OpenNovelty.org

Bayesian Parameter Shift Rules in Variational Quantum Eigensolvers

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
parameter shift rulevariational quantum eigensolverquantum computingconfidence regionGaussian process
Abstract:

Parameter shift rules (PSRs) are key techniques for efficient gradient estimation in variational quantum eigensolvers (VQEs). In this paper, we propose their Bayesian variant, where Gaussian processes with appropriate kernels are used to estimate the gradient of the VQE objective. Our Bayesian PSR offers flexible gradient estimation from observations at arbitrary locations with uncertainty information, and reduces to the generalized PSR in special cases. In stochastic gradient descent (SGD), the flexibility of Bayesian PSR allows reuse of observations in previous steps, which accelerates the optimization process. Furthermore, the accessibility to the posterior uncertainty, along with our proposed notion of gradient confident region (GradCoRe), enables us to minimize the observation costs in each SGD step. Our numerical experiments show that the VQE optimization with Bayesian PSR and GradCoRe significantly accelerates SGD, and outperforms the state-of-the-art methods, including sequential minimal optimization.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces a Bayesian variant of parameter shift rules for gradient estimation in variational quantum eigensolvers, using Gaussian processes to provide flexible gradient estimates with uncertainty quantification. It resides in the 'Bayesian and Probabilistic Gradient Methods' leaf, which contains only three papers total, indicating a relatively sparse research direction within the broader VQE gradient estimation landscape. This small cluster contrasts with more populated branches like natural gradient methods and adaptive ansatz construction, suggesting the Bayesian approach to gradient estimation remains an emerging niche rather than a crowded subfield.

The taxonomy reveals that gradient estimation methods split into deterministic parameter shift variants, Bayesian probabilistic approaches, efficient computation techniques exploiting circuit structure, and tensor network approximations. The original paper's leaf sits alongside 'Parameter Shift Rule Variants' containing two papers on generalized shift rules, and 'Efficient Gradient Computation Techniques' with three papers on parallel or structure-aware methods. The scope note explicitly distinguishes Bayesian frameworks from deterministic shift rules, positioning this work as a probabilistic alternative that trades statistical rigor for measurement flexibility. Neighboring branches in optimization algorithms and convergence theory provide complementary perspectives on how gradient estimates feed into VQE training dynamics.

Among thirty candidates examined, the contribution-level analysis shows limited prior work overlap within the search scope. The Bayesian PSR contribution examined ten candidates with one appearing to provide overlapping prior work, while GradCoRe examined ten with two potential overlaps, and the theoretical relationship contribution found three among ten candidates. These statistics reflect a top-K semantic search plus citation expansion, not an exhaustive literature review. The relatively low refutation counts across contributions suggest that within the examined candidate set, substantial portions of the proposed methods lack direct precedent, though the search scope inherently limits the strength of this conclusion.

Based on the limited search of thirty semantically related papers, the work appears to occupy a sparsely populated research direction where Bayesian gradient estimation remains underexplored. The taxonomy structure confirms that probabilistic gradient methods constitute a small fraction of VQE research compared to deterministic shift rules and optimizer design. However, the analysis cannot rule out relevant prior work outside the top-thirty semantic matches or in adjacent fields not captured by the VQE-focused taxonomy.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
6
Refutable Paper

Research Landscape Overview

Core task: gradient estimation in variational quantum eigensolvers. The field organizes around several complementary branches that address different facets of making VQE practical and efficient. Gradient Estimation Methods and Rules explores how to compute parameter derivatives on quantum hardware, ranging from parameter-shift techniques to Bayesian and probabilistic approaches. Optimization Algorithms and Strategies focuses on classical optimizers that consume these gradients, including natural gradient methods like Natural Gradient VQE[2] and particle-based schemes such as Particle Swarm VQE[1]. Convergence Theory and Optimization Landscape investigates the mathematical properties of VQE cost surfaces, including barren plateau phenomena addressed by works like Mitigating Barren Plateaus[5]. Adaptive and Problem-Tailored Ansatz Construction develops circuits that grow or adapt during optimization, while Application-Specific VQE Implementations and Resource Efficiency branches tackle domain-specific challenges and hardware constraints. General VQE Reviews and Methodological Surveys provide broad overviews, and Classical Simulation supports algorithm development before deployment on real devices. Within gradient estimation, a handful of works pursue probabilistic or Bayesian frameworks to handle noisy measurements and uncertainty quantification more systematically. Bayesian Parameter Shift[0] sits in this small cluster alongside Fast Gradient Estimation[3], which emphasizes computational speed, and an earlier Bayesian Parameter Shift[4] study. These methods contrast with deterministic parameter-shift rules and finite-difference schemes like Optimized Numerical Gradient[13], trading off statistical rigor for reduced measurement overhead. The original paper's Bayesian approach naturally complements efforts in convergence analysis such as VQE Convergence[6] and variance reduction strategies like Variance Minimization[31], as probabilistic gradient estimates can inform both optimizer design and theoretical guarantees. By embedding uncertainty directly into gradient computation, this line of work addresses a key challenge in noisy intermediate-scale quantum devices where measurement statistics dominate algorithmic performance.

Claimed Contributions

Bayesian Parameter Shift Rule (Bayesian PSR)

The authors introduce a Bayesian variant of parameter shift rules where Gaussian processes with the VQE kernel are used to estimate gradients. This approach allows flexible gradient estimation from observations at arbitrary locations with uncertainty quantification, and reduces to the generalized PSR in special cases.

10 retrieved papers
Can Refute
Gradient Confident Region (GradCoRe)

The authors propose a novel concept called gradient confident region, which is the region where the uncertainty of gradient estimation is below a specified threshold. This notion enables adaptive control of observation costs in each SGD step by determining the minimum number of measurement shots needed to achieve required gradient estimation accuracy.

10 retrieved papers
Can Refute
Theoretical relationship between Bayesian PSR and existing PSRs

The authors provide theoretical analysis showing how Bayesian PSR generalizes existing parameter shift rules and prove that the commonly used shift parameter of π/2 in first-order PSRs minimizes the uncertainty in gradient estimation.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Bayesian Parameter Shift Rule (Bayesian PSR)

The authors introduce a Bayesian variant of parameter shift rules where Gaussian processes with the VQE kernel are used to estimate gradients. This approach allows flexible gradient estimation from observations at arbitrary locations with uncertainty quantification, and reduces to the generalized PSR in special cases.

Contribution

Gradient Confident Region (GradCoRe)

The authors propose a novel concept called gradient confident region, which is the region where the uncertainty of gradient estimation is below a specified threshold. This notion enables adaptive control of observation costs in each SGD step by determining the minimum number of measurement shots needed to achieve required gradient estimation accuracy.

Contribution

Theoretical relationship between Bayesian PSR and existing PSRs

The authors provide theoretical analysis showing how Bayesian PSR generalizes existing parameter shift rules and prove that the commonly used shift parameter of π/2 in first-order PSRs minimizes the uncertainty in gradient estimation.

Table of Contents