quantum nature of the randomly generated numbers helped specifically with quantum computer simulations, but based on your reply you clearly just meant that you were using it as a multi-purpose RNG that is free of unwanted correlations between the randomly generated bits

It is used as the source of entropy for the simulator. Quantum mechanics is random, so to actually get the results you have to sample it. In quantum computing, this typically involves running the same program tens of thousands of times, which are called “shots,” and then forming a distribution of the results. The sampling with the simulator uses the QRNG for the source of entropy, so the sampling results are truly random.

Out of curiosity, have you found that the card works as well as advertised? I ask because it seems to me that any imprecision in the design and/or manufacture of the card could introduce systematic errors in the quantum measurements that would result in correlations in the sampled bits, so I am curious if you have been able to verify that is not something to be concerned about.

I have tried several hardware random number generators and usually there is no bias either because they specifically designed it not to have a bias or they have some level of post-processing to remove the bias. If there is a bias, it is possible to remove the bias yourself. There are two methods that I tend to use that depends upon the source of the bias.

To be “random” simply means each bit is statistically independent of each other bit, not necessarily that the outcome is uniform, i.e. 50% chance of 0 and 50% chance of 1. It can still be considered truly random with a non-uniform distribution, such as 52% chance of 0 and 48% chance of 1, as long as each successive bit is entirely independent of any previous bit, i.e. there is no statistical analysis you could ever perform on the bits to improve your chances of predicting the next one beyond the initial distribution of 52%/48%.

In the case where it is genuinely random (statistical independence) yet is non-uniform (which we can call nondeterministic bias), you can transform it into a uniform distribution using what is known as a von Neumann extractor. This takes advantage of a simple probability rule for statistically independent data whereby Pr(A)Pr(B)=Pr(B)Pr(A). Let’s say A=0 and B=1, then Pr(0)Pr(1)=Pr(1)Pr(0). That means you can read two bits at a time rather than one and throw out all results that are 00 and 11 and only keep results that are 01 or 10, and then you can map 01 to 0 and 10 to 1. You would then be mathematically guaranteed that the resulting distribution of bits are perfectly uniform with 50% chance of 0 and 50% chance of 1.

I have used this method to develop my own hardware random number generator that can pull random numbers from the air, by analyzing tiny fluctuations in electrical noise in your environment using an antenna. The problem is that electromagnetic waves are not always hitting the antenna, so there can often be long strings of zeros, so if you set something up like this, you will find your random numbers are massively skewed towards zero (like 95% chance of 0 and 5% chance of 1). However, since each bit still is truly independent of the successive bit, using this method will give you a uniform distribution of 50% 0 and 50% 1.

Although, one thing to keep in mind is the bigger the skew, the more data you have to throw out. With my own hardware random number generator I built myself that pulls the numbers from the air, it ends up throwing out the vast majority of the data due to the huge bias, so it can be very slow. There are other algorithms which throw out less data but they can be much more mathematically complicated and require far more resources.

In the cases where it may not be genuinely random because the bias is caused by some imperfection in the design (which we can call deterministic bias), you can still uniformly distribute the bias across all the bits so that not only would be much more difficult to detect the bias, but you will still get uniform results. The way to do this is to take your random number and XOR it with some data set that is non-random but uniform, which you can generate from a pseudorandom number generator like the C’s rand() function.

This will not improve the quality of the random numbers because, let’s say if it is biased 52% to 48% but you use this method to de-bias it so the distribution is 50% to 50%, if someone can predict the next value of the rand() function that would increase their ability to make a prediction back to 52% to 48%. You can make it more difficult to do so by using a higher quality pseudorandom number generator like using something like AES to generate the pseudorandom numbers. NIST even has standards for this kind of post-processing.

But ultimately using this method is only obfuscation, making it more and more difficult to discover the deterministic bias by hiding it away more cleverly, but does not truly get rid of it. It’s impossible to take a random data set with some deterministic bias and trulyget rid of the deterministic bias purely through deterministic mathematical transformations,. You can only hide it away very cleverly. Only if the bias is nondeterministic can you get rid of it with a mathematical transformation.

It is impossible to reduce the quality of the random numbers this way. If the entropy source is truly random and truly non-biased, then XORing it with the C rand() function, despite it being a low-quality pseudorandom number generator, is mathematically guaranteed to still output something truly random and non-biased. So there is never harm in doing this.

However, in my experience if you find your hardware random number generator is biased (most aren’t), the bias usually isn’t very large. If something is truly random but biased so that there is a 52% chance of 0 and 48% chance of 1, this isn’t enough of a bias to actually cause much issues. You could even use it for something like cryptography and even if someone does figure out the bias, it would not increase their ability to predict keys enough to actually put anything at risk. If you use a cryptographysically secure pseudorandom number generator (CSPRNG) in place of something like C rand(), they will likely not be able to discover the bias in the first place, as these do a very good job at obfuscating the bias to the point that it will likely be undetectable.