Many different algorithms exist all designed to solve specific mathematical problems with the use of physics.
The implementation of those algorithms is done with different kinds of gates that read and write the data to the qubits.
An analogy used to classical computers is qubits as the CPU and gates as the motherboard that prepares information and manages memory.
Error correction can be done at the gate, or at the qubit.
The number of logical qubits is one way to express the power of a quantum computer, but the error rate included is better expressed as quantum volume.
The main concern is that cryptography can be broken by an advanced algorithm, only available to a few people with the element of surprise.
The advances in Quantum Algorithms have frequently surpassed expectations.
Many literatures still refer to AES as “quantum safe” even though the implementation of Grover’s can be vastly superior through memory conserving techniques.