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Quantum Simulation of Quantum Field Theory

Bibak, Fatemeh | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51741 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid; Raeisi, Sadegh
  7. Abstract:
  8. Physics underlies computer science because computation is a physical process. The fundamental question about computers is: What computations can be performed efficiently, and what computations are intractable? This is a question about the laws of physics and the consequences of those laws.Though we don’t know how to prove it from first principles,we have good reasons to believe that there are computational problems which are too hard to solve using digital computers based on classical physics, yet can be solved by computers which exploit quantum phenomena such as interference and entanglement. This is one of deepest distinctions ever made between classical and quantum physics, and it poses the compelling challenge to identify those problems which are classically hard but quantumly easy. Quantum field theory is one of the fundamental frameworks in fundamental physics, which there are still open questions about this theory. So it’s interesting to answer the question of whether quantum computers are capable of simulating the quantum field theory. Because if quantum field theory can be simulated by means of quantum computers, then we can answer the deep questions in this theory. If it cannot be simulated, this means that we still have not fully utilized the computational ability of nature. In this thesis, we first review the quantum simulation by comparing this simulation with classical simulations. Then, we study the quantum field theory in particular the ϕ4 theory and show how difficult it is to simulate this theory with existing classical computers. Finally, we study the quantum algorithm to simulate the ϕ4 theory, and show by using quantum computers, we can simulate quantum field theory with both weak and strong interactions optimally
  9. Keywords:
  10. Quantum Simulation ; Quantum Field Theory ; Scattering Amplitude ; Digital Quantum Simulation

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