Abstract
Although quantum computation is regarded as a promising numerical method for computational quantum chemistry, current applications of quantum-chemistry calculations on quantum computers are limited to small molecules. This limitation can be ascribed to technical problems in building and manipulating more quantum bits (qubits) and the associated complicated operations of quantum gates in a quantum circuit when the size of the molecular system becomes large. As a result, reducing the number of required qubits is necessary to make quantum computation practical. Currently, the minimal STO-3G basis set is commonly used in benchmark studies because it requires the minimum number of spin orbitals. Nonetheless, the accuracy of using STO-3G is generally low and thus can not provide useful predictions. Herein, we propose to adopt Daubechies wavelet functions as an accurate and efficient method for quantum computations of molecular electronic properties. We demonstrate that a minimal basis set constructed from Daubechies wavelet basis can yield accurate results through a better description of the molecular Hamiltonian, while keeping the number of spin orbitals minimal. With the improved Hamiltonian through Daubechies wavelets, we calculate vibrational frequencies for and using quantum-computing algorithm to show that the results are in excellent agreement with experimental data. As a result, we achieve quantum calculations in which accuracy is comparable with that of the full configuration interaction calculation using the cc-pVDZ basis set, whereas the computational cost is the same as that of a STO-3G calculation. Thus, our work provides a more efficient and accurate representation of the molecular Hamiltonian for efficient quantum computations of molecular systems, and for the first time demonstrates that predictions in agreement with experimental measurements are possible to be achieved with quantum resources available in near-term quantum computers.
- Received 27 December 2021
- Accepted 13 May 2022
DOI:https://doi.org/10.1103/PRXQuantum.3.020360
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum chemistry calculation is consideredone of the most compelling application for quantum computing. However, this is technically limited to only small molecules due to the limitations on the number of qubits and the depth and complexity of computational circuits available in nowadays quantum computers. Consequently, reducing the number of required qubits is necessary to make the quantum computation of molecular systems practical. Currently, the minimal contracted Gaussian basis set is commonly used in benchmark studies because it requires the minimum number of spin orbitals and thus the minimal number of qubits; nonetheless, the accuracy is generally low and thus cannot provide useful predictions.
We demonstrate that a minimal basis set constructed from Daubechies wavelet functions for quantum computing can yield accurate results for H2 and LiH in excellent agreement with experimental data. This is an unprecedented demonstration of quantum computation with accuracy comparable with that of the full configuration interaction (FCI) method using a large basis set, whereas the computational cost is merely the same as that of a minimal basis set calculation. We also perform numerical experiments on a quantum simulator with a noise model implemented from a real quantum machine. We demonstrate that most of the error-mitigated data agree well with the exact FCI results within chemical accuracy. Thus, our work provides an efficient and accurate scheme for quantum computations of molecular systems, and for the first time demonstrates that predictions in agreement with experimental measurements are possible to be achieved with quantum resources available in near-term quantum computers.