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A short tutorial on Wirtinger Calculus with applications in quantum information

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arxiv 2312.04858 v1 pith:NTNFM44B submitted 2023-12-08 quant-ph

Kelvin Koor , Yixian Qiu , Leong Chuan Kwek , Patrick Rebentrost This is my paper · ORCID
classification quant-ph
keywords calculuswirtingerapplicationsinformationoptimizationparametersquantumsystem
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The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to extract the optimal solution. However, the system parameters often take the form of complex matrices. In such situations, conventional methods become unwieldy. The `Wirtinger Calculus' provides a relatively simple methodology for such optimization problems. In this tutorial, we provide a pedagogical introduction to Wirtinger Calculus. To illustrate the utility of this framework in quantum information theory, we also discuss a few example applications.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic gradients for low-rank quantum optimal control

    quant-ph 2026-07 accept novelty 7.0 of 10

    A new gradient-based quantum control algorithm propagates only a low-rank factorization of the density matrix, giving analytic gradients and quadratic speedups over full master-equation simulations for high-purity protocols.

  2. Second-order AAA algorithms for structured data-driven modeling

    math.NA 2025-06 accept novelty 7.0 of 10

    New AAA variants (LSO-AAA, SO-AAA, NSO-AAA) construct second-order structured models from frequency data, with a theorem linking the linearized variant to unstructured AAA.

  3. Full cross-correlation inversion for quantitative passive imaging with time-harmonic acoustic waves

    math.NA 2026-07 conditional novelty 6.0 of 10

    Expected cross-correlations of ambient acoustic signals can be inverted quantitatively for medium parameters via an adjoint-state HDG scheme, recovering structures comparable to active-source FWI on synthetic data.

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