## Quantum Operations: Arbitrary Initialization & State Fidelity

What if we want to initialize a qubit register to an arbitrary state? An arbitrary state for n qubits may

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## Quantum Operations, Non-Unitary Operations

These include measurements, reset of qubits, and classical conditional operations. # Measurements # Reset It is also possible to reset

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## Quantum Operations, Multi-Qubit Gates: Three-Qubit Gates

# Toffoli Gate (ccx Gate) The Toffoli gate flips the third qubit if the first two qubits (Least Significant Bit

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## Quantum Operations, Multi-Qubit Gates: Two-Qubit Gates

# Controlled Pauli Gates Controlled-X (or, controlled-NOT) gate The controlled-not gate flips the target qubit when the control qubit is

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## Quantum Operations, Single-Qubit Gates: Standard Rotation Gates

Rx Gate Rotation around X-axis Ry Gate Rotation around Y-axis Rz Gate Rotation around Z-axis Source = https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations.html Kode program

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## Quantum Operations, Single-Qubit Gates: C3 Gates

T Gate / Square Root of S Phase Gate T Dagger Gate / Conjugate of Square Root of S Phase

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## Quantum Operations, Single-Qubit Gates: Clifford Gates

Hadamard Gate S Gate / Square Root of Z Phase Gate The S gate is also known as the phase

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## Quantum Operations, Single-Qubit Gates: Pauli Gates

X: bit-flip gate The Pauli-X Gate is a single-qubit rotation through pi radians around the x-axis. X = sigma_x =

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## Quantum Operations, Single-Qubit Gates: Identity Gate

The Identity gate is a single-qubit operation that leaves the basis states |0> and |1> unchanged. I = ( 1

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## Quantum Operations, Single-Qubit Gates: U Gates

u1 gates: useful as it allows us to apply a quantum phase. u2 gates: useful gate as it allows us

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