Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits

TL;DR

This paper introduces an enhanced variational quantum algorithm embedding 1-layer QAOA into Instantaneous Quantum Polynomial circuits, improving ground state overlap and performance on quantum hardware for combinatorial optimization.

Contribution

It presents a novel embedding of 1-layer QAOA into IQP circuits with analytic parameter optimization, reducing barren plateaus and noise effects, and demonstrates superior performance on hardware.

Findings

Overlap with ground state scales as O(2^{-0.31 N}) for up to 29 qubits.

Achieved an average approximation ratio of 0.985 on SK problems.

Almost 44% of instances solved optimally with limited shots.

Abstract

We embed 1-layer QAOA circuits into the larger class of parameterized Instantaneous Quantum Polynomial circuits to produce an improved variational quantum algorithm for solving combinatorial optimization problems. The use of analytic expressions to find optimal parameters classically makes our protocol robust against barren plateaus and hardware noise. The average overlap with the ground state scales as $\mathcal{O}(2^{-0.31 N})$ with the number of qubits $N$ for random Sherrington-Kirkpatrick (SK) Hamiltonians of up to 29 qubits, a polynomial improvement over 1-layer QAOA. Additionally, we observe that performing variational imaginary time evolution on the manifold approximates low-temperature pseudo-Boltzmann states. Our protocol outperforms 1-layer QAOA on the recently released Quantinuum H2 trapped-ion quantum hardware and emulator, where we obtain an average approximation ratio of $0.985$ across 312 random SK instances of 7 to 32 qubits, from which almost $44\%$ are solved optimally using 4 to 1208 shots per instance.