Efficient Large-Scale Quantum Optimization via Counterdiabatic Ansatz
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909627758673920 |
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| author | Liu, Jie Wang, Xin |
| author_facet | Liu, Jie Wang, Xin |
| contents | Quantum Approximate Optimization Algorithm (QAOA) is one of the fundamental variational quantum algorithms, while a version of QAOA that includes counterdiabatic driving, termed Digitized Counterdiabatic QAOA (DC-QAOA), is generally considered to outperform QAOA for all system sizes when the circuit depth for the two algorithms are held equal. Nevertheless, DC-QAOA introduces more CNOT gates per layer, so the overall circuit complexity is a tradeoff between the number of CNOT gates per layer and the circuit depth and must be carefully assessed. In this paper, we conduct a comprehensive comparison of DC-QAOA and QAOA on MaxCut problem with the total number of CNOT gates held equal, and we focus on one implementation of counterdiabatic terms using nested commutators in DC-QAOA, termed as DC-QAOA(NC). We have found that DC-QAOA(NC) reduces the overall circuit complexity as compared to QAOA only for sufficiently large problems, and for MaxCut problem the number of qubits must exceed 16 for DC-QAOA(NC) to outperform QAOA. Additionally, we benchmark DC-QAOA(NC) against QAOA on the Sherrington-Kirkpatrick model under realistic noise conditions, finding that DC-QAOA(NC) exhibits significantly improved robustness compared to QAOA, maintaining higher fidelity as the problem size scales. Notably, in a direct comparison between one-layer DC-QAOA(NC) and three-layer QAOA where both use the same number of CNOT gates, we identify an exponential performance advantage for DC-QAOA(NC), further signifying its suitability for large-scale quantum optimization tasks. Moreover, based on our finding, we have devised an instance-sequential training method for DC-QAOA(NC) circuits, which, compared to traditional methods, offers performance improvement while using even fewer quantum resources. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Large-Scale Quantum Optimization via Counterdiabatic Ansatz Liu, Jie Wang, Xin Quantum Physics Quantum Approximate Optimization Algorithm (QAOA) is one of the fundamental variational quantum algorithms, while a version of QAOA that includes counterdiabatic driving, termed Digitized Counterdiabatic QAOA (DC-QAOA), is generally considered to outperform QAOA for all system sizes when the circuit depth for the two algorithms are held equal. Nevertheless, DC-QAOA introduces more CNOT gates per layer, so the overall circuit complexity is a tradeoff between the number of CNOT gates per layer and the circuit depth and must be carefully assessed. In this paper, we conduct a comprehensive comparison of DC-QAOA and QAOA on MaxCut problem with the total number of CNOT gates held equal, and we focus on one implementation of counterdiabatic terms using nested commutators in DC-QAOA, termed as DC-QAOA(NC). We have found that DC-QAOA(NC) reduces the overall circuit complexity as compared to QAOA only for sufficiently large problems, and for MaxCut problem the number of qubits must exceed 16 for DC-QAOA(NC) to outperform QAOA. Additionally, we benchmark DC-QAOA(NC) against QAOA on the Sherrington-Kirkpatrick model under realistic noise conditions, finding that DC-QAOA(NC) exhibits significantly improved robustness compared to QAOA, maintaining higher fidelity as the problem size scales. Notably, in a direct comparison between one-layer DC-QAOA(NC) and three-layer QAOA where both use the same number of CNOT gates, we identify an exponential performance advantage for DC-QAOA(NC), further signifying its suitability for large-scale quantum optimization tasks. Moreover, based on our finding, we have devised an instance-sequential training method for DC-QAOA(NC) circuits, which, compared to traditional methods, offers performance improvement while using even fewer quantum resources. |
| title | Efficient Large-Scale Quantum Optimization via Counterdiabatic Ansatz |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2409.15055 |