Relation between quantum computer and quantum field theory?

In summary, the conversation discusses the relationship between quantum computing and quantum field theory. Quantum field theory is a more comprehensive version of quantum mechanics and is often used in practical implementations of quantum computing. While quantum mechanics is a subset of quantum field theory, it may not always be enough to accurately describe more complex systems. This is why quantum computing may require a more complicated theory such as quantum field theory to maintain quantum coherence.
  • #1
erkant
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I'm a computer science and engineering student, who has recently developed interest about quantum computers. I can understand that quantum computers are totally linked with quantum mechanics. But I would like to learn whether there is any relation between quantum computing and quantum field theory? If someone can highlight me the differences between quantum mechanics and quantum field theory, and the possible relations of it with quantum computing, I would be glad.
 
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  • #2
Quantum field theory is a relativistic generalization of quantum mechanics. I.e. it incorporates both quantum and relativistic effects.

Quantum computing in principle could be done in plain QM. However, all practical implementations of quantum computing I have seen used the mathematics of QFT. I.e. the braid groups.

Quantum mechanics is a subset of quantum field theory, in a sense. It explains only a limited number od phenomena. If you find a way to do quantum computing on a system that can be described by QM, it would suffice. However, most systems are not that simple.

In the real world, maintaining quantum coherence is tricky, so we can expect that the system that keeps the coherence for the long time enough will need a rather complicated theory to be described. QM may not be enough in this case.
 
  • #3
Thank you very much haael for a great explanation.
 
Question 1: How does quantum field theory relate to quantum computing?

Quantum field theory is a theoretical framework used to describe the behavior of particles at the quantum level. Quantum computing, on the other hand, is a technology that utilizes the principles of quantum mechanics to perform computations. While both involve quantum mechanics, quantum field theory focuses on the behavior of particles in a field, whereas quantum computing deals with manipulating and processing information using quantum bits (qubits).

Question 2: Can quantum computers be used to simulate quantum field theories?

Yes, quantum computers have the potential to simulate certain aspects of quantum field theories. This is because quantum computers are better equipped to handle the complex calculations involved in simulating quantum systems. However, the current capabilities of quantum computers are limited and not yet able to fully simulate all aspects of quantum field theories.

Question 3: What role does entanglement play in the relation between quantum computers and quantum field theory?

Entanglement is a fundamental property of quantum mechanics that allows particles to be connected and share information even when separated by large distances. In the context of quantum computing and quantum field theory, entanglement plays a crucial role in the quantum algorithms used to simulate and analyze quantum field theories. It allows for the efficient processing and manipulation of large amounts of quantum information.

Question 4: Are there any real-world applications of the relation between quantum computers and quantum field theory?

Yes, there are potential applications of quantum computing and quantum field theory in various fields such as physics, chemistry, and machine learning. For example, quantum computers could potentially be used to simulate and study the behavior of complex materials and molecules, leading to advancements in drug development and materials science.

Question 5: Are there any challenges in combining quantum field theory and quantum computing?

Yes, there are several challenges in combining quantum field theory and quantum computing. One major challenge is the limited capabilities of current quantum computers, which are not yet powerful enough to fully simulate quantum field theories. Another challenge is the difficulty in translating the mathematical formalism of quantum field theory into a form that can be processed by quantum computers. Additionally, there are still many unanswered questions and debates surrounding the precise relationship between quantum field theory and quantum computing.

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