Circuit to Create and Entangled State

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SUMMARY

The discussion focuses on constructing the entangled quantum state \(\frac{1}{\sqrt{3}} \left( |00\rangle + |01\rangle + |11\rangle \right)\) using quantum circuits. The user attempts to utilize the Bell EPR circuit but encounters limitations due to its capacity to handle only two qubits. The challenge arises from the need for three components in the superposition, which the Bell circuit cannot accommodate. The conversation highlights the necessity of exploring alternative quantum circuit designs to achieve the desired entangled state.

PREREQUISITES
  • Understanding of quantum states and superposition
  • Familiarity with the Bell EPR circuit
  • Knowledge of qubit entanglement principles
  • Basic concepts of quantum circuit design
NEXT STEPS
  • Research multi-qubit quantum circuits for entangled state generation
  • Learn about the Quantum Fourier Transform and its applications
  • Explore the use of Grover's algorithm for state preparation
  • Investigate the capabilities of the IBM Qiskit framework for quantum programming
USEFUL FOR

Quantum computing enthusiasts, researchers in quantum information science, and students studying quantum mechanics who seek to understand entangled state construction and circuit design.

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Homework Statement


In a quantum information setting:

I'm trying to find a circuit to construct the state

[tex]\frac1{\sqrt3} \left( |00\rangle + |01\rangle + |11 \rangle \right)[/tex]

The Attempt at a Solution


This state is entangled, and so I've been playing with different input states to try and create this using the Bell EPR circuit. This hasn't worked so far, so if anyone has a better idea it would be much appreciated.
 
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Now I don't know much about quantum computing, but if you have three terms in the state, don't you need three components to build that state? And doesn't the Bell circuit only have two components?
 
The problem for me lies precisely in the fact that there's three components in the super-position. If the Bell circuit took three inputs though, we would have a superposition on three qubits rather than just two. Also, the Bell-circuit seemingly will only entangle for two components, since it's possible to create a four-component state but I don't think it's entangled.
 

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