A Novel Quantum-Classical Hybrid Algorithm for Determining Eigenstate Energies in Quantum Systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917787874623488 |
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| author | Xie, Qing-Xing Zhao, Yan |
| author_facet | Xie, Qing-Xing Zhao, Yan |
| contents | Developing efficient quantum computing algorithms is essential for tackling computationally challenging problems across various fields. This paper presents a novel quantum algorithm, XZ24, for efficiently computing the eigen-energy spectra of arbitrary quantum systems. Given a Hamiltonian $\hat{H}$ and an initial reference state $|ψ_{\text{ref}} \rangle$, the algorithm extracts information about $\langle ψ_{\text{ref}} | \cos(\hat{H} t) | ψ_{\text{ref}} \rangle$ from an auxiliary qubit's state. By applying a Fourier transform, the algorithm resolves the energies of eigenstates of the Hamiltonian with significant overlap with the reference wavefunction.
We provide a theoretical analysis and numerical simulations, showing XZ24's superior efficiency and accuracy compared to existing algorithms. XZ24 has three key advantages:
1. It removes the need for eigenstate preparation, requiring only a reference state with non-negligible overlap, improving upon methods like the Variational Quantum Eigensolver. 2. It reduces measurement overhead, measuring only one auxiliary qubit. For a system of size $L$ with precision $ε$, the sampling complexity scales as $O(L \cdot ε^{-1})$. When relative precision $ε$ is sufficient, the complexity scales as $O(ε^{-1})$, making measurements independent of system size. 3. It enables simultaneous computation of multiple eigen-energies, depending on the reference state.
We anticipate that XZ24 will advance quantum system simulations and enhance applications in quantum computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Novel Quantum-Classical Hybrid Algorithm for Determining Eigenstate Energies in Quantum Systems Xie, Qing-Xing Zhao, Yan Quantum Physics Computational Physics Developing efficient quantum computing algorithms is essential for tackling computationally challenging problems across various fields. This paper presents a novel quantum algorithm, XZ24, for efficiently computing the eigen-energy spectra of arbitrary quantum systems. Given a Hamiltonian $\hat{H}$ and an initial reference state $|ψ_{\text{ref}} \rangle$, the algorithm extracts information about $\langle ψ_{\text{ref}} | \cos(\hat{H} t) | ψ_{\text{ref}} \rangle$ from an auxiliary qubit's state. By applying a Fourier transform, the algorithm resolves the energies of eigenstates of the Hamiltonian with significant overlap with the reference wavefunction. We provide a theoretical analysis and numerical simulations, showing XZ24's superior efficiency and accuracy compared to existing algorithms. XZ24 has three key advantages: 1. It removes the need for eigenstate preparation, requiring only a reference state with non-negligible overlap, improving upon methods like the Variational Quantum Eigensolver. 2. It reduces measurement overhead, measuring only one auxiliary qubit. For a system of size $L$ with precision $ε$, the sampling complexity scales as $O(L \cdot ε^{-1})$. When relative precision $ε$ is sufficient, the complexity scales as $O(ε^{-1})$, making measurements independent of system size. 3. It enables simultaneous computation of multiple eigen-energies, depending on the reference state. We anticipate that XZ24 will advance quantum system simulations and enhance applications in quantum computing. |
| title | A Novel Quantum-Classical Hybrid Algorithm for Determining Eigenstate Energies in Quantum Systems |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2406.00296 |