arXiv subjects

Qing-Xing Xie

Publications and source records attributed to Qing-Xing Xie.

4 recordsLinked to original sources

arXiv2026

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

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.

quant-ph↗

arXiv2026

MQTE: A Measurement-Based Quantum Algorithm for Robust Energy Spectrum Estimation in the NISQ Era

Extracting energy spectra from quantum Hamiltonians is a fundamental task for quantum simulation, yet remains challenging on noisy intermediate-scale quantum (NISQ) devices. We propose Measured Quantum Time Evolution (MQTE), an ancilla-free algorithm that estimates energy gaps by applying real-time evolution to a reference state and measuring time-resolved probabilities via repeated projective measurements. Spectral analysis of these signals reveals oscillation frequencies corresponding to eigenvalue differences. Crucially, MQTE exhibits inherent robustness to quantum hardware noise and sampling errors: these disturbances manifest as a white-noise background, which does not distort the underlying spectral structure but rather obscures the frequency information. By increasing the number of measurement samples, the intensity of the background white noise can be suppressed, thereby recovering the original spectral content. We validate the algorithm's performance via numerical simulations on one- and two-dimensional Heisenberg models, demonstrating accurate extraction of energy gaps and resilience against both sampling and circuit-level noise. Experimental implementation on the superconducting quantum processor Tianyan-176-II further confirms the practical feasibility and noise tolerance of MQTE under real hardware conditions. This work provides a robust and scalable framework for quantum spectral estimation in the NISQ era.

quant-ph↗

arXiv2024

A Novel Quantum-Classical Hybrid Algorithm for Determining Eigenstate Energies in Quantum Systems

Developing efficient quantum computing algorithms is essential for tackling computationally challenging problems across various fields. This paper presents a novel quantum algorithm, XZ24, for efficiently computing the eigen-energy spectra of arbitrary quantum systems. Given a Hamiltonian $\hat{H}$ and an initial reference state $|ψ_{\text{ref}} \rangle$, the algorithm extracts information about $\langle ψ_{\text{ref}} | \cos(\hat{H} t) | ψ_{\text{ref}} \rangle$ from an auxiliary qubit's state. By applying a Fourier transform, the algorithm resolves the energies of eigenstates of the Hamiltonian with significant overlap with the reference wavefunction. We provide a theoretical analysis and numerical simulations, showing XZ24's superior efficiency and accuracy compared to existing algorithms. XZ24 has three key advantages: 1. It removes the need for eigenstate preparation, requiring only a reference state with non-negligible overlap, improving upon methods like the Variational Quantum Eigensolver. 2. It reduces measurement overhead, measuring only one auxiliary qubit. For a system of size $L$ with precision $ε$, the sampling complexity scales as $O(L \cdot ε^{-1})$. When relative precision $ε$ is sufficient, the complexity scales as $O(ε^{-1})$, making measurements independent of system size. 3. It enables simultaneous computation of multiple eigen-energies, depending on the reference state. We anticipate that XZ24 will advance quantum system simulations and enhance applications in quantum computing.

quant-ph↗

arXiv2021

Accurate Correlation Energy Functional for Uniform Electron Gas from an Interpolation Ansatz without Fitting Parameters

We report an analytical representation of the correlation energy ec(rs, zeta) for a uniform electron gas (UEG), where rs is the Seitz radius or density parameter and zeta is the relative spin polarization. The new functional, called W20, is constructed to capture the known high-density and low-density limit (for zeta = 0 and 1) without any fitting parameters. The comparative assessment against the recent quantum Monte Carlo (QMC) results shows that the performance of the W20 functional is comparable to the popular parametrized UEG correlation functionals. On average, W20 agrees with QMC and PW92 [Phys. Rev. B 45, 13244 (1992)] within 0.01 eV, and W20 recovers the correct high- and low-density limits, whereas the QMC-data fitted UEG correlation functionals do not.

physics.chem-ph↗