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

TL;DR

qSHIFT is an adaptive sampling protocol that improves quantum simulation efficiency by maintaining low circuit depth and achieving better error scaling through adaptive distribution updates and a classical linear solver.

Contribution

It introduces qSHIFT, a novel adaptive sampling method that overcomes existing trade-offs in quantum simulation, enabling higher precision with lower circuit complexity.

Findings

qSHIFT maintains L-independent gate complexity.

qSHIFT achieves an error scaling of O(t^{1+r}).

Numerical results confirm improved error scaling and resource efficiency.

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.