Variational Simulation of Schwinger's Hamiltonian with Polarisation Qubits

The numerical emulation of quantum physics and quantum chemistry often involves an intractable number of degrees of freedom and admits no known approximation in general form. In practice, representing quantum-mechanical states using available numerical methods becomes exponentially more challenging with increasing system size. Recently quantum algorithms implemented as variational models, have been proposed to accelerate such simulations. Here we study the effect of noise on the quantum phase transition in the Schwinger model, within a variational framework. The experiments are built using a free space optical scheme to realize a pair of polarization qubits and enable any two-qubit state to be experimentally prepared up to machine tolerance. We specifically exploit the possibility to engineer noise and decoherence for polarization qubits to explore the limits of variational algorithms for NISQ architectures in identifying and quantifying quantum phase transitions with noisy qubits. We find that despite the presence of noise one can detect the phase transition of the Schwinger Hamiltonian even for a two-qubit system using variational quantum algorithms.