Quantum computers use superposition and quantum interference to perform calculations on multiple qubit states simultaneously. In a classical computer, bits can be in one of two states, 0 or 1. However, in a quantum computer, qubits can exist in a superposition of both 0 and 1 states simultaneously.
Superposition allows quantum computers to represent and manipulate multiple states simultaneously. For example, if you have two qubits, each qubit can be in a superposition of states, representing all possible combinations of 0 and 1 for both qubits. This allows the quantum computer to perform calculations on all these combinations in parallel.
To perform calculations, quantum algorithms make use of quantum gates, which are analogous to the logic gates in classical computers. These gates can act on qubits to manipulate their states and create entanglement between qubits. Entanglement is a crucial property of quantum systems where the states of multiple qubits become correlated in such a way that the state of one qubit depends on the state of another.
Quantum algorithms take advantage of this entanglement and superposition to perform calculations on a large number of possible combinations simultaneously. By carefully designing the algorithm and applying quantum gates, it is possible to obtain the desired result by leveraging interference effects among the different quantum states. The interference allows canceling out unwanted states and amplifying the desired ones, leading to the final outcome of the computation.
Now, regarding your question about measurement and wave function collapse, you are correct that measuring a qubit collapses its superposition and forces it into a definite state of either 0 or 1. However, in quantum computation, measurements are typically performed at the end of the computation to extract the final result. During the computation itself, the qubits remain in a superposition, undergoing various quantum operations.
Quantum algorithms are designed to exploit the inherent parallelism of superposition and interference to obtain the desired computational advantage. The final result is obtained by measuring the qubits at the end of the computation, which collapses them into classical bits. So, until the final measurement, the quantum computer can operate on all possible combinations of qubit values simultaneously without collapsing the wave function.