An Iterative Methodology for Unitary Quantum Channel Search

• URL: http://arxiv.org/abs/2506.21455v1
• Date: Thu, 26 Jun 2025 16:35:28 GMT
• Title: An Iterative Methodology for Unitary Quantum Channel Search
• Authors: Matthew M. Lin, Hao-Wei Huang, Bing-Ze Lu,
• Abstract summary: We propose an iterative algorithm to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs.<n>We rigorously prove our proposed algorithm can ultimately identify a critical point, which is also a local minimum of the established objective function.
• Score: 0.27309692684728615
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal solution obtained from our method using one pair with a specific structure will generate an equivalent class, significantly reducing the dimension of the searching space. Furthermore, we prove that the unitary matrices describing the same channel differ by a complex number with modulus 1. We rigorously prove our proposed algorithm can ultimately identify a critical point, which is also a local minimum of the established objective function.

Related papers

• Efficient Quantum Access Model for Sparse Structured Matrices using Linear Combination of Things [0.6138671548064355]
  We present a novel framework for Linear Combination of Unitaries (LCU)-style decomposition tailored to structured sparse matrices.<n>LCU is a foundational primitive in both variational and fault-tolerant quantum algorithms.<n>We introduce the Sigma basis, a compact set of simple, non-unitary operators that can better capture sparsity and structure.
  arXiv  Detail & Related papers  (2025-07-04T17:05:07Z)
• High order schemes for solving partial differential equations on a quantum computer [0.0]
  We show that higher-order methods can reduce the number of qubits necessary for discretization, similar to the classical case.<n>This result has important consequences for the practical application of quantum algorithms based on Hamiltonian evolution.
  arXiv  Detail & Related papers  (2024-12-26T14:21:59Z)
• Fast and spectrally accurate construction of adaptive diagonal basis sets for electronic structure [2.2489531925874013]
  We combine the periodic sinc basis set with a curvilinear coordinate system for electronic structure calculations. We address two key challenges that arise while using basis sets obtained by such a coordinate transformation. The solution of both of these challenges enables mean-field calculations at a cost that is log-linear in the number of basis functions.
  arXiv  Detail & Related papers  (2024-07-08T17:48:40Z)
• Variable Substitution and Bilinear Programming for Aligning Partially Overlapping Point Sets [48.1015832267945]
  This research presents a method to meet requirements through the minimization objective function of the RPM algorithm. A branch-and-bound (BnB) algorithm is devised, which solely branches over the parameters, thereby boosting convergence rate. Empirical evaluations demonstrate better robustness of the proposed methodology against non-rigid deformation, positional noise, and outliers, when compared with prevailing state-of-the-art transformations.
  arXiv  Detail & Related papers  (2024-05-14T13:28:57Z)
• Sample Complexity for Quadratic Bandits: Hessian Dependent Bounds and Optimal Algorithms [64.10576998630981]
  We show the first tight characterization of the optimal Hessian-dependent sample complexity. A Hessian-independent algorithm universally achieves the optimal sample complexities for all Hessian instances. The optimal sample complexities achieved by our algorithm remain valid for heavy-tailed noise distributions.
  arXiv  Detail & Related papers  (2023-06-21T17:03:22Z)
• Quantum channel decomposition with pre- and post-selection [0.7597059965024503]
  This paper proposes a channel decomposition method for target unitaries that have their input and output conditioned on specific quantum states. We explicitly determine the requisite number of decomposing channels, which could be significantly smaller than the selection-free scenario. We demonstrate an application of this approach to the quantum linear solver algorithm, highlighting the efficacy of the proposed method.
  arXiv  Detail & Related papers  (2023-05-19T12:48:21Z)
• Linearization Algorithms for Fully Composite Optimization [61.20539085730636]
  This paper studies first-order algorithms for solving fully composite optimization problems convex compact sets. We leverage the structure of the objective by handling differentiable and non-differentiable separately, linearizing only the smooth parts.
  arXiv  Detail & Related papers  (2023-02-24T18:41:48Z)
• Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency [111.83670279016599]
  We study reinforcement learning for partially observed decision processes (POMDPs) with infinite observation and state spaces. We make the first attempt at partial observability and function approximation for a class of POMDPs with a linear structure.
  arXiv  Detail & Related papers  (2022-04-20T21:15:38Z)
• Improving Metric Dimensionality Reduction with Distributed Topology [68.8204255655161]
  DIPOLE is a dimensionality-reduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term. We observe that DIPOLE outperforms popular methods like UMAP, t-SNE, and Isomap on a number of popular datasets.
  arXiv  Detail & Related papers  (2021-06-14T17:19:44Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)

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.