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Upon measurement, the qubit's superposition collapses to one of the basis states, $|0\rangle$ or $|1\rangle$, with probabilities defined by the superposition state's amplitudes.

Entanglement is a more complex form of superposition where the states of two or more qubits are linked, such that the state of one qubit can instantaneously affect the state of the other, no matter the distance.

$|\Psi\rangle = (|0\rangle + e^{i\theta}|1\rangle)/\sqrt{2}$, where $\theta$ is the phase difference between the two states.

No, it is not possible to directly observe the superposition of a qubit; measurement will result in observing one of the basis states, with probabilities defined by the state's amplitudes.

The Hadamard gate is commonly used to put a qubit into a state of superposition.

The outcome is a qubit in an equal superposition state: $(|0\rangle + |1\rangle)/\sqrt{2}$.

The principle of quantum superposition means that quantum gates operate on superpositions of inputs, producing superpositions of outputs, thereby enabling complex state manipulations that are impossible with classical logic gates.

The phase in quantum superposition refers to the relative position of the peaks and troughs of the quantum states' wavefunctions, affecting the interference patterns observable after combining amplitudes.

The complex nature of probability amplitudes allows for interference effects between superposed states, which is critical for quantum algorithms to function effectively.

No, a single qubit can only be in a superposition of its two basis states, $|0\rangle$ and $|1\rangle$. However, systems of multiple qubits can exist in superpositions of many more combined states.

The probabilities are the squares of the absolute values of the probability amplitudes: $P(0) = |\alpha|^2$ and $P(1) = |\beta|^2$, for the state $|\Psi\rangle = \alpha|0\rangle + \beta|1\rangle$.

Classical computers can simulate superposition algorithms to some extent, but inefficiently, because they must explicitly calculate each possible state rather than naturally existing in all states at once.

Superposition enables quantum parallelism, allowing a quantum computer to process many inputs simultaneously, which can lead to exponential speed-ups in certain computations.

Quantum cryptography uses superposition to detect eavesdroppers, as any attempt to measure superposed quantum states will disturb them, revealing the presence of an interception.

Coherence time is the duration over which a quantum state, such as superposition, can be maintained before it degrades due to environmental interference. It's crucial for the performance of quantum computations relying on superposition.

$|\Psi\rangle = \alpha|0\rangle + \beta|1\rangle$, where $\alpha$ and $\beta$ are complex numbers representing probabilities amplitudes for the respective states.

Superposition is essential for these algorithms because it allows them to operate on many inputs simultaneously, leading to exponential speedup for Shor's factoring algorithm and quadratic speedup for Grover's search algorithm.

Superposition allows quantum computers to represent and evolve the states of quantum systems efficiently, enabling simulation of complex quantum systems that are intractable for classical computers.

Superposition refers to the phenomenon where a quantum system can exist in multiple states simultaneously until it is measured.