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controlled-Z gate

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description controlled-Z gate Overview

The controlled-Z gate is a two-qubit quantum logic gate. It performs a conditional phase shift on one qubit based on the state of another. This gate is notable for its role in creating entanglement and enabling algorithms like Shor’s algorithm. It's primarily utilized by researchers and developers working with Clifford gates and exploring complex quantum computations involving multiple qubits.

help controlled-Z gate FAQ

How is a controlled-Z (CZ) gate different from a CNOT gate?

A CNOT gate flips the target qubit's state from |0⟩ to |1⟩ when the control qubit is |1⟩. In contrast, a CZ gate applies a phase flip (multiplying by -1) to the target qubit's amplitude only when both qubits are in the |1⟩ state.

Why is the controlled-Z gate considered symmetric?

Unlike many other controlled gates where the control and target qubits play distinct roles, the CZ gate applies an identical phase shift to both qubits. Because both qubits receive the same phase if they are in the |1⟩ state, you can swap the control and target without changing the quantum circuit.

How do you physically implement a controlled-Z gate using single-qubit rotations?

You can construct a CZ gate by applying a Hadamard gate to the target qubit, performing a standard CNOT gate, and then applying another Hadamard gate to the target. This sequence translates the X-basis bit flip of the CNOT into the Z-basis phase flip required by the CZ gate.

What role does the controlled-Z gate play in creating quantum entanglement?

The CZ gate is a fundamental entangling gate used to generate Bell states from separable two-qubit systems. By applying a CZ gate to a control qubit in a superposition and a target qubit, the two qubits become highly correlated, which is crucial for quantum teleportation.

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