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Although quantum computation (QC) is regarded as a promising numerical methodfor computational quantum chemistry, current applications of quantum-chemistrycalculations on quantum computers are limited to small molecules. Thislimitation can be ascribed to technical problems in building and manipulatingmore qubits and the associated complicated operations of quantum gates in aquantum circuit when the size of the molecular system becomes large. As aresult, reducing the number of required qubits is necessary to make QCpractical. Currently, the minimal STO-3G basis set is commonly used inbenchmark studies because it requires the minimum number of spin orbitals.Nonetheless, the accuracy of using STO-3G is generally low and thus cannotprovide useful predictions. We propose to adopt Daubechies wavelet functions asan accurate and efficient method for QCs of molecular electronic properties. Wedemonstrate that a minimal basis set constructed from Daubechies wavelet basiscan yield accurate results through a better description of the molecularHamiltonian, while keeping the number of spin orbitals minimal. With theimproved Hamiltonian through Daubechies wavelets, we calculate vibrationalfrequencies for H$_2$ and LiH using quantum-computing algorithm to show thatthe results are in excellent agreement with experimental data. As a result, weachieve quantum calculations in which accuracy is comparable with that of thefull configuration interaction calculation using the cc-pVDZ basis set, whereasthe computational cost is the same as that of a STO-3G calculation. Thus, ourwork provides a more efficient and accurate representation of the molecularHamiltonian for efficient QCs of molecular systems, and for the first timedemonstrates that predictions in agreement with experimental measurements arepossible to be achieved with quantum resources available in near-term quantumcomputers.

prx quantum

Accurate and Efficient Quantum Computations of Molecular Properties  Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against  Experimental Data