Computational Supremacy of Quantum Eigensolver by Extension of Optimized Binary Configurations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913378910339072 |
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| author | Park, Hayun Lee, Hunpyo |
| author_facet | Park, Hayun Lee, Hunpyo |
| contents | We developed a quantum eigensolver (QE) which is based on an extension of optimized binary configurations measured by quantum annealing (QA) on a D-Wave Quantum Annealer (D-Wave QA). This approach performs iterative QA measurements to optimize the eigenstates $\vert ψ\rangle$ without the derivation of a classical computer. The computational cost is $ηM L$ for full eigenvalues $E$ and $\vert ψ\rangle$ of the Hamiltonian $\hat{H}$ of size $L \times L$, where $M$ and $η$ are the number of QA measurements required to reach the converged $\vert ψ\rangle$ and the total annealing time of many QA shots, respectively. Unlike the exact diagonalized (ED) algorithm with $L^3$ iterations on a classical computer, the computation cost is not significantly affected by $L$ and $M$ because $η$ represents a very short time within $10^{-2}$ seconds on the D-Wave QA. We selected the tight-binding $\hat{H}$ that contains the exact $E$ values of all energy states in two systems with metallic and insulating phases. We confirmed that the proposed QE algorithm provides exact solutions within the errors of $5 \times 10^{-3}$. The QE algorithm will not only show computational supremacy over the ED approach on a classical computer but will also be widely used for various applications such as material and drug design. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_03366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computational Supremacy of Quantum Eigensolver by Extension of Optimized Binary Configurations Park, Hayun Lee, Hunpyo Quantum Physics Materials Science Strongly Correlated Electrons Computational Physics We developed a quantum eigensolver (QE) which is based on an extension of optimized binary configurations measured by quantum annealing (QA) on a D-Wave Quantum Annealer (D-Wave QA). This approach performs iterative QA measurements to optimize the eigenstates $\vert ψ\rangle$ without the derivation of a classical computer. The computational cost is $ηM L$ for full eigenvalues $E$ and $\vert ψ\rangle$ of the Hamiltonian $\hat{H}$ of size $L \times L$, where $M$ and $η$ are the number of QA measurements required to reach the converged $\vert ψ\rangle$ and the total annealing time of many QA shots, respectively. Unlike the exact diagonalized (ED) algorithm with $L^3$ iterations on a classical computer, the computation cost is not significantly affected by $L$ and $M$ because $η$ represents a very short time within $10^{-2}$ seconds on the D-Wave QA. We selected the tight-binding $\hat{H}$ that contains the exact $E$ values of all energy states in two systems with metallic and insulating phases. We confirmed that the proposed QE algorithm provides exact solutions within the errors of $5 \times 10^{-3}$. The QE algorithm will not only show computational supremacy over the ED approach on a classical computer but will also be widely used for various applications such as material and drug design. |
| title | Computational Supremacy of Quantum Eigensolver by Extension of Optimized Binary Configurations |
| topic | Quantum Physics Materials Science Strongly Correlated Electrons Computational Physics |
| url | https://arxiv.org/abs/2406.03366 |