Beyond VQE and QPE: A Noise- and Sampling-Error-Tolerant Quantum Algorithm with Heisenberg-Limited Precision

TL;DR

This paper presents WQTE, a noise- and sampling-error-tolerant quantum algorithm that achieves Heisenberg-limited precision for eigen-energy spectra without eigenstate preparation, suitable for NISQ devices.

Contribution

The paper introduces WQTE, a novel quantum algorithm that efficiently computes eigen-energies with reduced complexity and enhanced noise resilience compared to existing methods.

Findings

WQTE achieves Heisenberg-limited precision.

Numerical simulations confirm robustness against noise.

Experimental validation on NMR quantum processor.

Abstract

This paper introduces Witnessed Quantum Time Evolution (WQTE), a novel quantum algorithm for efficiently computing the eigen-energy spectra of arbitrary quantum systems without requiring eigenstate preparation-a key limitation of conventional approaches. By leveraging a single ancillary qubit to control real-time evolution operators and employing Fourier analysis, WQTE enables parallel resolution of multiple eigen-energies. Theoretical analysis demonstrates that the algorithm achieves Heisenberg-limited precision and operates with only a non-zero wavefunction overlap between the reference state and target eigenstates, significantly reducing initialization complexity. Numerical simulations validate the algorithm's effectiveness in molecular systems (e.g., H4 chains) and lattice models (e.g., Heisenberg spin systems), confirming that computational error scales inversely with maximum evolution time while maintaining robustness against sampling errors and quantum noise. Experimental implementation on an NMR quantum processor further verifies its feasibility in real-world noisy environments. Compared to existing quantum algorithms (e.g., VQE, QPE and their variants), WQTE exhibits superior circuit depth efficiency, resource economy, and noise resilience, making it a promising solution for eigen-energy computation on noisy intermediate-scale quantum (NISQ) devices.