Simulation of free fermion transport on 2D lattice using constant-depth quantum circuits

In these simulations, we consider a fermion initialized on a reference lattice site, and observe how it evolves freely through a two-dimensional (2D) lattice.  The lattice comprises 16 sites with closed boundary conditions, and lattice site '0' is considered our reference site, where the fermion is initialized. We examine transport of a fermion on this 16-site lattice both with and without disorder.  To do this, we track the occupation number at varying distances $M$ from the reference site as the fermion evolves freely through time.  When there is no disorder in the system, we expect the fermion to behave ballistically and oscillate back and forth within the lattice. The file '4x4_2DFF_mu=0.0_nsteps=900_t=90.0_backend=ibm_washington_shot=50000_nis_ps_DD_M3.txt' has the results from simulating a free fermion on a 2D lattice with no disorder on the ibmq_washington QPU, while '4x4_2DFF_mu=0.0_nsteps=900_t=90.0_backend=qasm_sim_shot=100000_nis.txt' has the results from the noise-free quantum simulator. 

When there is large random disorder in the system, we expect the fermion to exhibit Anderson localization. '4x4_2DFF_mu=10.0_nsteps=900_t=90.0_backend=ibm_washington_shot=50000_nis_ps_DD_M3_Anderson_loc.txt'  shows results from simulating a free fermion on a 2D lattice with large random disorder on the ibmq\_washington QPU,  while '4x4_2DFF_mu=10.0_nsteps=900_t=90.0_backend=qasm_sim_shot=100000_nis.txt' shows results from the noise-free quantum simulator.  

Simulations on the the noise-free quantum simulator were performed with 100,000 shots.  Simulations on the QPU were performed with 50,000 shots and any shot that did not conserve particle number was discarded.  Two straightforward error mitigation techniques were also used to reduce noise in the results from the QPU.  The first was a scalable readout error mitigation method implemented with the mthree package, which reduces errors in quantum measurement via calibration.  The second was dynamical decoupling, a method that can suppress qubit decoherence via the application of a set of pulses (which together amount to application of the identity operator) to idling qubits which cancels the system-environment interaction.