Towards quantum chemistry on a quantum computer

Journal name:
Nature Chemistry
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Published online


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.

At a glance


  1. The quantum algorithm for calculating energies of many-body quantum systems and our experimental implementation with linear optics.
    Figure 1: The quantum algorithm for calculating energies of many-body quantum systems and our experimental implementation with linear optics.

    a, The iterative phase estimation algorithm15, 33 at iteration k represented using quantum circuit notation34. To produce an m–bit approximation to the phase of the eigenstate, ϕ (see Eqn 1), the algorithm is iterated m times. Each iteration obtains one bit of ϕ(ϕk); starting from the least significant (ϕm), k is iterated backwards from m to 1. The angle ωk depends on all previously measured bits as ωk = −2πb, where b, in the binary expansion of ϕ, is b = 0.0ϕk+1ϕk+2ϕm and ωm = 0. H is the standard Hadamard gate34. b, Quantum circuit model representation of our gate network for a two-qubit-controlled gate, as discussed in the Methods section. c, Two-qubit optical implementation of the IPEA. Photon pairs are generated by spontaneous parametric down-conversion (SPDC), coupled into a single-mode optical fibre and launched into free space optical modes C (control) and R (register). The operation of the optical-controlled gate is described by Lanyon31 et al. Coincident detection events (3.1 ns window) between single photon counting modules (SPCMs) D1 and D3 (D2 and D3) herald a successful run of the circuit and result in 0 (1) for ϕk. Waveplates are labelled with their corresponding operations. PPBS: partially polarizing beam splitter. X is the standard Pauli X gate (0 ↔ 1) and R[ncirc] is the rotation of the qubit about the [ncirc] axis of the Bloch sphere34. λ/2 (λ/4) is a half (quarter) wave plate.

  2. Experimental quantum algorithm results.
    Figure 2: Experimental quantum algorithm results.

    a, H2 potential energy curves in a minimal basis. Each point was calculated with a 20–bit iterative phase estimation algorithm, using n = 31 samples per bit (repetitions of each iteration). Measured phases are converted to energies via E = 2πϕEh + (e2/4πεR) − E; the second term accounts for the proton–proton Coulomb energy at atomic separation R and E is the ground state energy of two hydrogen atoms at infinite separation. Each case achieved the target precision of 20 bits corresponding to ± (2−20 × 2π)Eh ≈ 16 J mol−1. Curve G (E3) is the low (high) eigenvalue of Ĥ(1,6). Curve E1 is a triply degenerate spin-triplet state, corresponding to the lower eigenvalue of and Ĥ(3,4) as well as the eigenvalues Ĥ(2) and Ĥ(5). Curve E2 is the higher (singlet) eigenvalue of Ĥ(3,4). b, Curve G rescaled to highlight the bound state. c, Example of raw data for the ground state energy, obtained at the equilibrium bond length 73.48 pm. The measured binary phase is ϕ = 0.01001011101011100000, which is equal to the exact value in our minimal basis, to a precision of ±2−20 Eh. Note that the exact value has a remainder of δ ≈ 0.5 Eh after a 20-bit expansion, hence the low contrast in the measured 20th bit.


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Author information


  1. Department of Physics

    • B. P. Lanyon,
    • G. G. Gillett,
    • M. E. Goggin,
    • M. P. Almeida,
    • B. J. Powell,
    • M. Barbieri &
    • A. G. White
  2. Centre for Quantum Computer Technology

    • B. P. Lanyon,
    • G. G. Gillett,
    • M. P. Almeida,
    • M. Barbieri &
    • A. G. White
  3. Centre for Organic Photonics & Electronics, University of Queensland, Brisbane 4072, Australia

    • B. J. Powell
  4. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA

    • J. D. Whitfield,
    • I. Kassal,
    • J. D. Biamonte,
    • M. Mohseni &
    • A. Aspuru-Guzik
  5. Department of Physics, Truman State University, Kirksville, Missouri 63501, USA

    • M. E. Goggin
  6. Present address: Laboratoire Charles Fabry, Institut d'Optique, 91127 Palaiseau, France (M.B.); Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK (J.D.B.); Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA (M.M.)

    • J. D. Biamonte,
    • M. Mohseni &
    • M. Barbieri


B.P.L., J.D.W., I.K., M.M., A.A.G. and A.G.W. conceived and designed the experiments, B.P.L., G.G.G., M.E.G. and M.P.A. performed the experiments, B.P.L. and G.G.G. analysed the data, J.D.W. performed the classical preprocessing. All authors discussed the results and co-wrote the manuscript.

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