Understanding Qubits: How Superposition Powers Quantum Computers

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Discussion Overview

The discussion centers on the nature of qubits in quantum computing, particularly focusing on the concept of superposition and its implications for computational power compared to classical bits. Participants explore theoretical aspects, practical implications, and educational resources related to quantum computing.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about how superposition provides advantages over classical binary states, noting that measurement collapses qubits to either 1 or 0.
  • Another participant suggests that qubits can perform numerous computations in superposition before measurement, implying a potential for greater computational efficiency.
  • A participant clarifies that qubits are not simply bits with an additional state, emphasizing that they represent a 2-level quantum system capable of linear combinations of states, which differ from classical probabilities.
  • Discussion includes technical details about the mathematical representation of qubits and the implications of their properties, such as destructive interference and entanglement.
  • Several participants reference lecture notes by Scott Aaronson, indicating a desire to understand the material better, though some express concerns about missing content in the lectures.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of superposition for computational power, with some emphasizing its benefits while others question the clarity of the concept. There is also a lack of agreement on the completeness of the educational resources referenced.

Contextual Notes

Some participants mention gaps in the lecture notes, indicating potential limitations in understanding the material. The discussion reflects varying levels of familiarity with quantum mechanics and quantum computing concepts.

Who May Find This Useful

This discussion may be useful for individuals interested in quantum computing, particularly those seeking to understand the foundational concepts of qubits and superposition, as well as those looking for educational resources on the topic.

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Hi,

I'm having trouble understanding the power of qubits relating to quantum computers. I've read a number of times that the power comes from the fact that instead of simply holding an on or off state (1/0), they can hold both at the same time (superposition). However, when we measure them they 'decide' on a state.

My question is, how can this third state of superposition provide a huge benefit over the 1 and 0 states of transistors, since once we use them (observe them) the states available to us is still only a 1 or a 0?

Many thanks in advance http://www.thephysicsforum.com/images/smilies/smile.png
 
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Heinera said:
And if you have time to spare, these lecture notes by Scott Aaronson:
http://www.scottaaronson.com/democritus/

I'm looking at lecture 9 and there are many gaps. Maybe he's giving a slide show and the slides are not included.
 
Quantum computers are not ternary computers. Qubits are not just bits with a third state.

A qubit is a 2-level quantum system that can store states like ##a \left|0\right\rangle + b \left|1\right\rangle## where ##a^2 + b^2 = 1##.

Put ##n## qubits together, and you get a ##2^n##-level quantum system. For example, 3 qubits can store states like ##a \left|000\right\rangle + b \left|001\right\rangle + c \left|010\right\rangle + d \left|011\right\rangle + e \left|100\right\rangle + f \left|101\right\rangle + g \left|110\right\rangle + h \left|111\right\rangle## where ##a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2 = 1##.

In other words, quantum computers can store a linear combination of the classical states. But the weights of the linear combination are not probabilities, which would have to satisfy ##a + b + ... + h = 1##, they are the square roots of probabilities and must satisfy ##a^2 + b^2 + ... + h^2 = 1##.

Everything else flows from that square-root-of-probability thing. Operations correspond to complex orthonormal matrices. Destructive interference is possible. Copying doesn't quite work. Everything is reversible. Entanglement is a thing. Etc.
 
Hornbein said:
I'm looking at lecture 9 and there are many gaps. Maybe he's giving a slide show and the slides are not included.
Do you mean that you don't see any figures or formulas?
 
Heinera said:
Do you mean that you don't see any figures or formulas?

I see

ask me to
exp
the Bell inequality to them.

BUT when I copy this from the lecture notes and paste here, it comes out correctly!

ask me to explain the Bell inequality to them.

So I can paste the entire lecture to a Physics Forums reply box and read it that way. Golly. Well, whatever works, works.
 

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