stabilizer Generators:
X -> Z
Z -> -X

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +Y
Angle: -90 degrees
Angle: -90°

Bloch Rotation (Euler angles):

theta = 90°
phi = 180°
lambda = 180°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(180°) * RotY(90°) * RotZ(180°)
unitary = Z * SQRT_Y * Z

Unitary Matrix:

[+1-i, +1-i]
Expand Down Expand Up @@ -723,11 +849,20 @@ Stabilizer Generators:
X -> -Y
Z -> Z

Bloch Rotation:
Bloch Rotation (axis angle):

Axis: +Z
Angle: -90 degrees
Angle: -90°

Bloch Rotation (Euler angles):

theta = 0°
phi = 0°
lambda = -90°
unitary = RotZ(phi) * RotY(theta) * RotZ(lambda)
unitary = RotZ(0°) * RotY(0°) * RotZ(-90°)
unitary = I * I * S_DAG

Unitary Matrix:

[+1 , ]
Expand Down
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