Quantum Computing: Entangled Qubits & Hilbert Space

In summary, quantum computing is a type of computing that uses quantum-mechanical phenomena to perform operations on data. It utilizes qubits, which are quantum bits, to represent and process information. Entanglement is a key feature of quantum computing, where qubits are connected and share information, allowing for faster processing and increased computational power. Qubits can exist in multiple states simultaneously and are typically represented by physical systems such as atoms or photons. Hilbert space is a mathematical concept used to represent the possible states of qubits, with its size exponentially increasing as more qubits are added. Quantum computing has the potential to impact various fields such as cryptography, drug discovery, and artificial intelligence, by solving complex problems that are currently intractable for
  • #1
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I'm writing a paper on quantum computing.

First question:

Do entangled qubits, or generally, entangled particles occupy the same Hilbert space?

Thanks.
 
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  • #2
why not? Bell states are still states right?
 

1. What is quantum computing?

Quantum computing is a type of computing that uses quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. It is different from classical computing, which uses binary bits to represent and process data. Quantum computers use qubits, which are quantum bits, to represent and process data.

2. What is entanglement in quantum computing?

Entanglement is a phenomenon where two or more qubits are connected in such a way that the state of one qubit cannot be described without taking into account the state of the other qubits. This means that the qubits are correlated and share information, even if they are physically separated. Entanglement is a key feature of quantum computing and allows for faster processing and increased computational power.

3. What are qubits and how do they work?

Qubits are the basic unit of quantum information. Unlike classical bits, which can only have a value of 0 or 1, qubits can exist in multiple states simultaneously. This is known as superposition. Qubits can also become entangled with other qubits, allowing for complex calculations to be performed simultaneously. Qubits are typically represented by physical systems such as atoms, ions, or photons.

4. What is Hilbert space in quantum computing?

Hilbert space is a mathematical concept that describes the state of a quantum system. In quantum computing, Hilbert space is used to represent the possible states of qubits. The number of dimensions in Hilbert space corresponds to the number of qubits in a quantum system. As more qubits are added, the size of Hilbert space exponentially increases, allowing for more complex calculations to be performed.

5. What are the potential applications of quantum computing?

Quantum computing has the potential to greatly impact various fields such as cryptography, drug discovery, artificial intelligence, and financial modeling. It has the ability to solve complex problems that are currently intractable for classical computers. Some potential applications include faster and more accurate simulation of chemical reactions, breaking current encryption methods, and optimizing supply chain management.

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