Simulating quantum field theories on gate-based quantum computers
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 trade-offs 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 like cross-sections for various processes,
survival probabilities of various states, etc. 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.
Gayathree M. Vinod Anil Shaji