Quantum optimization with Instantaneous Quantum Polynomial circuits

We exploit the ability to embed 1-layer QAOA circuits into the larger class of parameterized IQP circuits to produce an improved variational quantum algorithm for solving combinatorial optimization problems. The 1-layer QAOA was recently shown to approximate low temperature pseudo-Boltzmann states, making it a suitable warm start for exploring the parameter space. We derive analytic expressions that allow us to explore the optimization landscape and find optimal parameters classically. The protocol is robust against barren plateaus and minimizes the necessary quantum resources compared to other traditional variational methods. We show numerically that the average overlap of the final state with the ground state scales like ∼ 2 − 0 . 31 N with the number of qubits N , a polynomial improvement over 1-layer QAOA, for random Sherrington-Kickpatrick Hamiltonians of up to 29 qubits. Additionally, we show that performing variational imaginary time evolution on the manifold approximates low temperature pseudo-Boltzmann states, which may be used for sampling thermal distributions.