Simulating Strongly Coupled Quantum Field Theory with Quantum Algorithms

Quantum field theory (QFT) is an over-arching theoretical framework that combines classical field theory, special relativity, and quantum mechanics under the same umbrella. While weakly coupled QFT problems have been solved and understood with current methods and techniques, strongly coupled QFTs remain elusive. Such problems can be tackled using numerical computation techniques. One such technique is “quantum simulation.”

Unfortunately, numerical techniques developed to tackle problems have had limited success with classical algorithms. Such methods are either non-efficient, lack accuracy, or are too specific and cannot be generalized to other problems. Interestingly, quantum computing algorithms have remained largely unexplored, partly because quantum simulations are usually performed using the Hamiltonian formalism. Moreover, techniques for applying quantum simulation using quantum computers are yet to be developed.

In this work, the charge-q Schwinger model on the open boundary condition was studied in the Hamiltonian formalism instead of the more commonly used path-integral formalism. The Hilbert space in the model is known to be decomposed into distinct sectors, called “universes.” The developed method was based on the so-called “adiabatic state preparation,” allowing the problem to be solved with a digital quantum simulation.

The model revealed that a repulsive force acts between particles with opposite charges, contrary to the traditional classical attraction, in particular circumstances. This observation was confirmed using a classical simulator of quantum devices. Predicting this phenomenon with a quantum computing algorithm, thus, demonstrated their potentially superior capability in handling strongly coupled QFT problems.

Quantum computing methods like these can be used to gain deeper insights into more complex QFT problems, such as the time evolution of the early universe. Such problems have long intrigued scientists but have remained intractable owing to the lack of adequate solving techniques.

The findings of this study open doors to further development and applications of quantum computing algorithms in QFT. This could lead to answers to long-awaited questions in QFT, broadening our understanding of the universe.