  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.
