Optimised Fermion-Qubit Encodings for Quantum Simulation with Reduced Transpiled Circuit Depth

TL;DR

This paper introduces a deterministic optimization method for fermion-qubit encodings that reduces circuit depth in quantum simulations without additional overhead, improving efficiency for various encodings.

Contribution

A new deterministic approach to optimize ternary tree encodings, reducing circuit depth without altering the tree structure or adding ancillae.

Findings

Reduces qDRIFT circuit depths by approximately 25% on average.

Applicable to various encoding schemes, including those based on device connectivity.

Achieves depth reduction without extra swap gates or ancilla qubits.

Abstract

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.