Relativize documentation links in tutorials (#3101)

Fixes #3097.

Some of these links are quite old, so I made a request for each URL and
recorded the redirect. I then replaced `https://docs.quantum.ibm.com` ->
`/docs` in the redirect, then replaced the original URLs with these
paths.

Author: frankharkins

docs/tutorials/chsh-inequality.ipynb

@@ -332,7 +332,7 @@
    "id": "76b721cc-7f45-4195-ae61-53d29e2bf8d4",
    "metadata": {},
    "source": [
-    "Similarly, we need to transform the observables to make it backend compatible before running jobs with [`Runtime Estimator V2`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2#run). We can perform the transformation using the `apply_layout` the method of `SparsePauliOp` object."
+    "Similarly, we need to transform the observables to make it backend compatible before running jobs with [`Runtime Estimator V2`](/docs/api/qiskit-ibm-runtime/estimator-v2#run). We can perform the transformation using the `apply_layout` the method of `SparsePauliOp` object."
    ]
   },
   {
@@ -361,7 +361,7 @@
    "id": "2d8ad9e1",
    "metadata": {},
    "source": [
-    "We can create a [Qiskit Runtime `Estimator`](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2) primitive to compute our expectation values. The `EstimatorV2.run()` method takes an iterable of `primitive unified blocs (PUBs)`. Each PUB is an iterable in the format `(circuit, observables, parameter_values: Optional, precision: Optional)`."
+    "We can create a [Qiskit Runtime `Estimator`](/docs/api/qiskit-ibm-runtime/estimator-v2) primitive to compute our expectation values. The `EstimatorV2.run()` method takes an iterable of `primitive unified blocs (PUBs)`. Each PUB is an iterable in the format `(circuit, observables, parameter_values: Optional, precision: Optional)`."
    ]
   },
   {

docs/tutorials/combine-error-mitigation-techniques.ipynb

@@ -72,7 +72,7 @@
    "source": [
     "## Step 1: Map classical inputs to a quantum problem\n",
     "\n",
-    "This tutorial assumes that the classical problem has already been mapped to quantum. Begin by constructing a circuit and observable to measure. While the techniques used in this tutorial apply to many different kinds of circuits, for simplicity this tutorial uses the [`EfficientSU2`](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.EfficientSU2#efficientsu2) circuit included in Qiskit's circuit library.\n",
+    "This tutorial assumes that the classical problem has already been mapped to quantum. Begin by constructing a circuit and observable to measure. While the techniques used in this tutorial apply to many different kinds of circuits, for simplicity this tutorial uses the [`EfficientSU2`](/docs/api/qiskit/qiskit.circuit.library.EfficientSU2#efficientsu2) circuit included in Qiskit's circuit library.\n",
     "\n",
     "`EfficientSU2` is a parameterized quantum circuit designed to be efficiently executable on quantum hardware with limited qubit connectivity, while still being expressive enough to solve problems in application domains like optimization and chemistry. It's built by alternating layers of parameterized single-qubit gates with a layer containing a fixed pattern of two-qubit gates, for a chosen number of repetitions. The pattern of two-qubit gates can be specified by the user. Here you can use the built-in `pairwise` pattern because it minimizes the circuit depth by packing the two-qubit gates as densely as possible. This pattern can be executed using only linear qubit connectivity."
    ]
@@ -136,7 +136,7 @@
     "\n",
     "In the mirror circuit technique, you concatenate the circuit with its inverse circuit, which is formed by inverting each gate of the circuit in reverse order. The resulting circuit implements the identity operator, which can trivially be simulated. Because the structure of the original circuit is preserved in the mirror circuit, executing the mirror circuit still gives an idea of how the quantum device would perform on the original circuit.\n",
     "\n",
-    "The following code cell assigns random parameters to your circuit, and then constructs the mirror circuit using the [`UnitaryOverlap`](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.UnitaryOverlap#unitaryoverlap) class. Before mirroring the circuit, append a [barrier](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.Barrier#barrier) instruction to it to prevent the transpiler from merging the two parts of the circuit on either side of the barrier. Without the barrier, the transpiler would merge the original circuit with its inverse, resulting in a transpiled circuit without any gates."
+    "The following code cell assigns random parameters to your circuit, and then constructs the mirror circuit using the [`UnitaryOverlap`](/docs/api/qiskit/qiskit.circuit.library.UnitaryOverlap#unitaryoverlap) class. Before mirroring the circuit, append a [barrier](/docs/api/qiskit/circuit#qiskit.circuit.Barrier) instruction to it to prevent the transpiler from merging the two parts of the circuit on either side of the barrier. Without the barrier, the transpiler would merge the original circuit with its inverse, resulting in a transpiled circuit without any gates."
    ]
   },
   {
@@ -185,7 +185,7 @@
     "\n",
     "- Pick a qubit layout that maps the virtual qubits of your circuit to physical qubits on the hardware.\n",
     "- Insert swap gates as needed to route interactions between qubits that are not connected.\n",
-    "- Translate the gates in your circuit to [Instruction Set Architecture (ISA)](https://docs.quantum.ibm.com/transpile#instruction-set-architecture) instructions that can directly be executed on the hardware.\n",
+    "- Translate the gates in your circuit to [Instruction Set Architecture (ISA)](/docs/guides/transpile#instruction-set-architecture) instructions that can directly be executed on the hardware.\n",
     "- Perform circuit optimizations to minimize the circuit depth and gate count.\n",
     "\n",
     "The transpiler built into Qiskit can perform all of these steps for you. Because this tutorial uses a hardware-efficient circuit, the transpiler should be able to pick a qubit layout that does not require any swap gates to be inserted for routing interactions.\n",
@@ -211,7 +211,7 @@
    "id": "0b607d83-e7a2-4c03-83c9-3b52d23f8772",
    "metadata": {},
    "source": [
-    "You can transpile your circuit for your chosen backend by creating a pass manager and then running the pass manager on the circuit. An easy way to create a pass manager is to use the [`generate_preset_pass_manager`](https://docs.quantum.ibm.com/api/qiskit/transpiler_preset#qiskit.transpiler.preset_passmanagers.generate_preset_pass_manager) function. See [Transpile with pass managers](https://docs.quantum.ibm.com/transpile/transpile-with-pass-managers) for a more detailed explanation of transpiling with pass managers."
+    "You can transpile your circuit for your chosen backend by creating a pass manager and then running the pass manager on the circuit. An easy way to create a pass manager is to use the [`generate_preset_pass_manager`](/docs/api/qiskit/qiskit.transpiler.generate_preset_pass_manager) function. See [Transpile with pass managers](/docs/guides/transpile-with-pass-managers) for a more detailed explanation of transpiling with pass managers."
    ]
   },
   {
@@ -246,9 +246,9 @@
    "id": "761595f3-99bd-4a75-b493-e1a89afce6f6",
    "metadata": {},
    "source": [
-    "The transpiled circuit now contains only ISA instructions. The single-qubit gates have been decomposed in terms of $\\sqrt{X}$ gates and $R_z$ rotations, and the CX gates have been decomposed into [ECR gates](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.ECRGate#ecrgate) and single-qubit rotations.\n",
+    "The transpiled circuit now contains only ISA instructions. The single-qubit gates have been decomposed in terms of $\\sqrt{X}$ gates and $R_z$ rotations, and the CX gates have been decomposed into [ECR gates](/docs/api/qiskit/qiskit.circuit.library.ECRGate#ecrgate) and single-qubit rotations.\n",
     "\n",
-    "The transpilation process has mapped the virtual qubits of the circuit to physical qubits on the hardware. The information about the qubit layout is stored in the `layout` attribute of the transpiled circuit. The observable was also defined in terms of the virtual qubits, so you need to apply this layout to the observable, which you can do with the [`apply_layout`](https://docs.quantum.ibm.com/api/qiskit/qiskit.quantum_info.SparsePauliOp#apply_layout) method of `SparsePauliOp`."
+    "The transpilation process has mapped the virtual qubits of the circuit to physical qubits on the hardware. The information about the qubit layout is stored in the `layout` attribute of the transpiled circuit. The observable was also defined in terms of the virtual qubits, so you need to apply this layout to the observable, which you can do with the [`apply_layout`](/docs/api/qiskit/qiskit.quantum_info.SparsePauliOp#apply_layout) method of `SparsePauliOp`."
    ]
   },
   {
@@ -292,12 +292,12 @@
     "\n",
     "Here you will submit five separate jobs, starting with no error suppression or mitigation, and successively enabling various error suppression and mitigation options available in Qiskit Runtime. For information about the options, refer to the following pages:\n",
     "\n",
-    "- [Overview of all options](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/options)\n",
-    "- [Dynamical decoupling](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions)\n",
-    "- [Resilience, including measurement error mitigation and zero-noise extrapolation (ZNE)](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.ResilienceOptionsV2)\n",
-    "- [Twirling](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.TwirlingOptions)\n",
+    "- [Overview of all options](/docs/api/qiskit-ibm-runtime/options)\n",
+    "- [Dynamical decoupling](/docs/api/qiskit-ibm-runtime/options-dynamical-decoupling-options)\n",
+    "- [Resilience, including measurement error mitigation and zero-noise extrapolation (ZNE)](/docs/api/qiskit-ibm-runtime/options-resilience-options-v2)\n",
+    "- [Twirling](/docs/api/qiskit-ibm-runtime/options-twirling-options)\n",
     "\n",
-    "Because these jobs can run independently of each other, you can use [batch mode](https://docs.quantum.ibm.com/run/run-jobs-batch) to allow Qiskit Runtime to optimize the timing of their execution."
+    "Because these jobs can run independently of each other, you can use [batch mode](/docs/guides/run-jobs-batch) to allow Qiskit Runtime to optimize the timing of their execution."
    ]
   },
   {

docs/tutorials/depth-reduction-with-circuit-cutting.ipynb

@@ -69,7 +69,7 @@
    "source": [
     "## Step 1: Map classical inputs to a quantum problem\n",
     "\n",
-    "We will implement our Qiskit Pattern using the four steps outlined in the [docs](https://docs.quantum.ibm.com/guides/intro-to-patterns). In this case, we will simulate expectation values on a circuit of a certain depth by cutting gates resulting in swap gates and executing subexperiments on shallower circuits. Gate cutting is relevant for Steps 2 (optimize circuit for quantum execution by decomposing distant gates) and 4 (post-processing to reconstruct expectation values on original circuit).\n",
+    "We will implement our Qiskit Pattern using the four steps outlined in the [docs](/docs/guides/intro-to-patterns). In this case, we will simulate expectation values on a circuit of a certain depth by cutting gates resulting in swap gates and executing subexperiments on shallower circuits. Gate cutting is relevant for Steps 2 (optimize circuit for quantum execution by decomposing distant gates) and 4 (post-processing to reconstruct expectation values on original circuit).\n",
     "In the first step, we'll generate a circuit from the Qiskit circuit library and define some observables.\n",
     "\n",
     "*   Input: Classical parameters to define a circuit\n",

docs/tutorials/error-mitigation-with-qiskit-functions.ipynb

@@ -14,9 +14,9 @@
    "id": "34260848-be4c-45f7-914f-9d9bcc2be504",
    "metadata": {},
    "source": [
-    "In this notebook, we will walk through an example of building and running a workflow using the IBM Circuit function. This function takes [Primitive Unified Blocs](https://docs.quantum.ibm.com/guides/primitive-input-output) (PUBs) as inputs and returns error-mitigated expectation values as outputs. It provides an automated and customized pipeline to optimize circuits and execute on quantum hardware so that researchers can focus on algorithm and application discovery.\n",
+    "In this notebook, we will walk through an example of building and running a workflow using the IBM Circuit function. This function takes [Primitive Unified Blocs](/docs/guides/primitive-input-output) (PUBs) as inputs and returns error-mitigated expectation values as outputs. It provides an automated and customized pipeline to optimize circuits and execute on quantum hardware so that researchers can focus on algorithm and application discovery.\n",
     "\n",
-    "Visit the documentation for an [introduction to Qiskit Functions](https://docs.quantum.ibm.com/guides/functions) and learn how to get started with the [IBM Circuit function](https://docs.quantum.ibm.com/guides/ibm-circuit-function)."
+    "Visit the documentation for an [introduction to Qiskit Functions](/docs/guides/functions) and learn how to get started with the [IBM Circuit function](/docs/guides/ibm-circuit-function)."
    ]
   },
   {
@@ -308,7 +308,7 @@
    "id": "34f5d0f9-f3ac-4362-ac8c-fd4d02fec265",
    "metadata": {},
    "source": [
-    "Now, we can pass the abstract circuit and observables to the IBM Circuit function. It will handle transpilation and execution on quantum hardware for us and return mitigated expectation values. First, we load the function from the [IBM Qiskit Functions Catalog](https://docs.quantum.ibm.com/guides/functions)."
+    "Now, we can pass the abstract circuit and observables to the IBM Circuit function. It will handle transpilation and execution on quantum hardware for us and return mitigated expectation values. First, we load the function from the [IBM Qiskit Functions Catalog](/docs/guides/functions)."
    ]
   },
   {
@@ -346,7 +346,7 @@
    "id": "082883fc-22fa-4539-a4e2-9f3ef97d7334",
    "metadata": {},
    "source": [
-    "We can also configure the `options` for transpilation, error suppression, and error mitigation. Default settings will be used if we don't wish to specify these. The IBM Circuit function comes with commonly used options for `optimization_level`, which controls how much circuit optimization to perform, and `mitigation_level`, which specifies how much error suppression and mitigation to apply. Note that the `mitigation_level` of the IBM Circuit function is distinct from the `resilience_level` used in the [Qiskit Runtime Estimator](https://docs.quantum.ibm.com/guides/configure-error-mitigation). For a detailed description of these commonly used options as well as other advanced options, visit the [documentation for the IBM Circuit function](http://docs.quantum.ibm.com/guides/ibm-circuit-function).\n",
+    "We can also configure the `options` for transpilation, error suppression, and error mitigation. Default settings will be used if we don't wish to specify these. The IBM Circuit function comes with commonly used options for `optimization_level`, which controls how much circuit optimization to perform, and `mitigation_level`, which specifies how much error suppression and mitigation to apply. Note that the `mitigation_level` of the IBM Circuit function is distinct from the `resilience_level` used in the [Qiskit Runtime Estimator](/docs/guides/configure-error-mitigation). For a detailed description of these commonly used options as well as other advanced options, visit the [documentation for the IBM Circuit function](http://docs.quantum.ibm.com/guides/ibm-circuit-function).\n",
     "\n",
     "In this tutorial, we will set the `default_precision`, `optimization_level: 3` and `mitigation_level: 3`, which will turn on gate twirling and Zero Noise Extrapolation (ZNE) via Probabilistic Error Amplification (PEA) on top of the default level 1 settings."
    ]
@@ -409,7 +409,7 @@
    "id": "e510ff6e-7022-48c6-b146-6e48611d7d12",
    "metadata": {},
    "source": [
-    "The result from running the function has the same format as the [Estimator](https://docs.quantum.ibm.com/guides/primitive-input-output#estimator-output)."
+    "The result from running the function has the same format as the [Estimator](/docs/guides/primitive-input-output#estimator-output)."
    ]
   },
   {

docs/tutorials/krylov-quantum-diagonalization.ipynb

@@ -423,7 +423,7 @@
    "source": [
     "#### Time evolution\n",
     "\n",
-    "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$ via the [Lie-Trotter approximation](https://docs.quantum.ibm.com/api/qiskit/qiskit.synthesis.LieTrotter)."
+    "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$ via the [Lie-Trotter approximation](/docs/api/qiskit/qiskit.synthesis.LieTrotter)."
    ]
   },
   {

docs/tutorials/long-range-entanglement.ipynb

@@ -230,7 +230,7 @@
    "source": [
     "#### Set primary parameters\n",
     "\n",
-    "In this section are definitions for some common parameters that you will use later. You'll need to specify these parameters for a particular backend. In order to do so, you will need an account on [IBM Quantum™ Platform](https://quantum-computing.ibm.com/). More details on how to initialize your account can be found in the [documentation](https://docs.quantum.ibm.com/start/setup-channel#set-up-to-use-ibm-quantum-platform)."
+    "In this section are definitions for some common parameters that you will use later. You'll need to specify these parameters for a particular backend. In order to do so, you will need an account on [IBM Quantum™ Platform](https://quantum-computing.ibm.com/). More details on how to initialize your account can be found in the [documentation](/docs/guides/setup-channel#set-up-to-use-ibm-quantum-platform)."
    ]
   },
   {

docs/tutorials/nishimori-phase-transition.ipynb

@@ -364,7 +364,7 @@
    "source": [
     "## Step 2: Optimize problem for quantum hardware execution\n",
     "\n",
-    "Transpiling quantum circuits for execution on hardware typically involves a [number of stages](https://docs.quantum.ibm.com/guides/transpiler-stages). Typically, the stages that incur the most computational overhead are choosing the qubit layout, routing the two-qubit gates to conform to the qubit connectivity of the hardware, and optimizing the circuit to minimize its gate count and depth. In the GEM protocol, the layout and routing stages are unnecessary because the hardware connectivity is already incorporated into the design of the protocol. The circuits already have a qubit layout, and the two-qubit gates are already mapped onto native connections. Furthermore, in order to preserve the structure of the circuit as the $R_{ZZ}$ angle is varied, only very basic circuit optimization should be performed.\n",
+    "Transpiling quantum circuits for execution on hardware typically involves a [number of stages](/docs/guides/transpiler-stages). Typically, the stages that incur the most computational overhead are choosing the qubit layout, routing the two-qubit gates to conform to the qubit connectivity of the hardware, and optimizing the circuit to minimize its gate count and depth. In the GEM protocol, the layout and routing stages are unnecessary because the hardware connectivity is already incorporated into the design of the protocol. The circuits already have a qubit layout, and the two-qubit gates are already mapped onto native connections. Furthermore, in order to preserve the structure of the circuit as the $R_{ZZ}$ angle is varied, only very basic circuit optimization should be performed.\n",
     "\n",
     "The `GemExperiment` class transparently transpiles circuits when executing the experiment. The layout and routing stages are already overridden by default to do nothing, and circuit optimization is performed at a level that only optimizes single-qubit gates. However, you can override or pass additional options using the `set_transpile_options` method. For the sake of visualization, the following code cell manually transpiles the circuit displayed previously, and draws the transpiled circuit."
    ]