Randomized algorithms such as qDRIFT provide an efficient framework for quantum simulation by sampling terms from a decomposition of the system's generator.However, existing error bounds for qDRIFT scale quadratically with the norm of the generator, limiting their efficiency for largescale closed or open quantum system simulation.In this work, we refine the qDRIFT error bound by incorporating Jensen's inequality and a careful treatment of the integral form of the error.This yields an improved scaling that significantly reduces the number of steps required to reach a fixed simulation accuracy.Our result applies to both closed and open quantum systems, and we explicitly recover the improved bound in the Hamiltonian case.To demonstrate the practical impact of this refinement, we apply it to three settings: quantum chemistry simulations, dissipative transverse field Ising models, and Hamiltonian encoding of classical data for quantum machine learning.In each case, our bound leads to a substantial reduction in gate counts, highlighting its broad utility in enhancing randomized simulation techniques.
This paper presents improved error bounds for the qDRIFT algorithm, which is used for efficient quantum simulation of both closed and open quantum systems. The authors refine the existing error bounds by utilizing Jensen's inequality and an integral error representation, resulting in a new bound that scales more favorably with the system's generator characteristics. The improved bounds significantly reduce the number of quantum gate operations required for simulation tasks, demonstrated through applications in quantum chemistry, dissipative transverse field Ising models, and Hamiltonian encoding in quantum machine learning. The study compares the new bounds against previous ones, showing orders of magnitude reduction in steps needed for different simulation scenarios.
This paper employs the following methods:
The following datasets were used in this research:
- Substantial reduction in gate counts for simulations across different application domains including quantum chemistry and Hamiltonian-based encoding.
The authors identified the following limitations:
- Current bounds may not fully account for complexities in extremely large-scale quantum systems.
- Number of GPUs: None specified
- GPU Type: None specified
- Compute Requirements: None specified