Simulating Quantum Field Theories on Gate-Based Quantum Computers

Abstract

We implement a simulation of a quantum field theory in 1+1 space–time dimensions on a gate-based quantum computer using the light-front formulation of the theory. The nonperturbative simulation of the Yukawa model field theory is verified on IBM's simulator and is also demonstrated on a small-scale IBM circuit-based quantum processor, on the cloud, using IBM Qiskit. The light-front formulation allows for controlling the resource requirement and complexity of the computation with commensurate tradeoffs in accuracy and detail by modulating a single parameter, namely, the harmonic resolution. Qubit operators for the Bosonic excitations were also created and were used along with the Fermionic ones already available, to simulate the theory involving all of these particles. With the restriction on the number of logical qubits available on the existent gate-based noisy intermediate-scale quantum (NISQ) devices, the Trotterization approximation is also used. We show that experimentally relevant quantities, such as cross sections for various processes and survival probabilities of various states, can be computed. We also explore the inaccuracies introduced by the bounds on achievable harmonic resolution and Trotter steps placed by the limited number of qubits and circuit depth supported by present-day NISQ devices.