Abstract
Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.
Highlights
We provide new theoretical results which lay the foundations for the generation of simulation experiments using quantum computers
Experimentalists are just beginning to command the level of control over quantum systems required to explore their information processing capabilities
Molecular energies are represented as the eigenvalues of an associated time-independent Hamiltonian Hand can be efficiently obtained to fixed accuracy, using a quantum algorithm with three distinct steps[6]: encoding a molecular wavefunction into qubits; simulating its time evolution using quantum logic gates; and extracting the approximate energy using the phase estimation algorithm[3,12]
Summary
We use the minimal STO-3G basis[27] for H2, consisting of one |1s -type atomic orbital per atom. These two functions are combined to form the bonding (antibonding) molecular orbitals[28]. Finding the eigenvalues of the two 2×2 submatrices in the Hamiltonian—H (1,6) and H (3,4)—amounts to performing the FCI. Estimating the eigenvalues of 2x2 matrices is the simplest problem for the IPEA. For our proof-of-principle demonstration, all necessary molecular integrals are evaluated classically (Methods, Section C) using the Hartree-Fock procedure[28]. We use these integrals to calculate the matrix elements of Hand.
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