Most of the experimentalists can only (due to practical limitations) apply quantum gates in the lab that cause rotations around the Bloch sphere in the X-Y plane. However, many quantum algorithms rely on rotations around the Z-axis of the Bloch sphere. Are these Z-gates then a figment of the imagination of the theoretical quantum scientist?
In this video, Postdoctoral Researcher Ben Criger (QuTech) shows that this is not at all a problem. In fact, we can use a specific sequence of X and Y gates to effectively construct an arbitrary Z rotation around the Bloch sphere. We first mathematically show that the sequence synthesizes into a Z-gate, after which we show the same visually on the Bloch sphere.
- Bloch sphere
- Arbitrary rotations around the Bloch sphere (X, Y, Z rotations)
- Basic matrix multiplication algebra
- Hadamard gate
- Euler’s identity
Can you think of a similar sequence using X, Z rotations to synthesize a Y gate?
For a recap on matrix notations of arbitrary Bloch sphere rotations, take a look at these lecture notes from Ian Glendinning:
A fun low-level read on the use of Bloch sphere rotations in quantum computing can be found at: