🤖 AI Summary
Quantum simulation of fermionic Hamiltonians often suffers from excessive circuit depth due to inefficient qubit encodings. Method: This work proposes a deterministic ternary-tree encoding optimization method jointly tailored to hardware connectivity and Hamiltonian structure. Preserving the ternary-tree topology, it employs analytical modeling, graph-structure-driven encoding construction, and qDRIFT time-evolution analysis to achieve auxiliary-qubit-free, zero-SWAP-overhead encoding customization. Contribution/Results: Unlike existing heuristic or resource-augmented approaches, this is the first deterministic, hardware-aware optimization that co-adapts to both device constraints and Hamiltonian features. In STO-3G-basis water molecule simulations, it reduces uncompiled and compiled qDRIFT circuit depths by 27.7% and 26.0% on average, respectively—significantly enhancing simulation efficiency on noisy intermediate-scale quantum (NISQ) devices.
📝 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.