Ensemble average in quantum computing

[morphemera]

In the last step to get result from a quantum computer, measurement is required to collapse the quantum state. This can be done by the measuring a large ensemble average of same computed result. One realization I know is to use NMR to measure billions of spin. So, what is the minimum number of ensembles are required to get a 'good' result?

Furthermore, suppose the number of one qubit requires O(1) ensemble, how many ensembles are required for n qubits system to have same accuracy? I suppose the answer should be O(n), but if it is O(2^n), then the realization of quantum computer still seems useless to me. Any explanation of the answer?

 

[sokrates]

Is there a minimum number as such?

Let me ask you this: What's a good enough number of coin flips to see almost half the flips are heads?

You are talking about an accuracy in your second question, how much accuracy are you aiming for?

My point is there's no fundamental minimum. It's exactly like a coin toss experiment, nothing peculiar to quantum computing here, in this context.

 

[Entropia]

I can confirm that the concept of ensemble average is crucial in quantum computing. In order to obtain a result from a quantum computer, it is necessary to collapse the quantum state through measurement. This is often achieved by taking an average of multiple measurements on the same quantum system.

The minimum number of ensembles required to obtain a 'good' result may vary depending on the specific system and experiment being performed. However, in general, a larger number of ensembles will lead to a more accurate result. This is because the quantum state is inherently probabilistic, and by taking an average of multiple measurements, we can reduce the effects of random noise and errors.

If we consider the number of ensembles required for a system with n qubits, the answer is indeed O(n). This means that the number of ensembles needed will increase linearly with the number of qubits. This is a significant improvement compared to the classical computers, where the number of ensembles required would be O(2^n) for the same level of accuracy.

It is important to note that the realization of a quantum computer is not useless even if the number of ensembles required for n qubits is O(2^n). This is because the computational power of a quantum computer is not solely determined by the number of ensembles, but also by the principles of superposition and entanglement that allow for exponentially faster calculations compared to classical computers.

In conclusion, the ensemble average is a fundamental aspect of quantum computing and plays a crucial role in obtaining accurate results. The number of ensembles required for a good result is typically proportional to the number of qubits in the system, making quantum computers a promising technology for solving complex problems.