# Extraction of a particular quantum state from a quantum circuit

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• ubergewehr273
In summary, the conversation revolves around implementing a quantum circuit that yields a superposition state of |01> + |10>, using parameterized gates. The initial state is |01> + e^(i*phi)|10>, and the goal is to further process it to achieve the desired state with phi = 0. The solution involves using a beam splitter and a phase shifter, and a reference circuit has already been proposed. The question is whether there are other ways to implement this circuit using parameterized gates, and where the phase phi comes from. A paper is mentioned that describes a setup for transforming the bipartite state into four Bell states.
ubergewehr273
TL;DR Summary
Created state ##\frac{1}{\sqrt{2}}(|01\rangle + e^{i\phi} |10 \rangle)## using a quantum circuit. I wish to further process this state to achieve ##\frac{1}{\sqrt{2}} (|01 \rangle + |10 \rangle)## in particular.
Hello everyone!

I'm trying to implement a quantum circuit that yields a superposition state $$\frac{1}{\sqrt{2}} (|01 \rangle + |10 \rangle)$$ I'm using parameterized gates to achieve this. I have been able to create the state $$\frac{1}{\sqrt{2}}(|01\rangle + e^{i\phi} |10 \rangle)$$ Is there a way to further process this state to achieve $$\frac{1}{\sqrt{2}} (|01 \rangle + |10 \rangle)$$ in particular?

Thanks!

This should be possible with a beam splitter and a phase shifter in one branch.

Thanks but I'm asking if some circuit components can be added somehow to process the former state to be the final state in question.

ubergewehr273 said:
Thanks but I'm asking if some circuit components can be added somehow to process the former state to be the final state in question.
How do you build your state? where is phi coming from?

This is my reference circuit. This clearly produces the state ##\frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)##. This is obviously until the measurement is done.

However, I'm trying to implement a circuit which essentially gives me a 50-50 chance of getting either ##|01\rangle## or ##|10\rangle##. And with this condition in mind, I am able to produce the state ##\frac{1}{\sqrt{2}}(|01\rangle + e^{i\phi}|10\rangle)## with some arbitrary ##\phi##. What I want to know if some further processing quantum gates can be done to produce the particular state with ##\phi = 0## $$\frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)$$

Seems like a questions for @Strilanc ...

That said, I am still a bit confused about the question. The circuit you show already solves this problem; are you trying to come up with another implementation using parameterized gates?
Also, what is phi? It is obviously a phase, but where does it come from?

vanhees71
f95toli said:
Seems like a questions for @Strilanc ...

That said, I am still a bit confused about the question. The circuit you show already solves this problem; are you trying to come up with another implementation using parameterized gates?
Also, what is phi? It is obviously a phase, but where does it come from?
Such a device would transform 01-10 into 01+10 (a bell state into another one)

vanhees71

## 1. What is the purpose of extracting a particular quantum state from a quantum circuit?

The extraction of a particular quantum state from a quantum circuit allows for the measurement and observation of a specific state within the circuit. This can provide valuable information about the behavior and properties of the circuit, and can also be used for various applications in quantum computing and quantum information processing.

## 2. How is a particular quantum state extracted from a quantum circuit?

The extraction process typically involves applying a measurement operation to the desired qubit or qubits within the circuit. This measurement collapses the quantum state into one of its possible classical states, which can then be observed and analyzed.

## 3. Can a particular quantum state be extracted without affecting the rest of the circuit?

In most cases, the extraction of a particular quantum state will cause some degree of disturbance to the rest of the circuit. However, there are techniques such as quantum error correction that can help mitigate these effects and minimize the impact on the overall performance of the circuit.

## 4. What are some real-world applications of extracting a particular quantum state?

One potential application is in quantum cryptography, where the extraction of a particular state can be used to generate secure encryption keys. It can also be used in quantum simulations to study complex systems, and in quantum algorithms for tasks such as database searching and optimization.

## 5. Are there any challenges or limitations to extracting a particular quantum state from a quantum circuit?

One challenge is the fragility of quantum states, which can be easily disturbed or destroyed by external factors. Additionally, the extraction process can be time-consuming and resource-intensive, which can limit its practicality in certain applications.

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