Quantum computers utilize quantum bits, or qubits, as the fundamental units of information. Unlike classical bits, which can only represent values of 0 or 1, qubits can exist in a superposition of states, allowing them to simultaneously represent both 0 and 1, as well as any combination of these states.
In a classical computer, bits are represented by physical entities like transistors, which can be in either an "on" or "off" state, corresponding to 1 and 0, respectively. In a quantum computer, qubits are implemented using quantum systems that exhibit superposition, such as individual atoms, ions, or superconducting circuits.
Superposition is a fundamental property of quantum mechanics, which allows quantum systems to exist in a combination of different states at the same time. Mathematically, the state of a qubit is described by a complex probability amplitude, which can be represented as a linear combination of the basis states |0⟩ and |1⟩. This superposition is typically denoted as α|0⟩ + β|1⟩, where α and β are complex numbers called probability amplitudes that determine the probabilities of measuring the qubit in the states |0⟩ and |1⟩, respectively. The probabilities are obtained by taking the absolute squares of the probability amplitudes.
When a qubit is measured, it collapses into one of its basis states |0⟩ or |1⟩ with a probability determined by the magnitudes of the probability amplitudes. For example, if the qubit is in the state α|0⟩ + β|1⟩, the probability of measuring 0 is |α|^2, and the probability of measuring 1 is |β|^2. The sum of the probabilities is always 1, ensuring that the outcome of the measurement corresponds to a valid classical bit value.
Therefore, while a qubit can be in a superposition of states between 0 and 1, the final measurement outcome will always be a definite classical bit value of either 0 or 1. The ability to manipulate and perform computations with qubits in superposition is what gives quantum computers their unique computational power and potential for solving certain problems more efficiently than classical computers.