  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.

Quantum Physics