Proper trademarking of IBM and third-party names (#746)

Closes #726 

The first instance on a page of every trademarked name (whether IBM or
third-party) should be marked with the trademark symbol (except in
headings, where the code will not render as a symbol).

Outstanding questions: Where does the trademark symbol occur if the
following are the first instance on a page?:
(editing to add: preliminary guidance directs us as follows: )

- [ ] IBM Quantum™ systems
- [ ] Qiskit® Runtime service
- [ ] Qiskit® Runtime
- [ ] Qiskit IBM Provider (still unknown)
- [ ] Qiskit® Patterns
- [ ] Qiskit® Experiments
- [ ] Qiskit® 1.0
- [ ] Qiskit® Runtime IBM Client
- [ ] Qiskit® Runtime IBM REST API
- [ ] IBM Quantum™ Network

References: 
https://www.ibm.com/brand/experience-guides/quantum/voice#usage
https://www.ibm.com/legal/copyright-trademark


### Progress

- [x] Migration guides
- [x] Start
- [x] Build
- [x] Transpile
- [x] Verify
- [x] Run
- [x] Support

---------

Co-authored-by: Eric Arellano <[email protected]>

README.md

@@ -12,7 +12,7 @@ Read on for more information about how to support this project:
 
 ### 1. Report bugs, inaccuracies or general content issues
 
-This is the quickest, easiest, and most helpful way to contribute to this project and improve the quality of Qiskit and IBM Quantum documentation. There are a few different ways to report issues, depending on where it was found:
+This is the quickest, easiest, and most helpful way to contribute to this project and improve the quality of Qiskit® and IBM Quantum™ documentation. There are a few different ways to report issues, depending on where it was found:
 
 - For problems you've found in the [Qiskit API Reference](https://docs.quantum.ibm.com/api/qiskit) section, open an issue in the Qiskit repo [here](https://github.com/Qiskit/qiskit/issues/new/choose).
 - For problems you've found in the [Qiskit Runtime IBM Client](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime) section, open an issue in the Qiskit IBM Runtime repo [here](https://github.com/Qiskit/qiskit-ibm-runtime/issues/new/choose).
@@ -541,3 +541,32 @@ To display a qasm operation (like a not gate), you can use the `Operation` compo
 ```mdx
 <Operation name="x" />
 ```
+
+## Proper marking and attribution
+
+**All information needs to identify, mark, and attribute IBM and applicable third-party trademarks.** We do this the first time an IBM trademark appears on each page. See the [Copyright and trademark information](https://www.ibm.com/legal/copyright-trademark) page for more details.
+
+Some companies require a special attribution notice. View a list of the companies to include in a special attribution notice at the [Special attributions](https://www.ibm.com/legal/copyright-trademark#special) section of the IBM Legal site.
+
+<details>
+<summary>A (non-exhaustive) list of trademarked names found in our docs:</summary>
+
+- IBM&reg;
+- IBM Cloud&reg;
+- IBM Quantum&trade;
+- Qiskit&reg;
+</details>
+
+See the Usage section of the IBM Quantum Experience Guide for guidance on when to use IBM and when to use IBM Quantum.
+
+### Trademark symbols
+
+To create the symbols in markdown:
+
+Use `&reg;` to get &reg; for registered trademarks.
+
+use `&trade;` to get &trade; for nonregistered trademarks.
+
+<Admonition type="caution">
+  Do not include trademarks in headings. The code will display rather than the symbol.
+</Admonition

docs/api/migration-guides/index.mdx

@@ -6,7 +6,7 @@ description: Migrate to using the newest from Qiskit and Qiskit Runtime
 
 # Introduction
 
-We've prepared various migration guides to help you more effectively use Qiskit and Qiskit Runtime:
+We've prepared various migration guides to help you more effectively use Qiskit® and Qiskit Runtime:
 
 * Migrate to Qiskit Runtime
    * [How to migrate](./qiskit-runtime)
@@ -15,4 +15,4 @@ We've prepared various migration guides to help you more effectively use Qiskit
 * Qiskit 0.44 changes
    * [`qiskit.algorithms` new interface](./qiskit-algorithms-module)
    * [`qiskit.opflow` deprecation](./qiskit-opflow-module)
-   * [`QuantumIntance` deprecation](./qiskit-quantum-instance)
+   * [`QuantumInstance` deprecation](./qiskit-quantum-instance)

docs/api/migration-guides/qiskit-1.0.mdx

@@ -5,7 +5,7 @@ description: Adapt to changes in installing and depending on Qiskit 1.0
 
 # Qiskit 1.0 packaging changes
 
-Qiskit 1.0 uses a different packaging structure than previous Qiskit versions and might cause problems in environments that use packages that are not ready for Qiskit 1.0.
+Qiskit® 1.0 uses a different packaging structure than previous Qiskit versions and might cause problems in environments that use packages that are not ready for Qiskit 1.0.
 
 <Admonition type="caution">
 Do not try to upgrade an existing Python virtual environment to Qiskit 1.0 in-place.
@@ -397,7 +397,7 @@ Further complications aren't necessary to understand the problems described in t
 
 ### The old Qiskit structure
 
-Historically, Qiskit was comprised of many Python distributions: `qiskit-terra`, the compiler core; `qiskit-aer`, the high-performance simulator; the original IBM Quantum provider; and several now-obsolete packages providing particular exploratory algorithmic or experiment-running features.
+Historically, Qiskit was comprised of many Python distributions: `qiskit-terra`, the compiler core; `qiskit-aer`, the high-performance simulator; the original IBM Quantum&trade; provider; and several now-obsolete packages providing particular exploratory algorithmic or experiment-running features.
 For user ease, we also provided a Python distribution called `qiskit`, which contained no code of its own, but caused all the other components to be installed.
 We called this the _metapackage_, by analogy to similar concepts in other package managers.
 The code of the core of Qiskit lived in `qiskit-terra`, which owned the root of the Python package `qiskit`. In other words, `qiskit-terra` controlled what happened when you ran `import qiskit`.
@@ -467,7 +467,7 @@ Exit Jupyter, activate the Qiskit virtual environment on the command line, run `
 
 ### `import qiskit` succeeds, but trying to do anything returns "AttributeError: module 'qiskit' has no attribute '...'"
 
-This likely means that your environment had an old version of Qiskit in it alongside a package that extended its namespace (such as old versions of Qiskit Aer, or the long-obsolete Qiskit IBMQ Provider), and then Qiskit was uninstalled.
+This likely means that your environment had an old version of Qiskit in it alongside a package that extended its namespace (such as old versions of Qiskit Aer, or the long-obsolete Qiskit IBM Q&reg; Provider), and then Qiskit was uninstalled.
 The easiest thing to do is to start a new virtual environment, and only install recent, non-obsolete packages into it.
 
 If you have just started a new virtual environment, or you're sure that legacy packages are not the problem, make sure that your current working directory (the directory your shell session was in when you launched Python / Jupyter) does not contain a folder called `qiskit`.

docs/api/migration-guides/qiskit-algorithms-module.mdx

@@ -5,7 +5,7 @@ description: Use the new interface for `qiskit.algorithms`
 
 # Algorithms migration guide
 
-  In Qiskit 0.44 and later releases, the `qiskit.algorithms` module has been superseded by a new standalone library, `qiskit_algorithms`,
+  In Qiskit® 0.44 and later releases, the `qiskit.algorithms` module has been superseded by a new standalone library, `qiskit_algorithms`,
   available on [GitHub](https://github.com/qiskit-community/qiskit-algorithms) and 
   [PyPi](https://pypi.org/project/qiskit-algorithms). The `qiskit.algorithms` module  was migrated to a
   separate package in order to clarify the purpose of Qiskit and make a distinction between the tools and libraries built on top of it.
@@ -86,7 +86,7 @@ Once you know which primitive you want to use, choose the primitive implementati
 
 * For running on quantum hardware choose from these options:
 
-   - Access services with native primitive implementations, such as the IBM Qiskit Runtime service by using [`qiskit_ibm_runtime.Sampler`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler) and [`qiskit_ibm_runtime.Estimator`.](../qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator)
+   - Access services with native primitive implementations, such as the Qiskit Runtime service by using [`qiskit_ibm_runtime.Sampler`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler) and [`qiskit_ibm_runtime.Estimator`.](../qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator)
    - Wrap any system with `Backend` primitives ([`qiskit.primitives.BackendSampler`](../qiskit/qiskit.primitives.BackendSampler) and [`qiskit.primitives.BackendEstimator`](../qiskit/qiskit.primitives.BackendEstimator)). These wrappers implement a primitive interface on top of a backend that only supports `backend.run()`.
 
 For detailed information and examples, particularly on the use of the `Backend` primitives, refer to

docs/api/migration-guides/qiskit-opflow-module.mdx

@@ -8,7 +8,7 @@ description: Stop using the deprecated `qiskit.opflow` module
 The new [`qiskit.primitives`](../qiskit/primitives), in combination with the [`qiskit.quantum_info`](../qiskit/quantum_info) module, have superseded
 functionality of [`qiskit.opflow`](../qiskit/0.44/opflow), which is being deprecated.
 
-This migration guide contains instructions and code examples to migrate code that uses 
+This migration guide contains instructions and code examples to migrate Qiskit® code that uses 
 the [`qiskit.opflow`](../qiskit/0.44/opflow) module to the [`qiskit.primitives`](../qiskit/primitives) and [`qiskit.quantum_info`](../qiskit/quantum_info) modules.
 
 <Admonition type="note">
@@ -20,7 +20,7 @@ the [`qiskit.opflow`](../qiskit/0.44/opflow) module to the [`qiskit.primitives`]
 <span id="attention_primitives"></span>
 <Admonition type="note">
   Most references to the [`qiskit.primitives.Sampler`](../qiskit/qiskit.primitives.Sampler) or [`qiskit.primitives.Estimator`](../qiskit/qiskit.primitives.Estimator) in this guide
-  can be replaced with instances of any primitive implementation. For example Aer primitives ([`qiskit_aer.primitives.Sampler`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Sampler.html)/[`qiskit_aer.primitives.Estimator`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html)) or the IBM Qiskit Runtime primitives ([`qiskit_ibm_runtime.Sampler`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler)/[`qiskit_ibm_runtime.Estimator`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator)).
+  can be replaced with instances of any primitive implementation. For example Aer primitives ([`qiskit_aer.primitives.Sampler`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Sampler.html)/[`qiskit_aer.primitives.Estimator`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html)) or the Qiskit Runtime primitives ([`qiskit_ibm_runtime.Sampler`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler)/[`qiskit_ibm_runtime.Estimator`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator)).
   Specific systems can be wrapped with ([`qiskit.primitives.BackendSampler`](../qiskit/qiskit.primitives.BackendSampler), [`qiskit.primitives.BackendEstimator`](../qiskit/qiskit.primitives.BackendEstimator)) to also present primitive-compatible interfaces.
 
   Certain classes, such as the
@@ -91,9 +91,9 @@ These were mainly used for didactic purposes or quick prototyping and can easily
 [`qiskit.quantum_info`](../qiskit/quantum_info) class: [`qiskit.quantum_info.Pauli`](../qiskit/qiskit.quantum_info.Pauli), [`qiskit.quantum_info.Clifford`](../qiskit/qiskit.quantum_info.Clifford) or
 [`qiskit.quantum_info.Statevector`](../qiskit/qiskit.quantum_info.Statevector).
 
-### 1-qubit paulis
+### Single-qubit Paulis
 
-The 1-qubit paulis were commonly used for algorithm testing, as they could be combined to create more complex operators
+The single-qubit Paulis were commonly used for algorithm testing, as they could be combined to create more complex operators
 (for example, `0.39 * (I ^ Z) + 0.5 * (X ^ X)`).
 These operations implicitly created operators of type  [`qiskit.opflow.primitive_ops.PauliSumOp`](../qiskit/0.44/qiskit.opflow.primitive_ops.PauliSumOp), and can be replaced by
 directly creating a corresponding [`qiskit.quantum_info.SparsePauliOp`](../qiskit/qiskit.quantum_info.SparsePauliOp), as shown in the following examples.
@@ -477,7 +477,7 @@ or [`qiskit.opflow.state_fns`](../qiskit/0.44/qiskit.opflow.state_fns). The [`qi
 
 | Opflow | Alternative |
 | --- | --- |
-| [`qiskit.opflow.list_ops.ListOp`](../qiskit/0.44/qiskit.opflow.list_ops.ListOp) | No direct replacement. This is the base class for operator lists. In general, these could be replaced with a Python `list`s. For [`qiskit.quantum_info.Pauli`](../qiskit/qiskit.quantum_info.Pauli) operators, there are a few alternatives, depending on the use case. One alternative is [`qiskit.quantum_info.PauliList`](../qiskit/qiskit.quantum_info.PauliList). |
+| [`qiskit.opflow.list_ops.ListOp`](../qiskit/0.44/qiskit.opflow.list_ops.ListOp) | No direct replacement. This is the base class for operator lists. In general, these could be replaced with a Python `list`. For [`qiskit.quantum_info.Pauli`](../qiskit/qiskit.quantum_info.Pauli) operators, there are a few alternatives, depending on the use case. One alternative is [`qiskit.quantum_info.PauliList`](../qiskit/qiskit.quantum_info.PauliList). |
 | [`qiskit.opflow.list_ops.ComposedOp`](../qiskit/0.44/qiskit.opflow.list_ops.ComposedOp) | No direct replacement. Current workflows do not require composing states and operators within one object (no lazy evaluation). |
 | [`qiskit.opflow.list_ops.SummedOp`](../qiskit/0.44/qiskit.opflow.list_ops.SummedOp) | No direct replacement. For [`qiskit.quantum_info.Pauli`](../qiskit/qiskit.quantum_info.Pauli) operators, use [`qiskit.quantum_info.SparsePauliOp`](../qiskit/qiskit.quantum_info.SparsePauliOp). |
 | [`qiskit.opflow.list_ops.TensoredOp`](../qiskit/0.44/qiskit.opflow.list_ops.TensoredOp) | No direct replacement. For [`qiskit.quantum_info.Pauli`](../qiskit/qiskit.quantum_info.Pauli) operators, use [`qiskit.quantum_info.SparsePauliOp`](../qiskit/qiskit.quantum_info.SparsePauliOp). |

docs/api/migration-guides/qiskit-quantum-instance.mdx

@@ -28,7 +28,7 @@ The remainder of this guide focused on the [`qiskit.utils.QuantumInstance.execut
 [`qiskit.primitives`](../qiskit/primitives) migration path.
 
 <Admonition type="caution">
-  **Background on the Qiskit primitives**
+  **Background on the Qiskit&reg; primitives**
 
   The Qiskit primitives are algorithmic abstractions that encapsulate system or simulator access for easy integration into algorithm workflows.
 
@@ -39,14 +39,14 @@ The remainder of this guide focused on the [`qiskit.utils.QuantumInstance.execut
   wrappers for `backend.run()` that follow the primitives interface.
 
   Providers can implement these primitives as subclasses of [`qiskit.primitives.BaseSampler`](../qiskit/qiskit.primitives.BaseSampler) and [`qiskit.primitives.BaseEstimator`](../qiskit/qiskit.primitives.BaseEstimator), respectively.
-  IBM Qiskit Runtime ([`qiskit_ibm_runtime`](../qiskit-ibm-runtime/qiskit_ibm_runtime.QiskitRuntimeService)) and Aer ([`qiskit_aer.primitives`](https://qiskit.org/ecosystem/aer/apidocs/aer_primitives.html)) are examples of native implementations of primitives.
+  Qiskit Runtime ([`qiskit_ibm_runtime`](../qiskit-ibm-runtime/qiskit_ibm_runtime.QiskitRuntimeService)) and Aer ([`qiskit_aer.primitives`](https://qiskit.org/ecosystem/aer/apidocs/aer_primitives.html)) are examples of native implementations of primitives.
 
   This guide uses the following naming convention:
 
   - *Primitives* - Any Sampler or Estimator implementation using base classes [`qiskit.primitives.BackendSampler`](../qiskit/qiskit.primitives.BackendSampler) and a [`qiskit.primitives.BackendEstimator`](../qiskit/qiskit.primitives.BackendEstimator).
   - *Reference primitives* -  [`qiskit.primitives.Sampler`](../qiskit/qiskit.primitives.Sampler) and [`qiskit.primitives.Estimator`](../qiskit/qiskit.primitives.Estimator) are reference implementations that come with Qiskit.
   - *Aer primitives* - The [Aer](https://qiskit.org/ecosystem/aer) primitive implementations [`qiskit_aer.primitives.Sampler`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Sampler.html) and [`qiskit_aer.primitives.Estimator`](https://qiskit.org/ecosystem/aer/stubs/qiskit_aer.primitives.Estimator.html).
-  - *Qiskit Runtime primitives* - The IBM Qiskit Runtime primitive implementations [`qiskit_ibm_runtime.Sampler`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler) and [`qiskit_ibm_runtime.Estimator`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator).
+  - *Qiskit Runtime primitives* - The Qiskit Runtime primitive implementations [`qiskit_ibm_runtime.Sampler`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler) and [`qiskit_ibm_runtime.Estimator`](../qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator).
   - *`Backend` primitives* - Instances of [`qiskit.primitives.BackendSampler`](../qiskit/qiskit.primitives.BackendSampler) and [`qiskit.primitives.BackendEstimator`](../qiskit/qiskit.primitives.BackendEstimator). These allow any system to implement primitive interfaces.
 
 </Admonition>

docs/api/migration-guides/qiskit-runtime-examples.mdx

@@ -6,7 +6,7 @@ description: Examples of migrating from using backend.run to using Qiskit Runtim
 
 # Migration examples
 
-Follow these examples to design a Qiskit Runtime algorithm.
+Follow these examples to design a Qiskit® Runtime algorithm.
 
 <span id="estimator-algorithm"></span>
 ## Use Estimator to design an algorithm

docs/api/migration-guides/qiskit-runtime-from-provider.mdx

@@ -5,7 +5,7 @@ description: How to migrate `backend.run()` from Qiskit IBM Provider to Qiskit I
 
 # Migrate `backend.run()` from `qiskit_ibm_provider` to `qiskit_ibm_runtime`
 
-The Qiskit Runtime interface includes two packages:
+The Qiskit® Runtime interface includes two packages:
 Qiskit IBM Provider (the [`qiskit_ibm_provider`](../qiskit-ibm-provider) package) and
 Qiskit IBM Runtime (the [`qiskit_ibm_runtime`](../qiskit-ibm-runtime) package). Until now,
 primitives (`Sampler` and `Estimator`)
@@ -16,7 +16,7 @@ In the `qiskit-ibm-runtime` 0.15 release, we added support for running custom ci
 so users can run all programs through Runtime.
 
 This guide describes how to migrate code that implemented `IBMBackend.run()`
-using Qiskit IBM Provider to use Qiskit IBM Runtime instead.
+using qiskit_ibm_provider to use qiskit_ibm_runtime instead.
 
 **Example 1: Straightforward execution of IBMBackend.run()**
 

docs/api/migration-guides/qiskit-runtime.mdx

@@ -11,11 +11,11 @@ in_page_toc_max_heading_level: 2
 
 This guide describes key patterns of behavior and use cases with code
 examples to help you migrate code from the legacy `qiskit-ibmq-provider`
-package to use the Qiskit Runtime primitives.
+package to use the Qiskit® Runtime primitives.
 
 ## Overview
 
-There are two methods for accessing IBM Quantum systems. First, the `qiskit-ibm-provider` package provides the `backend.run()` interface, allowing direct access to IBM Quantum systems with no pre- or post-processing involved. This level of access is suitable for those users who want **precise control** over circuit execution and result processing. This level of access is needed for those at the level of kernel developer who are looking to develop, for example, circuit optimization routines or error mitigation techniques, or who want to characterize quantum systems.
+There are two methods for accessing IBM Quantum™ systems. First, the `qiskit-ibm-provider` package provides the `backend.run()` interface, allowing direct access to IBM Quantum systems with no pre- or post-processing involved. This level of access is suitable for those users who want **precise control** over circuit execution and result processing. This level of access is needed for those at the level of kernel developer who are looking to develop, for example, circuit optimization routines or error mitigation techniques, or who want to characterize quantum systems.
 
 In contrast, Qiskit Runtime is designed to **streamline algorithm and application construction** by removing the need for users to understand technical hardware and low-level software details. Advanced processing techniques for error suppression and mitigation are automatically applied, giving users high-fidelity results without the burden of having to code these routines themselves. Sessions within Qiskit Runtime allow users to run iterative algorithm circuits back to back, or batch collections of circuits without having to re-queue each job. This results in more efficient quantum processor use and reduces the time users spend running complex computations.
 

docs/build/bit-ordering.mdx

@@ -11,7 +11,7 @@ these bits both in computer memory and when displayed on-screen.
 
 ## Qiskit conventions
 
-Here's how Qiskit orders bits in different scenarios.
+Here's how Qiskit® orders bits in different scenarios.
 
 ### Quantum circuits
 
@@ -75,7 +75,7 @@ usually write numbers with the most significant digit on the left, and in
 Qiskit, bit $n$ is interpreted as the most significant bit.
 
 For example, the following cell defines a `Statevector` from a string of
-single-qubit states. In this case, qubit $0$ is in state $|{+}\rangle$, and
+single-qubit states. In this case, qubit $0$ is in state $|+\rangle$, and
 qubit $1$ in state $|0\rangle$.
 
 ```python