VQE for the Schwinger Model, with Applications to Classical Simulations

[avkhadiev]

The project builds on a variational quantum eigensolver for the Schwinger model (1803.03326), with applications for Monte-Carlo simulations in mind (1908.04194).

A couple of immediate goals:

1. Run VQE on a quantum device and estimate the ground state and the first excited state of the Schwinger model at some very small volume (2 spatial sites) and harsh truncation on values of electric field flux.
2. Test a circuit that would create an equal superposition of these variationally determined states. Hopefully it's not too noisy! It is interesting to study the noise in this circuit: what do the error rates look like for 2-qubit gates vs 1-qubit gates, and can we employ any error mitigation strategies efficiently?
3. The exact form of the variational ansatz for this system is known; however, we are told (by authors of 1803.03326) to be too noisy. We have an approximate form for the ansatz in the form of a circuit for a 2-qubit system, and would like to understand what a good variational layer looks like in the general case. Perhaps we could run VQE for this system at a slightly larger volume (4-5 qubits).
4. Since our variational form is rather simple, we could build a classical optimizer that uses an analytic form for the gradient (as opposed to a finite gradient method in SPSA), and compare their performance.