Quantum computers can take advantage of superposition to perform computations by representing information in quantum bits or qubits, which can exist in a superposition of multiple states simultaneously. This allows quantum computers to explore a much larger space of possibilities in parallel compared to classical computers.
In a classical computer, information is stored in bits that can be either 0 or 1. However, in a quantum computer, qubits can be in a state that is a combination of 0 and 1. This superposition property enables quantum computers to perform computations on multiple inputs simultaneously.
Quantum algorithms, such as Shor's algorithm for factoring large numbers or Grover's algorithm for searching unstructured databases, take advantage of superposition and interference effects to speed up certain types of calculations. These algorithms use quantum gates to manipulate the qubits, applying operations that exploit the properties of superposition and entanglement to perform computational tasks more efficiently than classical algorithms.
Now, regarding the elimination of randomness associated with superposition in order to make useful computations, it's important to note that superposition is not inherently random. It's a property that allows a qubit to exist in a combination of states, and when measurements are performed, the qubit collapses into one of the possible states with a certain probability. This probability is determined by the coefficients of the superposition.
To obtain useful computation results from a quantum computer, techniques such as quantum error correction and quantum algorithms are employed. Quantum error correction is a field of study that focuses on developing methods to protect quantum information from errors and noise that can disrupt the delicate quantum states. By applying error correction techniques, the impact of random errors and decoherence can be mitigated.
Furthermore, quantum algorithms are designed to exploit the quantum properties of superposition and interference to obtain meaningful results. These algorithms are specifically developed to take advantage of the unique capabilities of quantum computers, often achieving exponential speedup compared to classical algorithms for certain tasks.
While quantum computers are subject to the probabilistic nature of measurements and the challenge of errors, advances in error correction, fault-tolerant computation, and algorithm design aim to minimize the impact of these factors, making useful computation possible with quantum systems. However, it's worth noting that quantum computing is still an active area of research, and there is ongoing work to overcome these challenges and improve the reliability and performance of quantum computers.