Accurate ground state energy estimation with noise and imperfect state preparation

• URL: http://arxiv.org/abs/2603.21873v1
• Date: Mon, 23 Mar 2026 12:04:52 GMT
• Title: Accurate ground state energy estimation with noise and imperfect state preparation
• Abstract summary: We introduce a classical estimator for the post-processing of quantum phase estimation data.<n>We show that our methods are robust in the presence of both additional phases outside the promise region and global depolarizing noise.<n>The robustness of the moment-projection estimator in the presence of both multiple eigenvalues and realistic noise makes phase estimation with limited depth practical for early fault tolerant quantum experiments.
• Score: 0.005587571498826265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a classical estimator for the post-processing of quantum phase estimation data generated either by quantum-Fourier-transform-based or quantum-signal-processing-based methods. We focus on the estimation of a single target phase promised to be within an interval where no other phases are present, which is typical of e.g. ground state energy estimation of gapped quantum systems. This allows us to perform phase estimation by filtering the signal within the promise region and recovering the phase through a moment-projection estimator. We show that our methods are robust in the presence of both additional phases outside the promise region and global depolarizing noise. In the noiseless case our estimator can achieve an exponential suppression of bias with respect to a naive mean estimator. In the presence of global depolarizing noise our estimator achieves a bias exponentially small in the circuit depth $t$ at fixed circuit fidelity $F$, and a variance proportional to $t^{-2}$, improving by a factor of $t^2$ over the naive shifted-and-rescaled-mean approach. To mitigate realistic circuit-level noise, we combine our method with the explicit unbiasing scheme described in [Dutkiewicz et al., 2025]. As an illustrative example, we implement these estimators on a small-scale simulation of the Ising model, validating our theoretical results and finding better-than-expected performance for a global depolarizing noise approximation. The robustness of the moment-projection estimator in the presence of both multiple eigenvalues and realistic noise makes phase estimation with limited depth practical for early fault tolerant quantum experiments.

Related papers

• Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation [48.887627688666974]
  Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies.<n>Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a simulation method, the Jump Method (TJM)<n>We demonstrate the approach on two noise models in the Ising model, in which independent dissipation rates are learned for each site up to $N_mathrmsite=16$.<n>This combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices.
  arXiv  Detail & Related papers  (2026-08-25T15:07:11Z)
• From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regime [52.459513910242485]
  We develop a general statistical framework for studying optimal noise-level allocation in diffusion training.<n>We show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels.<n>We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable.
  arXiv  Detail & Related papers  (2026-07-10T20:59:06Z)
• Benchmark of quantum algorithms for ground state preparation in the presence of noise [0.19999259391104388]
  We compare the performance of representative cooling, adiabatic, and optimization algorithms for ground-state preparation in the presence of noise.<n>We show that for this model the cooling protocol exhibits enhanced robustness to parameter imperfections.
  arXiv  Detail & Related papers  (2026-06-18T17:57:56Z)
• Low-depth amplitude estimation via statistical eigengap estimation [3.6696978514328715]
  Amplitude estimation is equivalent to estimating the energy gap of an effective Hamiltonian.<n>We develop two amplitude estimation algorithms for both Heisenberg-limited and low-depth circuit regimes.
  arXiv  Detail & Related papers  (2026-03-05T18:45:52Z)
• In-Context Parametric Inference: Point or Distribution Estimators? [66.22308335324239]
  We show that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems.<n>Our experiments indicate that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems.
  arXiv  Detail & Related papers  (2025-02-17T10:00:24Z)
• Bayesian Quantum Amplitude Estimation [46.03321798937855]
  We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation.<n>In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically characterize it and self-adapt.<n>We propose a benchmark for amplitude estimation algorithms and use it to test BAE against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Lindblad-like quantum tomography for non-Markovian quantum dynamical maps [46.350147604946095]
  We introduce Lindblad-like quantum tomography (L$ell$QT) as a quantum characterization technique of time-correlated noise in quantum information processors.<n>We discuss L$ell$QT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function.
  arXiv  Detail & Related papers  (2024-03-28T19:29:12Z)
• Robust ground-state energy estimation under depolarizing noise [4.969229261095783]
  We present a novel ground-state energy estimation algorithm that is robust under global depolarizing error channels. Our research demonstrates the feasibility of ground-state energy estimation in the presence of depolarizing noise.
  arXiv  Detail & Related papers  (2023-07-20T22:30:12Z)
• Noise-resilient phase estimation with randomized compiling [0.0]
  We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the noise channels with only Hermitian Kraus operators do not change the phases of a unitary operator. Our method paves the way for the utilization of quantum phase estimation before the advent of fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2022-08-08T12:46:00Z)
• Dual-Frequency Quantum Phase Estimation Mitigates the Spectral Leakage of Quantum Algorithms [76.15799379604898]
  Quantum phase estimation suffers from spectral leakage when the reciprocal of the record length is not an integer multiple of the unknown phase. We propose a dual-frequency estimator, which approaches the Cramer-Rao bound, when multiple samples are available.
  arXiv  Detail & Related papers  (2022-01-23T17:20:34Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Error mitigation via verified phase estimation [0.25295633594332334]
  This paper presents a new error mitigation technique based on quantum phase estimation. We show that it can be adapted to function without the use of control qubits.
  arXiv  Detail & Related papers  (2020-10-06T07:44:10Z)
• Path Sample-Analytic Gradient Estimators for Stochastic Binary Networks [78.76880041670904]
  In neural networks with binary activations and or binary weights the training by gradient descent is complicated. We propose a new method for this estimation problem combining sampling and analytic approximation steps. We experimentally show higher accuracy in gradient estimation and demonstrate a more stable and better performing training in deep convolutional models.
  arXiv  Detail & Related papers  (2020-06-04T21:51:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.