Snapshot-QAOA: Extending QAOA to Quantum Hamiltonian Simulation
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910053171200000 |
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| author | Tate, Reuben Langfitt, Quinn Pelofske, Elijah Kirmani, Ammar Bärtschi, Andreas Golden, John Eidenbenz, Stephan |
| author_facet | Tate, Reuben Langfitt, Quinn Pelofske, Elijah Kirmani, Ammar Bärtschi, Andreas Golden, John Eidenbenz, Stephan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17990 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Snapshot-QAOA: Extending QAOA to Quantum Hamiltonian Simulation Tate, Reuben Langfitt, Quinn Pelofske, Elijah Kirmani, Ammar Bärtschi, Andreas Golden, John Eidenbenz, Stephan Quantum Physics 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. |
| title | Snapshot-QAOA: Extending QAOA to Quantum Hamiltonian Simulation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.17990 |