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

• URL: http://arxiv.org/abs/2512.13580v1
• Date: Mon, 15 Dec 2025 17:35:17 GMT
• Title: Optimised Fermion-Qubit Encodings for Quantum Simulation with Reduced Transpiled Circuit Depth
• Authors: Michael Williams de la Bastida, Thomas M. Bickley, Peter V. Coveney,
• Abstract summary: Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates.<n>Many alternative encodings exist, with quantum circuits and simulation results being sensitive to choice of encoding, device connectivity and Hamiltonian characteristics.<n>We develop a deterministic method which optimises ternary tree encodings without changing the underlying tree structure.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. Across a suite of standard encoding methods applied to water in STO-3G basis, including Jordan-Wigner, our method reduces qDRIFT circuit depths on average by $27.7\%$ and $26.0\%$ for untranspiled and transpiled circuits respectively.

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