How is the answer obtained from quantum calculations?

[david_8956]

The calculation process of a quantum computer

I've just started reading up about quantum computers and it's fascinating stuff but I need some help understanding something.

I understand how a qubit can be in the classical "0" or "1" state used in a conventional computer and it can also be in a superposition of two states at the same time. It seems that there are certain calculations that would be best suited to quantum computing, for example factorizing a large number.

In a conventional computer I guess this is just trial and error until the lowest prime factor is found. But if the quantum computer had many quibits all in a state of superposition in the input register then it could perform all of these calculations in parallel, simultaneously.

From my understanding you would then have many possible results but only one answer. I can't seem to find anywhere that explains this in a way in which I can understand, but how do you get your answer from the jumbled mess of results?

Would you not need to take a final measurement thus causing the wave function collapse that would leave you with one random result, but not necessarily the right answer? I read that you can manipulate the end result without taking a measurement and get your answer through quantum interference, but how exactly would this work?

 

[eljose79]

let me try to break this down for you in simpler terms.

First of all, let's talk about how a conventional computer works. In a classical computer, information is represented in bits, which can have a value of either 0 or 1. This is known as binary code. To perform a calculation, the computer uses logic gates to manipulate these bits according to predetermined rules. This is a sequential process, meaning that each calculation is performed one after the other.

Now, let's compare this to a quantum computer. Instead of bits, a quantum computer uses qubits, which can exist in multiple states at the same time. This is known as superposition. In a quantum computer, calculations are performed using quantum gates, which manipulate the qubits according to the rules of quantum mechanics. This allows for calculations to be performed simultaneously, rather than sequentially.

Now, let's talk about the example you mentioned - factorizing a large number. In a conventional computer, this would indeed be a trial and error process. However, a quantum computer can perform this calculation much more efficiently by using a quantum algorithm called Shor's algorithm. This algorithm takes advantage of the quantum properties of superposition and entanglement to quickly find the factors of a large number.

But how does the quantum computer get the right answer from the jumbled mess of results? This is where quantum interference comes into play. Without going into too much detail, quantum interference is a phenomenon where the superposition of multiple states can produce a specific outcome when measured. In the case of factorization, the quantum computer manipulates the qubits in such a way that when measured, the result is the correct factors of the number. This is known as the "right answer."

But you may be wondering, how can we manipulate the qubits without taking a measurement and collapsing the wave function? This is where quantum error correction comes into play. Quantum error correction is a crucial aspect of quantum computing that allows for the manipulation of qubits without causing decoherence (the loss of quantum information). This allows for the quantum computer to perform calculations without collapsing the wave function until the very end, when the correct answer can be extracted.

I hope this helps to clarify the calculation process of a quantum computer. It's a complex and fascinating field, and there is still much research being done to fully understand and harness the power of quantum computing. Keep learning and exploring, and who knows what amazing discoveries you may make!