The cnot with outer product control qubit

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Thread starter Galaxion
Start date Dec 29, 2019
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Control Outer product Product Qubit

In summary, a cnot with outer product control qubit is a specific type of quantum gate that uses the outer product of two qubits as the control qubit. This allows for more flexibility and precision in quantum operations. It works by applying a controlled not operation to two qubits, where the control qubit is the outer product of two qubits. It has advantages such as allowing for more precise and flexible quantum operations and potentially reducing the number of physical qubits needed. However, it may also have limitations such as requiring additional qubits and operations and being unsuitable for certain types of computations. It is different from other types of controlled not gates in that it uses the outer product of qubits as the control qubit and may require

Dec 29, 2019

Galaxion

I have a simple question...the control qubit is A and the the target is B.
The cnot is applied on |1_A> <0_A|⊗|0_B0_C>.
...
How does it work.
Thanks in advance.

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Jan 3, 2020

jedishrfu

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Insights Author

First here's wikipedia's discussion on it:

https://en.wikipedia.org/wiki/Controlled_NOT_gate

and further on medium:

and here's how a QC works:

1. What is the cnot gate with outer product control qubit?

The cnot gate with outer product control qubit is a quantum gate used in quantum computing. It is a controlled NOT gate, meaning that it performs a NOT operation on the target qubit (the one being controlled) if and only if the control qubit (the one controlling the operation) is in the state |1>. The outer product control qubit refers to the fact that the control qubit is in a superposition of states, allowing for more complex operations to be performed.

2. How does the cnot gate with outer product control qubit work?

The cnot gate with outer product control qubit works by applying a NOT operation (flipping the state from |0> to |1> or vice versa) on the target qubit if and only if the control qubit is in the state |1>. If the control qubit is in the state |0>, then the target qubit remains unchanged. This gate is represented by the matrix [1 0 0 0; 0 1 0 0; 0 0 0 1; 0 0 1 0], where the first two entries represent the states of the control qubit and the last two represent the states of the target qubit.

3. What is the significance of the cnot gate with outer product control qubit in quantum computing?

The cnot gate with outer product control qubit is significant in quantum computing because it is a fundamental gate that is used in many quantum algorithms and circuits. It allows for the manipulation of multiple qubits at once, which is necessary for performing more complex operations and achieving quantum speedup in certain tasks.

4. How is the cnot gate with outer product control qubit different from a regular cnot gate?

The cnot gate with outer product control qubit differs from a regular cnot gate in that the control qubit is in a superposition of states, rather than being in a single state. This allows for more flexibility and complexity in the operations that can be performed. Additionally, the matrix representation of the gate is different, with the outer product control qubit gate having a 1 in the bottom right corner instead of the top left corner.

5. What are some potential applications of the cnot gate with outer product control qubit?

The cnot gate with outer product control qubit has many potential applications in quantum computing, such as in quantum error correction, quantum teleportation, and quantum algorithms for tasks such as factoring large numbers and searching large databases. It is also a key component in building larger quantum circuits and systems.