CNOT Gate: What is it & How Does it Work?

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Discussion Overview

The discussion centers around the CNOT gate, a fundamental component in quantum information theory, exploring its function, truth table, and relationship to other gates like the XOR gate. Participants also touch upon the broader context of quantum information technology and the universality of quantum gates.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants describe the CNOT gate as a reversible gate that flips the second bit if the first bit is 1, while doing nothing if the first bit is 0.
  • There is a claim that the CNOT gate is also referred to as the reversible XOR gate, although some participants express uncertainty about this equivalence.
  • One participant notes that one-bit and two-bit gates like the CNOT are non-universal and cannot compute all operations by themselves, introducing the Toffoli gate as a universal gate.
  • Another participant challenges the assertion that the CNOT gate is the same as the XOR gate, emphasizing that XOR gives a true output only if one of the inputs is true but not both.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between the CNOT gate and the XOR gate, with some asserting they are the same while others contest this claim. The discussion remains unresolved regarding the exact nature of this relationship.

Contextual Notes

There are limitations in the discussion regarding the definitions of terms like "universal gate" and the specific operations that can be performed by the CNOT gate and the Toffoli gate. Some assumptions about the nature of quantum gates and their functionalities are not fully explored.

Mk
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Yeah so, scientists in Japan have the CNOT gate, control not. What does it do? What's the truth table... other stuff. Are gates made of transistors?
 
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Could you please provide some context? I have no idea what you're talking about.

- Warren
 
http://strc.herts.ac.uk/tp/info/areas/qip/qu_gates.html

This relates to qubits and quantum information theory i suppose
 
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chroot said:
Could you please provide some context? I have no idea what you're talking about.

- Warren

Mk, is talking about Quantum-Information-Technology, chroot. The CNOT gate is one of them reversible gates, and it is also named the reversible XOR-gate. Basically the gate flips the second bit if the first is 1 and does nothing if the first bit is zero (hence the name controlled-not).

This gate performs a NOT on the second bit if the first bit is set to 1 and it performs a copy-operation if the second bit is initially set to 0.


The problem is that all these one-bit and twobit gates are non-universal, they cannot compute any operation using just the gate in question. The "first" universal gate is the three-bit Toffoli-gate or the controlled-controlled-NOT-gate.

It computes : (x,y,z) ---->(x,y,z + xy) where the sum is the sum modulo 2

This gate performs all the operations (NAND, COPY) necessary to be universal...

regards
marlon
 
marlon said:
Mk, is talking about Quantum-Information-Technology, chroot. The CNOT gate is one of them reversible gates, and it is also named the reversible XOR-gate. Basically the gate flips the second bit if the first is 1 and does nothing if the first bit is zero (hence the name controlled-not).

This gate performs a NOT on the second bit if the first bit is set to 1 and it performs a copy-operation if the second bit is initially set to 0.

The problem is that all these one-bit and twobit gates are non-universal, they cannot compute any operation using just the gate in question. The "first" universal gate is the three-bit Toffoli-gate or the controlled-controlled-NOT-gate.

This gate performs all the operations (NAND, COPY) necessary to be universal...

regards
marlon

Thanks a lot. Exactly what I needed... but I'm not sure about the CNOT is the XOR. XOR aka EOR (eyore, the donkey!), is eXclusive OR. XOR gives a true if either A and B but not both, are true.
 
The CNOT gate is just the same as the reversible XOR-gate


regards
marlon
 
Ahhh! I see. :smile:
 

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