Optimised Fermion-Qubit Encodings for Quantum Simulation with Reduced Transpiled Circuit Depth
This work provides a practical improvement for quantum simulation of fermionic systems by reducing circuit depth, which is a key bottleneck for near-term quantum computers.
The authors develop a deterministic optimization method for ternary tree fermion-qubit encodings that reduces Pauli weight without ancillae or swap-gate overhead. For water in the STO-3G basis, their method reduces qDRIFT circuit depths by 24.7% (untranspiled) and 26.5% (transpiled) on average.
Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates, the most widely used being the Jordan-Wigner transform. Many alternative encodings exist, with quantum circuits and simulation results being sensitive to choice of encoding, device connectivity and Hamiltonian characteristics. Non-stochastic optimisation of the ternary tree class of encodings to date has targeted either the device or Hamiltonian. We develop a deterministic method which optimises ternary tree encodings without changing the underlying tree structure. This enables reduction in Pauli-weight without ancillae or additional swap-gate overhead. We demonstrate this method for a variety of encodings, including those which are derived from the qubit connectivity graph of a quantum computer. Numerical results for a suite of standard encoding methods applied to water in the STO-3G basis indicate that our method reduces qDRIFT circuit depths on average by 24.7% and 26.5% for untranspiled and transpiled circuits respectively.