qSHIFT: An Adaptive Sampling Protocol for Higher-Order Quantum Simulation

• URL: http://arxiv.org/abs/2604.26263v2
• Date: Thu, 30 Apr 2026 00:37:18 GMT
• Title: qSHIFT: An Adaptive Sampling Protocol for Higher-Order Quantum Simulation
• Abstract summary: Quantum simulation is a cornerstone application for quantum computing.<n>Standard methods face a trade-off between circuit depth and accuracy.<n>We introduce qSHIFT, an adaptive sampling protocol that overcomes these limitations.
• Score: 0.5635658368100682
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum simulation is a cornerstone application for quantum computing, yet standard methods face a trade-off between circuit depth and accuracy: Trotterization depth scales with the number of Hamiltonian terms $L$, while sampling-based qDRIFT is restricted to $O(t^2)$ error scaling. Here, We introduce qSHIFT, an adaptive sampling protocol that overcomes these limitations. By adaptively updating sampling distributions, qSHIFT maintains $L$-independent gate complexity while achieving an improved error scaling of $O(t^{1+r})$ for an adjustable parameter $r$. This performance is enabled by a classical subroutine solving $L^r$ linear equations per sampling round. Numerical demonstrations confirm the $O(t^{1+r})$ scaling, showcasing qSHIFT as a resource-efficient framework for high-precision quantum simulation. Furthermore, the protocol's reduced circuit depth enhances its compatibility with physical error mitigation, making it a promising candidate for implementation on near-term quantum devices. In addition to its role as a standalone algorithm, qSHIFT can provide a high-precision foundation for modular quantum frameworks such as qSWIFT or Krylov quantum diagonalization.

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