Improving quantum algorithms for quantum chemistry (pp0001-0021)
          Matthew B. Hastings, Dave Wecker, Bela Bauer, and Matthias Troyer
          doi: https://doi.org/10.26421/QIC15.1-2-1
Abstracts: We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Our modification does not require additional ancilla qubits. Then, we demonstrate how many operations can be parallelized, leading to a further linear decrease in the parallel depth of the circuit, at the cost of a small constant factor increase in number of qubits required. Thirdly, we modify the term order in the Trotter-Suzuki decomposition, significantly reducing the error at given Trotter-Suzuki timestep. A final improvement modifies the Hamiltonian to reduce errors introduced by the non-zero Trotter-Suzuki timestep. All of these techniques are validated using numerical simulation and detailed gate counts are given for realistic molecules.
Key words: Quantum Chemistry, Algorithms, Jordan-Wigner transformations, quantum computer