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I have been looking into the creation of truly random numbers using a quantum computer, but I have been having trouble with finding resources on this problem. Is it possible to create a truly random number using a quantum computer?

In theory, my thinking is that we can prepare a qubit in the $|0\rangle$ state, apply a Hadamard to obtain a $|+\rangle$, and then measure in the logical basic to get a 0 with probability $\frac{1}{2}$ and a 1 with probability $\frac{1}{2}$. Repeat the process as many times as you want to create a random number in binary (i.e. 0110001...)

Now there are obviously problems with this practically (regarding the accuracy of our state initiation, Hadamard transform, and measurement). But is the theory correct? In theory can we therefore produce a truly random number using a quantum computer?

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Yes, it is possible to use quantum computer as a true random number generator, by applying Hadamard gates to all available qubits in initial $|0\rangle$ state and measuring them in the standard basis; but this is inefficient way of generating random numbers because quantum computer requires time to cool down its qubits to the initial state before starting a new computation.

There are other cheaper and faster methods of generating random numbers using quantum effects, see for example ANU Quantum Random Numbers Server

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    $\begingroup$ I'm always somewhat sceptical about TRNGs that use a cryptographic hash /cipher technique for randomness extraction, AES-128 in your ANU case. It's very dangerous. You can pass all the typical randomness tests simply by encrypting the output from BBC Radio 1, especially if you use a home made crystal receiver that picks up atmospheric noise/ next door's arc welder. It sounds too much like the dodgy random.org. The ANU staff also share this concern if you read their write up. $\endgroup$ – Paul Uszak Jan 1 '17 at 17:17
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    $\begingroup$ @PaulUszak I believe realworld quantum computer also requires randomness extractor to pass standard randomness tests, because as the questioner noticed there are always some errors in the qubit's state initialization, gates and measurements, that possibly lead to a biased random output. $\endgroup$ – kludg Jan 1 '17 at 19:15
  • $\begingroup$ @kludg Thanx for ANU reference. $\endgroup$ – Vadym Fedyukovych Jan 2 '17 at 12:11

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