What is the significance of 'i' in quantum computation notation?

In summary, The conversation discusses the confusion regarding the appearance of the letter 'i' in brackets [1, i] in a quantum state and its connection to complex numbers. The person asking the question is a beginner in quantum computation and is seeking an explanation for the notation. The response explains that the 'i' represents the square root of -1 and is used in column vector notation to denote the components of the vector. It also emphasizes the importance of understanding complex numbers in quantum mechanics. The conversation ends with the person expressing their gratitude for the explanation.
  • #1
Quark Effect
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TL;DR Summary
The meaning of notation 'i'?
Hi guys, I am currently having some difficulties with this quantum state. I don't entirely understand what that letter 'i' means, where it comes from and why it appears in brackets [1, i]. Shouldn't there be a '0' instead?
Formula q.png

I am an absolute beginner in quantum computation. I've been following a tutorial for beginners while this quantum state appeared with the letter 'i' and there's no further explanation where it comes from and what it means.
 
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  • #2
Quark Effect said:
I don't entirely understand what that letter 'i' means

It's the square root of ##-1##.
 
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  • #3
Quark Effect said:
I am an absolute beginner

Thread level changed to "B" accordingly.
 
  • #5
PeterDonis said:
It's the square root of ##-1##.
mfb said:
You'll need to know complex numbers for everything in quantum mechanics.
Thanks a lot!
 
  • #6
Quark Effect said:
why it appears in brackets [1, i]. Shouldn't there be a '0' instead?

No. What you have shown is column vector notation. You have a vector space with two basis vectors, ##|0\rangle## and ##|1\rangle##. The upper number in the column vector is the ##|0\rangle## component of the vector and the lower number is the ##|1\rangle## component. The image you showed has factored out the common ##1 / \sqrt{2}## factor, so that leaves ##\begin{bmatrix} 1 \\ i \end{bmatrix}## since the coefficient in front of ##|0\rangle## is ##1## and the coefficient in front of ##|1\rangle## is ##i##.
 
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  • #7
PeterDonis said:
No. What you have shown is column vector notation. You have a vector space with two basis vectors, ##|0\rangle## and ##|1\rangle##. The upper number in the column vector is the ##|0\rangle## component of the vector and the lower number is the ##|1\rangle## component. The image you showed has factored out the common ##1 / \sqrt{2}## factor, so that leaves ##\begin{bmatrix} 1 \\ i \end{bmatrix}## since the coefficient in front of ##|0\rangle## is ##1## and the coefficient in front of ##|1\rangle## is ##i##.
Finally understood it. Thanks a lot man!
 
  • #8
Quark Effect said:
Thanks a lot man!

You're welcome!
 

Related to What is the significance of 'i' in quantum computation notation?

1. What is quantum computation notation?

Quantum computation notation is a system of symbols and rules used to represent and manipulate quantum information in quantum computing. It is similar to traditional computer programming notation, but is specifically designed to work with the unique properties of quantum systems.

2. How is quantum computation notation different from traditional computing notation?

Quantum computation notation differs from traditional computing notation in several ways. Firstly, it incorporates symbols and operations that are specific to quantum mechanics, such as quantum gates and qubits. Additionally, it allows for the representation of quantum states, which can exist in multiple states simultaneously. This is in contrast to traditional computing, where bits can only exist in one state at a time.

3. Can anyone learn quantum computation notation?

Yes, anyone with a basic understanding of quantum mechanics and computer programming can learn quantum computation notation. However, it can be quite complex and requires a solid understanding of quantum concepts and mathematical notation.

4. What are the benefits of using quantum computation notation?

The use of quantum computation notation allows for the efficient representation and manipulation of quantum information, which is necessary for performing complex quantum algorithms. It also allows for the translation of classical algorithms into quantum algorithms, which can potentially provide significant speedups for certain types of calculations.

5. Are there different types of quantum computation notation?

Yes, there are several different types of quantum computation notation, each with its own set of symbols and rules. Some of the most commonly used include Dirac notation, Bra-Ket notation, and Quantum circuit notation. These notations may vary in their level of complexity and the types of operations they can represent.

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