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Most quantum computing algorithms are based on probability distriubtion measurement and it requires a lot of iteration of the experiment; for example, when dealing with 2 qubits in an experiment, the total number of computational basis is 4, so the experiment should run 4 times for 4 different computational basis measurement.

But if we use quantum non-demolition (QND) measurement, the number of running will be just one.

It seems like every quantum computation experiement reported theses days is not based on the QND measurement, am I correct?

If so, is quantum computation performed so far based on multiple running for measuring the whole probability distribution (for example, four times of running for two-qubit probability distribution measurement)?

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  • $\begingroup$ what do you mean precisely with "total number of computational basis is 4"? With two qubits, the computational basis has 4 elements, if that's what you mean. There are infinitely many possible bases for any system. Estimating probabilities corresponding to measuring in any basis, regardless of how many elements it contains, will require to sample (generally) a lot more than just 4 times (depending on the wanted degree of accuracy) $\endgroup$
    – glS
    Jun 10 at 8:05
  • $\begingroup$ I think you're also a bit confused about what a QND measurement is. A QND measurement does not mean that you don't collapse the state. It means that when you make a measurement in one basis, the increase in uncertainty from the other basis does not lead to the state changing in the first basis over time. So most measurements in your typical QC models are in fact QND en.wikipedia.org/wiki/Quantum_nondemolition_measurement $\endgroup$ Jun 10 at 14:24

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when dealing with 2 qubits in an experiment, the total number of computational basis is 4, so the experiment should run 4 times

This is wrong. That would imply using 3000 qubits would running $2^{3000}$ times, which is just not true at all.

It seems like every quantum computation experiement reported theses days is not based on the QND measurement, am I correct?

Nope. For example, here's an experiment that used repetitive measurement: "Realization of real-time fault-tolerant quantum error correction".

is quantum computation performed so far based on multiple running for measuring the whole probability distribution [...]?

Nope. Good algorithms, like Shor's algorithm or Grover's algorithm, involve preparing and sampling only a few times.

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  • $\begingroup$ Then, how can we measure the whole computational basis at once or just after a few times of running? The quantum state will be collapsed by a certain computational basis measurement, so for another computational basis measurement, the quantum state after processing a certain algorithm should be prepared again. $\endgroup$
    – William
    Jun 9 at 21:36
  • $\begingroup$ As you can see in this paper, arxiv.org/pdf/1603.04512.pdf, they said "For the population distributions measured in figures 3 and 4 and the reported algorithm fidelities, multi-qubit detection is performed by signal-averaging the populations of all 2n states over a few thousand experimental repetitions. In this way, detection and crosstalk errors are removed by decomposing the measurements into the known detector array response of all 32 possible qubit states". From this statement, they measured each computational basis separately for the Detusch-Jozsa and Bernstein-Vazirani algorithm. $\endgroup$
    – William
    Jun 9 at 21:58

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