Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913781949399040 |
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| author | Kiss, Oriel Azad, Utkarsh Requena, Borja Roggero, Alessandro Wakeham, David Arrazola, Juan Miguel |
| author_facet | Kiss, Oriel Azad, Utkarsh Requena, Borja Roggero, Alessandro Wakeham, David Arrazola, Juan Miguel |
| contents | We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure of a Hamiltonian and the identification of its discontinuities. Scaling these methods to larger system sizes reveals three key challenges: the smoothness of the CDF for large supports, the lack of tight lower bounds on the overlap with the true ground state, and the difficulty of preparing high-quality initial states. To address these challenges, we propose a signal processing approach to find these estimates automatically, in the regime where the quality of the initial state is unknown. Rather than aiming for exact ground-state energy, we advocate for improving classical estimates by targeting the low-energy support of the initial state. Additionally, we provide quantitative resource estimates, demonstrating a constant-factor improvement in the number of samples required to detect a specified change in CDF. Our numerical experiments, conducted on a 26-qubit fully connected Heisenberg model, leverage a truncated density-matrix renormalization group (DMRG) initial state with a low bond dimension. The results show that the predictions from the quantum algorithm align closely with the DMRG-converged energies at larger bond dimensions while requiring several orders of magnitude fewer samples than theoretical estimates suggest. These findings underscore that CDF-based quantum algorithms are a practical and resource-efficient alternative to quantum phase estimation, particularly in resource-constrained scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03754 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation Kiss, Oriel Azad, Utkarsh Requena, Borja Roggero, Alessandro Wakeham, David Arrazola, Juan Miguel Quantum Physics We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure of a Hamiltonian and the identification of its discontinuities. Scaling these methods to larger system sizes reveals three key challenges: the smoothness of the CDF for large supports, the lack of tight lower bounds on the overlap with the true ground state, and the difficulty of preparing high-quality initial states. To address these challenges, we propose a signal processing approach to find these estimates automatically, in the regime where the quality of the initial state is unknown. Rather than aiming for exact ground-state energy, we advocate for improving classical estimates by targeting the low-energy support of the initial state. Additionally, we provide quantitative resource estimates, demonstrating a constant-factor improvement in the number of samples required to detect a specified change in CDF. Our numerical experiments, conducted on a 26-qubit fully connected Heisenberg model, leverage a truncated density-matrix renormalization group (DMRG) initial state with a low bond dimension. The results show that the predictions from the quantum algorithm align closely with the DMRG-converged energies at larger bond dimensions while requiring several orders of magnitude fewer samples than theoretical estimates suggest. These findings underscore that CDF-based quantum algorithms are a practical and resource-efficient alternative to quantum phase estimation, particularly in resource-constrained scenarios. |
| title | Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.03754 |