How can I map a complex number to a qubit in Q#?

Question

In theory, the state of a qubit is defined by 2 complex numbers, following this formula:

The rule is that the amount of complex numbers needed to define the state of a set of qubits is equal to 2ⁿ, where n is the number of used qubits.

if i have an array of complex numbers, how can I map or assign each number to a qubit?

For instance: I have this complex number: 0.0020908999722450972 + i*0.001669629942625761. What would the state of a qubit be in this case? Would I be needing more qubits to represent this number?

Answer 1

I think that depends on what are you going to do with these numbers after you have mapped them to qubits.

If you need to use 2ⁿ numbers to prepare a quantum state on n qubits that is a weighted superposition of the basis states, you can use PrepareArbitraryState operation which does exactly that. Internally it implements the paper Synthesis of Quantum Logic Circuits by Shende, Bullock, Markov.

If you need to represent these numbers in a way that would allow you to read them out by measuring the qubits, you might have to do something like convert them in binary and store each bit in a separate qubit.