Simulating quantum and classical field theories with a quantum computer

Jincheng Zhang

Quantum field theory (QFT) encompasses a vast and complex landscape of physical phenomena, making accurate simulation a significant challenge. Classical computers struggle to handle the exponential scaling of the computational cost with increasing system size, limiting the exploration of these theories. Hybrid quantum-classical simulation offers a promising path toward overcoming these limitations by intelligently leveraging the strengths of both paradigms. This research investigates a novel hybrid solver, the 'Quantum-Classical Hybrid Solver,' designed to efficiently simulate complex QFTs. We demonstrate the method's ability to surpass classical simulation capabilities in certain regimes while maintaining computational efficiency, offering a significant advancement in the field. The core mechanism centers around a dynamic switching between classical and quantum techniques, tailored to the specific problem at hand. This paper details the design, implementation, and preliminary results of the Hybrid Quantum-Classical Solver, highlighting its potential for accelerating QFT research.

Yannick Meurice

Lior Cohen, Anthony J. Brady, Zichang Huang +4 more

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as Boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is Loop Quantum Gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spinfoam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the class BQP -- which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer, which can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.

Alexander J. Buser, Tanmoy Bhattacharya A, Shailesh Chandrasekharan A +2 more

Yannick Meurice

Erik Gustafson, Stephen P. Jordan, Yannick Meurice +3 more

This thesis looks at how we can leverage current and near future quantum computers to effectively simulate quantum field theories. The scope of this thesis covers how to simulate the (1+1)-D Transverse Ising model on digital quantum computers and the methods to handle multiple types of machine errors to effectively extract real-time dynamic information. We leverage modifications to the transverse Ising model to study the calculation of phase shifts from scattering a particle off of simple potentials and demonstrate that these calculations are feasible on current quantum hardware. In looking toward the future we demonstrate two different state preparation algorithms. One algorithm projected cooling we show can extract information about the second order phase transition in the Transverse Ising Model and has excellent scaling properties. The second algorithm involves leveraging classical field theory simulations to circumvent quantum state preparation methods on that should prove tractable on near term quantum computing hardware. These tools together highlight the promise of quantum computing to tackle interesting problems in high energy physics.