Add functions overview tables

docs/guides/algorithmiq-tem.ipynb

@@ -52,9 +52,9 @@
     "\n",
     "As an advantage, TEM leverages informationally complete measurements to give\n",
     "access to a vast set of mitigated expectation values of observables and has\n",
-    "optimal sampling overhead on the quantum hardware, as described in Filippov at\n",
+    "optimal sampling overhead on the quantum hardware, as described in Filippov et \n",
     "al. (2023), [arXiv:2307.11740](https://arxiv.org/abs/2307.11740), and  Filippov\n",
-    "at al. (2024), [arXiv:2403.13542](https://arxiv.org/abs/2403.13542). The\n",
+    "et al. (2024), [arXiv:2403.13542](https://arxiv.org/abs/2403.13542). The\n",
     "measurement overhead refers to the number of additional measurements required to\n",
     "perform efficient error mitigation, a critical factor in the feasibility of\n",
     "quantum computations. Therefore, TEM has the potential to enable quantum\n",
@@ -366,6 +366,9 @@
     "<Admonition type=\"tip\" title=\"Recommendations\">\n",
     "\n",
     "- [Request access to Algorithmiq Tensor-network error mitigation](https://quantum.cloud.ibm.com/functions?id=algorithmiq-tem)\n",
+    "- Review [Filippov, S., et al. (2023). Scalable tensor-network error mitigation for near-term quantum computing. arXiv preprint arXiv:2307.11740.](https://arxiv.org/abs/2307.11740)\n",
+    "- Review [Filippov, S., et al. (2024). Scalability of quantum error mitigation techniques: from utility to advantage. arXiv preprint arXiv:2403.13542.](https://arxiv.org/abs/2403.13542)\n",
+    "- Review [Fischer, E. F., et al. (2024). Dynamical simulations of many-body quantum chaos on a quantum computer. arXiv preprint arXiv:2411.00765.](https://arxiv.org/abs/2411.00765)\n",
     "\n",
     "</Admonition>"
    ]

docs/guides/colibritd-pde.ipynb

@@ -5,7 +5,7 @@
    "id": "f7d9993f",
    "metadata": {},
    "source": [
-    "{/* cspell:ignore CMAES Hypoelastic edgecolor royalblue rstride cstride colibritd xlabel ylabel zlabel */}"
+    "{/* cspell:ignore CMAES, Hypoelastic, edgecolor, royalblue, rstride, cstride, colibritd, xlabel, ylabel, zlabel, Jaffali */}"
    ]
   },
   {
@@ -477,6 +477,7 @@
     "<Admonition type=\"tip\" title=\"Recommendations\">\n",
     "- Fill out the form to [request access to the QUICK-PDE function.](https://forms.cloud.microsoft/e/3Wi9cbjQPK)\n",
     "- Try modeling a flowing non-viscous fluid using QUICK-PDE in the [tutorial](/docs/tutorials/colibritd-pde).\n",
+    "- Review [Jaffali, H., et al. (2025).  H-DES: a Quantum-Classical Hybrid Differential Equation Solver. arXiv preprint arXiv:2410.01130.](https://arxiv.org/abs/2410.01130)\n",
     "</Admonition>"
    ]
   }

docs/guides/functions.ipynb

@@ -1,5 +1,12 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "{/* cspell:ignore Jarman, HIVQE, Cadavid, Chandarana, Leclerc, Sachdeva, HUBO, Filippov, Downfolding, Aharonov, Mundada, Yamauchi, supersymmetric, Paterakis, Gharibyan, Jaffali, Pellow */}"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "97b94d47-ba58-4251-91f2-93097e50f2c9",
@@ -46,18 +53,42 @@
     "\n",
     "| Type | What does it do? | Example inputs and outputs | Who is it for? |\n",
     "| - | - | - | - |\n",
-    "| Circuit function | Simplified interface for running circuits. Abstracts transpilation, error suppression, error mitigation | **Input**: Abstract `PUB` objects <br/> **Output**: Mitigated expectation values | Researchers using Qiskit to discover new algorithms and applications, without needing to focus on optimizing for hardware or handling error. Circuit functions can be used to build custom application functions. |\n",
-    "| Application function | Covers higher-level tasks, like exploring algorithms and domain-specific use cases. Abstracts quantum workflow to solve tasks, with classical inputs and outputs | **Input**: Molecules, graphs <br/> **Output**: Ground + excited state energy, optimal values for cost function | Researchers in non-quantum domains, integrating quantum into existing large-scale classical workflows, without needing to map classical data to quantum circuits. |"
+    "| Circuit function | Simplified interface for running circuits. Abstracts transpilation, error suppression, and error mitigation | **Input**: Abstract `PUB` objects <br/> **Output**: Mitigated expectation values | Researchers using Qiskit to discover new algorithms and applications, without needing to focus on optimizing for hardware or handling error. Circuit functions can be used to build custom application functions. |\n",
+    "| Application function | Covers higher-level tasks, such as exploring algorithms and domain-specific use cases. Abstracts quantum workflow to solve tasks, with classical inputs and outputs | **Input**: Molecules, graphs <br/> **Output**: Ground + excited state energy, optimal values for cost function | Researchers in non-quantum domains, integrating quantum into existing large-scale classical workflows, without needing to map classical data to quantum circuits. |"
    ]
   },
   {
    "cell_type": "markdown",
    "id": "5e5b0531-f286-4573-8b1e-664ca5496d2d",
    "metadata": {},
    "source": [
-    "Functions are provided by IBM&reg; and third-party partners. Each is performant for specific workload characteristics and have unique performance-tuning options. Premium, Flex, and On-Prem (via IBM Quantum Platform API) Plan users can get started with IBM Qiskit Functions for free, or procure a license from one of the partners who have contributed a function to the catalog.\n",
+    "Functions are provided by IBM&reg; and third-party partners. Each is performant for specific workload characteristics and has unique performance-tuning options. \n",
+    "\n",
+    "## Overview of available functions\n",
+    "\n",
+    "<span id=\"circuit\"></span>\n",
+    "### Circuit functions\n",
+    "\n",
+    "| Name                                                                 | Provider     | Recommended use                                                                                                                                                                           | Unique benefits                                                                                                                                                                                                                                                                                                                                                              |\n",
+    "|----------------------------------------------------------------------|--------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n",
+    "| [Tensor-Network Error Mitigation](/docs/guides/algorithmiq-tem)      | Algorithmiq  | Workloads that have low-weight observables and loop-free circuits.                                                                                                                        | Reduces measurement overhead and variance, outperforming standard error mitigation baselines such as Zero Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC) for relevant circuit classes.                                                                                                                                                                 |\n",
+    "| [QESEM: Error Suppression and Error Mitigation](/docs/guides/qedma-qesem)    | Qedma        | Workloads that  include circuits with fractional or parameterized gates, high-weight observables,  and workflows that require unbiased expectation values and accurate runtime estimates. | Produces unbiased expectation values with lower variance and resource overhead, outperforming ZNE and PEC for relevant circuit classes.                                                                                                                                                                                                                                      |\n",
+    "| [Performance Management](/docs/guides/q-ctrl-performance-management) | Q-CTRL       | Workloads that contain parametric circuits, deep circuits, or require many circuit executions.                                                                                            | Automatically applies AI-driven error suppression to quantum algorithms, maximizing the performance of IBM devices to deliver accurate results while reducing the number of shots, compute time, and cost required. <br/><br/>Zero-overhead method that improves execution accuracy for the Sampler and the Estimator primitives, compatible with any weight of observables. |\n",
+    "\n",
+    "<span id=\"application\"></span>\n",
+    "### Application functions\n",
+    "\n",
+    "| Name                                                                      | Provider             | Recommended use                                                                                                                                                                           | Unique benefits                                                                                                                                                                                                                                                                                                                                                              |\n",
+    "|---------------------------------------------------------------------------|----------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n",
+    "| [QUICK-PDE](/docs/guides/colibritd-pde)                                   | ColibriTD            | Use quantum computation for multi-physics PDEs.<br/><br/>Prepare simulation workflows for quantum hardware, while keeping full control over both quantum and physical modeling parameters.                     | Offers a robust hybrid VQA framework that delivers precise, scalable PDE solutions through advanced solution encoding and spectral methods, making it an ideal entry point for teams trying to build quantum-ready simulation capabilities.                                                                                                                                                                                                                   |\n",
+    "| [Quantum Portfolio Optimizer](/docs/guides/global-data-quantum-optimizer) | Global Data Quantum  | Workloads for financial optimization, seeking optimal portfolio strategies over time while minimizing risk and maximizing returns, enabling trading strategy back-testing.                                   | Solves combinatorial optimization problems through a highly specialized adaptation of the VQE quantum algorithm for this financial use case, using optimized execution strategies and optimizers, along with noise-aware error mitigation techniques tailored to portfolio optimization.                                                                                                                                                                      |\n",
+    "| [HI-VQE Chemistry](/docs/guides/qunova-chemistry)                         | Qunova Computing     | Workloads in computational chemistry, molecular simulation, materials science, or any Hamiltonian simulation that require solving many-body electronic structure problems.                                   | Solves molecular electronic structures by using enhanced SQD with achieving chemical accuracy (1 kcal/mol, 1.6 mHa) for problems modeled with 40 to 60 qubits, outperforming some classical solutions on supercomputers or standard SQD in convergence speed or accuracy, respectively, by orders of magnitude.                                                                                                                                               |\n",
+    "| [Iskay Quantum Optimizer](/docs/guides/kipu-optimization)                 | Kipu Quantum         | Optimization workloads such as  scheduling, logistics, routing, and QUBO/HUBO problems. <br/><br/>                                                                                                             | Integrated tunable classical pre- and post-processing methods for the quantum optimization routine. <br/><br/>Delivers runtime advantage over classical solvers (CPLEX, simulated annealing, and tabu search) on selected HUBO benchmarks. <br/><br/>Market Split `ms_5_100`, a hard challenge, solved within hours (see [this tutorial](/docs/tutorials/solve-market-split-problem-with-iskay-quantum-optimizer)).                                        |\n",
+    "| [Singularity Machine Learning](multiverse-computing-singularity)          | Multiverse Computing | Classical machine learning classification workflows that could benefit from improved accuracy or computational efficiency by leveraging quantum optimization executed on IBM hardware.               | Delivers accuracy comparable to or exceeding classical models such as Random Forest or XGBoost, while operating with significantly fewer learners and a more compact ensemble. <br/><br/>Powered by quantum-optimized voting, it selects the most informative learners and refines decision boundaries, resulting in greater efficiency, reduced model complexity, and more robust performance.                                                                 |\n",
+    "| [Optimization Solver](/docs/guides/q-ctrl-optimization-solver)            | Q-CTRL               | Binary optimization problems or any combinatorial problem that can be mapped to a binary cost function.  <br/><br/>Cost functions of any order and problem sizes up to the maximum device scale are supported. | Noise-aware, end-to-end quantum optimization solution that enables inputs of high-level problem definitions and automatically finds accurate solutions to classically challenging combinatorial problems on utility-scale quantum hardware. <br/><br/>It abstracts away complexity by handling error suppression, efficient mapping, and hybrid quantum-classical optimization to solve optimization tasks at full device scale without deep quantum expertise. |\n",
     "\n",
     "## Get started with Qiskit Functions\n",
+    "Premium, Flex, and On-Prem (through the IBM Quantum Platform API) Plan users can get started with IBM Qiskit Functions for free, or can procure a license from one of the partners who have contributed a function to the catalog.\n",
     "\n",
     "### Request a free trial for third-party Qiskit Functions\n",
     "\n",
@@ -453,6 +484,23 @@
     "If a program status is `ERROR`, use `job.error_message()` to fetch the error message as follows:"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "qiskit.exceptions.QiskitError: 'Workflow execution failed -- https://docs.quantum.ibm.com/errors#9999'\n"
+     ]
+    }
+   ],
+   "source": [
+    "job.error_message()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "709b39ca-5dbd-42c0-830c-1248c2e5d63c",

docs/guides/global-data-quantum-optimizer.ipynb

@@ -921,6 +921,7 @@
     "*   Read [the associated research paper](https://arxiv.org/pdf/2412.19150).\n",
     "*   Request access to the function by filling in [this form](https://www.globaldataquantum.com/en/quantum-portfolio-optimizer/#form).\n",
     "*   Try the [Dynamic Portfolio Optimization](/docs/tutorials/global-data-quantum-optimizer) tutorial.\n",
+    "\n",
     "</Admonition>"
    ]
   }

docs/guides/kipu-optimization.ipynb

@@ -5,7 +5,7 @@
    "id": "f7d9993f",
    "metadata": {},
    "source": [
-    "{/* cspell:ignore Kipu, DCQO, QUBO, HUBO, counterdiabatic, Iskay, bitflips */}"
+    "{/* cspell:ignore Kipu, DCQO, QUBO, HUBO, counterdiabatic, Iskay, bitflips, Cadavid, Chandarana */}"
    ]
   },
   {
@@ -767,7 +767,11 @@
    "source": [
     "## Next steps\n",
     "\n",
-    "[Request access to the Quantum Optimizer by Kipu Quantum](https://share-eu1.hsforms.com/2Ff8cgWvTR9ukT_fPoaNhDw2dqpz5)"
+    "- [Request access to the Quantum Optimizer by Kipu Quantum](https://share-eu1.hsforms.com/2Ff8cgWvTR9ukT_fPoaNhDw2dqpz5)\n",
+    "- Try the [Solve the Market Split problem with Kipu Quantum's Iskay Quantum Optimizer](/docs/tutorials/solve-market-split-problem-with-iskay-quantum-optimizer) tutorial.\n",
+    "- Review [Romero, S. V., et al. (2025).  Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization. arXiv preprint arXiv:2409.04477.](https://arxiv.org/abs/2409.04477)\n",
+    "- Review [Cadavid, A. G., et al. (2024).  Bias-field digitized counterdiabatic quantum optimization. arXiv preprint arXiv:2405.13898.](https://arxiv.org/abs/2405.13898)\n",
+    "- Review [Chandarana, P., et al. (2025).  Runtime Quantum Advantage with Digital Quantum Optimization. arXiv preprint arXiv:2505.08663.](https://arxiv.org/abs/2505.08663)\n"
    ]
   },
   {

docs/guides/multiverse-computing-singularity.ipynb

@@ -5,7 +5,7 @@
    "id": "fe74e692",
    "metadata": {},
    "source": [
-    "{/* cspell:ignore hyperparameters */}"
+    "{/* cspell:ignore hyperparameters, Leclerc */}"
    ]
   },
   {
@@ -1096,6 +1096,7 @@
     "<Admonition type=\"tip\" title=\"Recommendations\">\n",
     "\n",
     "- Request access to [Multiverse Computing's Singularity Machine Learning Classification function](https://quantum.cloud.ibm.com/functions?id=multiverse-singularity).\n",
+    "- Review [Leclerc, L., et al. (2023). Financial risk management on a neutral atom quantum processor. Physical Review Research, 5, 043117.](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.043117)\n",
     "\n",
     "</Admonition>"
    ]

docs/guides/q-ctrl-optimization-solver.ipynb

@@ -1,5 +1,13 @@
 {
  "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "11ea9666",
+   "metadata": {},
+   "source": [
+    "{/* cspell:ignore Sachdeva */}"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "dde95705",
@@ -610,6 +618,12 @@
     "\n",
     "- Request access to [Q-CTRL Optimization Solver.](https://quantum.cloud.ibm.com/functions?id=q-ctrl-optimization-solver)\n",
     "- Try the [Solve higher-order binary optimization problems with Q-CTRL's Optimization Solver](/docs/tutorials/solve-higher-order-binary-optimization-problems-with-q-ctrls-optimization-solver) tutorial.\n",
+    "- Review [Sachdeva, N., et al. (2024).  Quantum optimization using a 127-qubit gate-model IBM quantum computer can outperform quantum annealers for nontrivial binary optimization problems. arXiv preprint arXiv:2406.01743.](https://arxiv.org/abs/2406.01743)\n",
+    "- Review [Loco, D., et al. (2026).  Practical protein-pocket hydration-site prediction for drug discovery on a quantum computer. arXiv preprint arXiv:2512.08390.](https://arxiv.org/abs/2512.08390)\n",
+    "- Review the [Mazda](https://q-ctrl.com/case-study/tackling-a-costly-bottleneck-in-automotive-design) case study.\n",
+    "- Review the [Network Rail](https://q-ctrl.com/case-study/accelerating-the-schedule-for-quantum-enhanced-rail) case study.\n",
+    "- Review the [Australian Army](https://q-ctrl.com/case-study/improving-army-logistics-with-quantum-computing) case study.\n",
+    "- Review the [Transport for New South Wales](https://q-ctrl.com/case-study/delivering-quantum-computing-for-faster-commuting) case study.\n",
     "\n",
     "</Admonition>"
    ]