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arXiv · 2412.17990

Snapshot-QAOA: Extending QAOA to Quantum Hamiltonian Simulation

Reuben Tate·Quinn Langfitt·Elijah Pelofske·Ammar Kirmani·Andreas Bärtschi·John Golden·Stephan Eidenbenz
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Abstract

We present Snapshot-QAOA, a variation of the Quantum Approximate Optimization Algorithm (QAOA) that finds approximate minimum energy eigenstates of a large set of quantum Hamiltonians (i.e. Hamiltonians with non-diagonal terms). Traditionally, QAOA targets the task of approximately solving combinatorial optimization problems; Snapshot-QAOA enables a significant expansion of the use case space for QAOA to more general quantum Hamiltonians, where the goal is to approximate the ground-state. Such ground-state finding is a common challenge in quantum chemistry and material science applications. Snapshot-QAOA retains desirable variational-algorithm qualities of QAOA, in particular small parameter count and relatively shallow circuit depth. Snapshot-QAOA is thus a better trainable alternative to the NISQ-era Variational Quantum Eigensolver (VQE) algorithm, while retaining a significant circuit-depth advantage over the QEC-era Quantum Phase Estimation (QPE) algorithm. Our fundamental approach is inspired by the idea of Trotterization of a continuous-time linear adiabatic anneal schedule, which for sufficiently large QAOA depth gives very good performance. Snapshot-QAOA restricts the QAOA evolution to not phasing out the mixing Hamiltonian completely at the end of the evolution, instead evolving only a partial typical linear QAOA schedule, thus creating a type of snapshot of the typical QAOA evolution. As a test case, we simulate Snapshot-QAOA on a 16 qubit J1-J2 frustrated square transverse field Ising model with periodic boundary conditions.

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Reuben Tate, Quinn Langfitt, Elijah Pelofske, Ammar Kirmani, Andreas Bärtschi, John Golden, Stephan Eidenbenz. 2024-12-23. Snapshot-QAOA: Extending QAOA to Quantum Hamiltonian Simulation. https://arxiv.org/abs/2412.17990

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