Introduction to Quantum Gates
In classical computing, we represent information using bits, which can be either 0 or 1. However, in quantum computing, we use quantum bits or qubits, which can exist in a superposition of both 0 and 1 states simultaneously.
To manipulate qubits, we use quantum gates, which are analogous to classical logic gates. However, unlike classical gates, quantum gates can perform complex operations on qubits, taking advantage of their quantum properties.
Understanding Axes
In classical computing, we usually think in terms of a single axis, often depicted as a line, where the two states, 0 and 1, lie at opposite ends. In quantum computing, however, we often deal with states that are not just 0 or 1, but can exist anywhere on the surface of a sphere, known as the Bloch sphere.
Applying Gates
When we apply a gate, we essentially rotate the qubit’s state around the corresponding axis on the Bloch sphere. For example:
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Applying an X gate rotates the qubit’s state around the X-axis.
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Applying a Z gate rotates the qubit’s state around the Z-axis.
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Applying a H gate (hadamard gate , creates superposition by rotating the qubit state around an axis that lies between the X and Z axes on the Bloch sphere.
X,Y and Z axis:
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X Axis:
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Mathematically, the X gate corresponds to a rotation by πpiπ radians (180 degrees) around the X axis on the Bloch sphere.
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Y Axis:
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Mathematically, the Y gate corresponds to a rotation by πpiπ radians (180 degrees) around the Y axis on the Bloch sphere.
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Z Axis:
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Mathematically, the Z gate corresponds to a rotation by πpiπ radians (180 degrees) around the Z axis on the Bloch sphere.
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This rotation introduces a phase flip without affecting the probability amplitudes of the qubit states.
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Conclusion
Understanding the concept of axes helps us visualize how quantum gates manipulate qubit states. Each gate performs a rotation around a specific axis, enabling us to perform various quantum operations, such as creating superposition, introducing phase changes, and entangling qubits.
Additional reading(Microsoft blog post)
https://quantum.microsoft.com/en-us/explore/concepts/single-qubit-gates