The Bravyi-Kitaev transformation for quantum computation of electronic structure.
Seeley, Jacob T.
Richard, Martin J.
Love, Peter J.
- Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here, we develop an alternative method of simulating fermions with qubits, ... read morefirst proposed by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002)10.1006/aphy.2002.6254; e-print arXiv:quant-ph/0003137v2], that reduces the simulation cost to O(logn) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure. © 2012 American Institute of Physics.read less
- Seeley, Jacob T., Martin J. Richard, and Peter J. Love. "The Bravyi-Kitaev Transformation for Quantum Computation of Electronic Structure." The Journal of Chemical Physics 137, no. 22 (December 14, 2012): 224109. doi:10.1063/1.4768229.