Quantum logic gate measurement?

In summary, quantum logic gates are unitary and do not perform measurements. Therefore, when a cNOT gate is applied to a pair of cubits with the given wavefunction, the result would be 1/\sqrt{2} |11> + 1/\sqrt{2} |00>, an entangled state. This confirms that the states are not cloned, as that would be unlikely.
  • #1
nfelddav
22
0
Do quantum logic gates perform measurements? (collapse the wavefunction)

For example:

If I apply a cNOT gate to a pair of cubits with wavefunction 1/[tex]\sqrt{2}[/tex] |10> + 1/[tex]\sqrt{2}[/tex] |00>
what would I expect as the result?

1/[tex]\sqrt{2}[/tex] |11> + 1/[tex]\sqrt{2}[/tex] |00>
?

or

1|11>
or
1|00>

or
are the states not entangled? This seems unlikely because it would be cloning...
 
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  • #2
nfelddav said:
Do quantum logic gates perform measurements? (collapse the wavefunction)

For example:

If I apply a cNOT gate to a pair of cubits with wavefunction 1/[tex]\sqrt{2}[/tex] |10> + 1/[tex]\sqrt{2}[/tex] |00>
what would I expect as the result?

1/[tex]\sqrt{2}[/tex] |11> + 1/[tex]\sqrt{2}[/tex] |00>
?

or

1|11>
or
1|00>

or
are the states not entangled? This seems unlikely because it would be cloning...

A logic gate is unitary, a measurement (when described as including the collapse) is not unitary. So, the result of the cnot is 1/[tex]\sqrt{2}[/tex] |11> + 1/[tex]\sqrt{2}[/tex] |00>. And yes, this is an entangled state.
 
  • #3
Thank you,
That's what seemed the most reasonable, but I wasn't sure.
 

1. What is a quantum logic gate measurement?

A quantum logic gate measurement is a process in which the state of a quantum system is measured using quantum logic gates. These gates are used to manipulate the quantum state of a system by performing operations like superposition, entanglement, and measurement.

2. How does a quantum logic gate measurement work?

A quantum logic gate measurement works by applying a series of quantum logic gates to a quantum system, which changes the state of the system. Then, a final measurement is taken using another quantum logic gate, which provides information about the state of the system.

3. What is the purpose of a quantum logic gate measurement?

The purpose of a quantum logic gate measurement is to accurately determine the state of a quantum system. This is important in quantum computing, as it allows for the manipulation and measurement of quantum bits (qubits), which are the building blocks of quantum computers.

4. What are some examples of quantum logic gates used in measurements?

There are several types of quantum logic gates used in measurements, including the Hadamard gate, the Pauli gates (X, Y, Z), the CNOT gate, and the Toffoli gate. These gates are used to manipulate and measure the state of qubits, and are often combined in various ways to perform more complex operations.

5. What challenges are associated with quantum logic gate measurements?

One of the main challenges of quantum logic gate measurements is maintaining the fragile quantum state of the system. Any external interference or measurement error can cause the state to collapse, leading to inaccurate measurements. Additionally, the design and implementation of quantum logic gates can also be challenging due to their complex nature and the need for precise control and manipulation of qubits.

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