Understanding Qubits and Complex Scalars: The Role of Imaginary Numbers

In summary, the conversation discusses the use of complex numbers in quantum mechanics and why they are necessary. The speakers agree that there is no problem with using complex numbers and that they are effective in representing 2d positions, translations, and rotations. They also mention that there are multiple reasons for using complex numbers in QM.
  • #1
kaje
23
0
Hi,

Does anybody know why we have complex scalers to represent qubits..I mean why they are not real numbers.

Thanks
 
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  • #2
What does it matter that they're not real numbers? There are complex numbers that don't correspond to the number of cows you can have in a field... so what? You also can't have -1 cows in a field, or fit fifty trillion cows in a field. While we're at it, you can't have "F=ma" cows in a field either.

We're not counting cows in fields, so why would we expect to only use mathematical abstractions matched to that task?

I really just don't see the problem here. We have a mathematical model that works, we know how to map between the model and reality, and the model happens to internally use values that are good at representing 2d positions, translations, and rotations. There's nothing amiss. We can rewrite our laws to use pairs of real numbers instead of complex numbers, but why would we do that? It would just double the amount of symbol manipulation.
 
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Likes kaje
  • #4
Strilanc said:
I really just don't see the problem here. We have a mathematical model that works, we know how to map between the model and reality, and the model happens to internally use values that are good at representing 2d positions, translations, and rotations. There's nothing amiss. We can rewrite our laws to use pairs of real numbers instead of complex numbers, but why would we do that? It would just double the amount of symbol manipulation.

That's true.

I interpret such questions as why do we have complex numbers in QM for which there are quite a few reasons.

Thanks
Bill
 

1. What are qubits and how do they differ from classical bits?

Qubits, or quantum bits, are the basic unit of information in quantum computing. Unlike classical bits, which can only store information as a 0 or 1, qubits can exist in multiple states at the same time due to quantum superposition. This allows for much more complex calculations and data storage.

2. What is the role of imaginary numbers in qubits and complex scalars?

Imaginary numbers are an essential part of the mathematics behind qubits and complex scalars. They are used to represent the superposition of states in qubits, as well as the complex numbers that make up the quantum state of a system.

3. How do complex scalars relate to qubits?

Complex scalars are used to describe the quantum state of a qubit. They are made up of a real part and an imaginary part, which represent the probability amplitudes for the qubit to be in a certain state. These scalars are used in calculations and measurements in quantum computing.

4. Can you give an example of how imaginary numbers are used in qubits and complex scalars?

Sure, imagine a qubit that is in a superposition of states, with a probability amplitude of 0.7 for being in the state 0 and 0.3 for being in the state 1. This can be represented by the complex scalar 0.7 + 0.3i, where i is the imaginary unit. The probabilities for each state can be found by taking the absolute value squared of the scalar's real and imaginary parts.

5. What is the significance of understanding qubits and complex scalars in quantum computing?

Qubits and complex scalars are the fundamental building blocks of quantum computing. Understanding how they work and how to manipulate them is crucial for developing and programming quantum computers. It allows for the harnessing of the unique properties of quantum mechanics to solve complex problems and perform calculations that would be impossible with classical computers.

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