# Representation of real numbers in quantum computers

In classical binary computers, real numbers are often represented using the IEEE 754 standard. With quantum computers you can of course do this as well - and for measurements this (or a similar standard) will probably be necessary since the result of any measurement is binary. But could real numbers be modeled more easily and / or more precisely within the qubits using different methods before the measurement happens? If so, are there any use cases where this is actually useful, seeing that (I'm assuming) any additional precision will be lost when measurements are performed?

To be clear, I'm not (necessarily) looking for existing standards, just for ideas or suggestions on how to represent those numbers. If there's any research into it, that would be useful too of course.

• I think this really depends on the specific algorithm or problem to solve. As you see, 'number standards' are basically engineering. Not science, useful, but not the frontier. Let's get working stuff first. I think you need to clarify if you want examples, literature or something else because I think this is too vague. Mar 25, 2018 at 0:21
• @Discretelizard I agree, that it is an engineering question rather than a science one but I disagree about it not being the frontier. For quantum computers to live up to their potential we need to know what their potential is. And you can't solve numerical problems without a numerical representation. Mar 25, 2018 at 9:10
• Okay. Perhaps it is a good idea then to clarify that the question is essentially one of 'engineering'. Mar 25, 2018 at 10:02

There have been efforts to implement construct "floating point" representation of small rotations of qubit states, such as: Floating Point Representations in Quantum Circuit Synthesis. But there doesn't seem to be any international standard like the one you mentioned i.e. IEEE 754. IEEE 7130 - Standard for Quantum Computing Definitions is an ongoing project. Anyhow, representation of floating point will automatically be dependent on the precision you want. If you want to follow the path in the first paper I linked (i.e. using qubit rotations) I can already imagine the possibility of errors during such rotation operations and you'd have to deal with them accordingly.

• That paper looks very interesting, thank you. Only having read the abstract so far I do see your point about errors. Of course that's a general problem we have to solve. And I'm not surprised that there aren't any standards yet - I just mentioned IEEE 754 as an example of how numbers can be represented. Mar 25, 2018 at 9:17

I am afraid that while interesting work is being done here, it should be clear that the quantum computer architecture is very much non-standardised and hence this is all subject to change.

The IEEE 754 standard describes how to implement a feature that decades of engineering and research have shown to be useful and hence machines are to be expected to do this.

In contrast, scientists and engineers are still figuring out how to best create an 'universal' quantum computer. They have some ideas on how to do this, as Blue mentions. However, there is no 'one true idea' on which engineers can base standards.

Perhaps it would even turn out complex numbers are easier to represent on a quantum computer and we have a standard for complex number data-types, instead!

So, while work is being done here, an IEEE standard seems very much in the far future.

• I do realize this, yes. I didn't expect there to be an existing standard either; I've added something to that effect to the question, hopefully clarifying what I'm looking for. Mar 25, 2018 at 14:57
• @blalasaadri. Good. I am aware that this probably isn't the answer you're looking for, but it could be reasonable advice for other readers. Mar 25, 2018 at 15:10