diff --git a/.github/workflows/cla_assistant.yml b/.github/workflows/cla_assistant.yml
index 58b2b51..e725bee 100644
--- a/.github/workflows/cla_assistant.yml
+++ b/.github/workflows/cla_assistant.yml
@@ -13,7 +13,7 @@ jobs:
steps:
- name: "CLA Assistant"
if: (github.event.comment.body == 'recheck' || github.event.comment.body == 'I have read the Contributor License Agreement and I hereby accept the Terms.') || github.event_name == 'pull_request_target'
- uses: cla-assistant/github-action@v2.1.3-beta
+ uses: cla-assistant/github-action@v2.3.1
env:
GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
PERSONAL_ACCESS_TOKEN : ${{ secrets.CLA_BOT_ACCESS_TOKEN }}
@@ -26,4 +26,4 @@ jobs:
custom-pr-sign-comment: 'I have read the Contributor License Agreement and I hereby accept the Terms.'
allowlist: user1,bot*
# edit the path below (if needed) to point to the document containing the CLA that a contributor agrees to
- path-to-document: 'https://github.com/qir-alliance/qir-spec/blob/main/Contributor_License_Agreement.md'
+ path-to-document: 'https://github.com/qir-alliance/qir-spec/blob/main/Contributor_License_Agreement.md'
diff --git a/.github/workflows/link_and_spell_check.yml b/.github/workflows/link_and_spell_check.yml
index f18bc5e..b24aeca 100644
--- a/.github/workflows/link_and_spell_check.yml
+++ b/.github/workflows/link_and_spell_check.yml
@@ -11,7 +11,7 @@ jobs:
runs-on: ubuntu-latest
name: "Check spelling, linting and links"
steps:
- - uses: actions/checkout@v2
+ - uses: actions/checkout@v4
- run: |
wget https://github.com/qir-alliance/.github/archive/refs/heads/main.zip -O clone.zip &&
unzip clone.zip && mv .github-main out && rm clone.zip &&
@@ -38,11 +38,10 @@ jobs:
if: ${{ success() || failure() }}
- name: "Check spelling in changed files"
# cspell:words streetsidesoftware
- uses: streetsidesoftware/cspell-action@v1.2.4
+ uses: streetsidesoftware/cspell-action@v6
with:
inline: warning
# Only warn on spelling errors, since there's likely a lot of false
# positives with terminology in quantum computing.
strict: false
incremental_files_only: true
- config: 'utils/spelling_allowlist.json'
diff --git a/.markdownlint.yaml b/.markdownlint.yaml
new file mode 100644
index 0000000..e97ffe4
--- /dev/null
+++ b/.markdownlint.yaml
@@ -0,0 +1,25 @@
+# Reference: https://github.com/DavidAnson/markdownlint/blob/main/schema/.markdownlint.yaml
+
+# MD013/line-length : Line length : https://github.com/DavidAnson/markdownlint/blob/v0.33.0/doc/md013.md
+MD013:
+ # Number of characters
+ line_length: 80
+ # Number of characters for headings
+ heading_line_length: 80
+ # Number of characters for code blocks
+ code_block_line_length: 180
+ # Include code blocks
+ code_blocks: true
+ # Include tables
+ tables: false
+ # Include headings
+ headings: true
+ # Strict length checking
+ strict: false
+ # Stern length checking
+ stern: false
+
+# MD033/no-inline-html : Inline HTML : https://github.com/DavidAnson/markdownlint/blob/v0.33.0/doc/md033.md
+MD033:
+ # Allowed elements
+ allowed_elements: ["br"]
diff --git a/README.md b/README.md
index c23e3f9..f83e980 100644
--- a/README.md
+++ b/README.md
@@ -18,8 +18,8 @@ documentation to facilitate working with QIR.
### Asking and Answering Questions
-Have a question? This repository is great places to ask questions about QIR and
-the available tools to work with it. Your question will serve as resource to
+Have a question? This repository is a great place to ask questions about QIR and
+the available tools to work with it. Your question will serve as a resource to
others searching for help. Please file an issue to ask your question
[here](https://github.com/qir-alliance/qir-spec/issues/new).
@@ -51,7 +51,7 @@ have any questions or would like to revoke your consent, please contact
[qiralliance@mail.com](mailto:qiralliance@mail.com).
For more information about the development process for specifications under the
-QIR Alliance, please see the the governance policy available
+QIR Alliance, please see the governance policy available
[here](https://github.com/qir-alliance/.github/blob/main/Governance.md).
### Contributing an Implementation
@@ -72,4 +72,4 @@ possible. Thank you for taking the time to contribute.
This project has adopted the community specification [Code of
Conduct](https://github.com/qir-alliance/.github/blob/main/Code_of_Conduct.md#contributor-covenant-code-of-conduct).
Please contact [qiralliance@mail.com](mailto:qiralliance@mail.com) for Code of
-Conduct issues or inquires.
+Conduct issues or inquiries.
diff --git a/Resources.md b/Resources.md
index 0c4b830..a59aa81 100644
--- a/Resources.md
+++ b/Resources.md
@@ -17,7 +17,7 @@ about:
- [A quick introduction to
LLVM](https://hub.packtpub.com/introducing-llvm-intermediate-representation/)
- [Gitbook about LLVM-based
- compilers](https://mapping-high-level-constructs-to-llvm-ir.readthedocs.io/en/latest/README.html)
+ compilers](https://mapping-high-level-constructs-to-llvm-ir.readthedocs.io/en/latest/)
- [Language reference manual](https://llvm.org/docs/LangRef.html)
- [Wikipedia entry](https://en.wikipedia.org/wiki/LLVM)
- [Original publication](https://llvm.org/pubs/2004-01-30-CGO-LLVM.pdf)
diff --git a/specification/under_development/profiles/Adaptive_Profile.md b/specification/under_development/profiles/Adaptive_Profile.md
new file mode 100644
index 0000000..f10da4a
--- /dev/null
+++ b/specification/under_development/profiles/Adaptive_Profile.md
@@ -0,0 +1,947 @@
+# Adaptive Profile
+
+This profile defines a subset of the QIR specification to support a coherent set
+of functionalities and capabilities that might be offered by a quantum backend.
+Like all profile specifications, this document is primarily intended for
+[compiler backend](https://en.wikipedia.org/wiki/Compiler#Back_end) authors as
+well as contributors to the [targeting
+stage](../Compilation_And_Targeting.md#targeting) of the QIR compiler.
+
+The Adaptive Profile specifies supersets of the [Base
+Profile](./Base_Profile.md) that enable control flow based on mid-circuit
+measurements and classical computations while quantum resources remain coherent.
+A backend can support this profile by supporting a minimum set of features
+beyond the [Base Profile](./Base_Profile.md) and can opt in for features beyond
+that.
+
+To support the Adaptive Profile without any of its optional features, a backend
+must support the following [mandatory capabilities](#mandatory-capabilities):
+
+1. It can execute a sequence of quantum instructions that transform the quantum
+ state.
+2. A backend must support applying a measurement operation at any point in the
+ execution of the program. Qubits not undergoing the measurement should not
+ have their state affected.
+3. A backend must be able to apply quantum instructions conditionally on a
+ measurement outcome. Specifically, forward branching using the LLVM branch
+ instruction `br` must be supported, along with the necessary runtime function
+ to convert a measurement to an `i1` value and the LLVM instructions for
+ computations on `i1` values defined in detail below.
+4. It must produce one of the specified [output schemas](../output_schemas/).
+
+This means that at minimum, backends supporting Adaptive Profile programs should
+support mid-circuit measurement, turning measurements into booleans, and
+branching based on those booleans. The QIR Adaptive Profile in particular also
+requires that branches can be arbitrarily nested. This includes a requirement
+that it must be possible to perform a measurement within a branch, and then
+branch again on that measurement. However, it is not a requirement to support
+loops within the control flow graph.
+
+Beyond the providing the required capabilities above, a backend can opt into one
+or more of the following [optional capabilities](#optional-capabilities) to
+support more advanced adaptive computations:
+
+
+5. Computations on classical (non-composite) data types, specifically on
+ integers or floating-point numbers.
+6. IR-defined functions and calls of these functions at any point in the
+ program.
+7. Support for control flow loops (backwards branching).
+8. Multiple target branching.
+9. Multiple return points.
+
+
+
+
+The use of these optional features is represented as a [module
+flag](#module-flags-metadata) in the program IR. Any backend that supports
+capabilities 1-4, and as many of capabilities 5-9 as it desires, is considered
+as supporting Adaptive Profile programs. Static analysis/verification tools
+should be able to determine what capabilities of the Adaptive Profile a backend
+is implementing and should run a verification pass to ensure Adaptive Profile
+programs that are using capabilities not supported by a backend are rejected
+with an informative message. More details about each of the aforementioned
+capabilities are outlined in the following sections.
+
+## Mandatory Capabilities
+
+**Bullet 1: Quantum transformations**
+
+The set of available instructions that transform the quantum state may vary
+depending on the targeted backend. The profile specification defines how to
+leverage and combine the available instructions to express a program, but does
+not dictate which quantum instructions may be used. Targeting a program to a
+specific backend requires choosing a suitable profile and quantum instruction
+set (QIS). Both can be chosen largely independently, though certain instruction
+sets may be incompatible with this (or other) profile(s). The section on the
+[quantum instruction set](#quantum-instruction-set) defines the requirements for
+a QIS to be compatible with the Adaptive Profile. More information about the
+role of the QIS, recommendations for front- and backend providers, as well as
+the distinction between runtime functions and quantum instructions, can be found
+in this [document](../Instruction_Set.md).
+
+**Bullet 2: Measurements**
+
+As for the Base Profile, a measurement function is a QIS function marked with an
+[`irreversible` attribute](./Base_Profile.md#quantum-instruction-set) that
+populates a value of type `%Result`. The available measurement functions are
+defined by the executing backend as part of the QIS. Unlike the Base Profile,
+the Adaptive Profile relieves a restriction that qubits can only be measured at
+the end of the program and that no quantum operations can be performed after or
+conditionally on a measurement outcome.
+
+Within the Adaptive Profile, there are no restrictions on when these
+measurements are performed during program execution. Correspondingly, it must be
+possible to measure individual qubits, or subsets of qubits depending on the
+supported QIS, without impacting the state of the non-measured qubits.
+Furthermore, it must be possible to use the measured qubit(s) afterwards and
+apply additional quantum instructions to the same qubit(s).
+
+**Bullet 3: Forward Branching**
+
+Additionally, the Adaptive Profile requires that it must be possible to take
+action based on a measurement result. Specifically, it must be possible to
+execute subsequent quantum instructions conditionally on the produced `%Result`
+value. To that end, a runtime function must be provided that converts a
+`%Result` value into a value of type `i1`; see the section on [Runtime
+Functions](#runtime-functions) for further clarification. Additionally, the LLVM
+branch instruction `br` must be supported; see the section on [Classical
+Instructions](#classical-instructions) for further clarification.
+
+The Adaptive Profile allows for arbitrary forward branching based on `i1`
+values. While arbitrary nesting of branches must be supported, an Adaptive
+Profile program must ensure that the program terminates. Unless the profile
+makes use of the optional capability of backward branching (**Bullet 7**), the
+control flow structure of a program is hence a tree without any cycles. A static
+analysis to determine the validity of the program should check for cycles in the
+control flow graph and reject any program with a cycle as invalid unless support
+for backward branching is enabled.
+
+While the Adaptive Profile requires that it must be possible to use a qubit
+after it was measured, the availability of a `reset` instruction depends on the
+QIS supported by the backend. If a single-qubit measurement is supported as part
+of the QIS, it is always possible to reset that qubit, if needed for qubit reuse
+later in the program, using forward branching as illustrated for example by the
+following IR snippet:
+
+```llvm
+...
+ tail call void @__quantum__qis__mz__body(%Qubit* null, %Result* writeonly null)
+ %0 = tail call i1 @__quantum__rt__read_result(%Result* readonly null)
+ br i1 %0, label %then, label %continue
+then: ; preds = ...
+ tail call void @__quantum__qis__x__body(%Qubit* null)
+ br label %continue
+continue:
+ ...
+```
+
+Although forward branching can be useful when combined with purely classical
+operations within a quantum program, the real utility is being able to
+conditionally perform quantum instructions depending on measurement outcomes,
+for example when performing real-time error-correction as part of a quantum
+programs.
+
+**Bullet 4: Program output**
+
+The specifications of QIR and all its profiles need to accurately reflect the
+program intent. This includes being able to define and customize the program
+output. The Base Profile and Adaptive Profile specifications hence require
+explicitly expressing which values/measurements are returned by the program and
+in which order. How to express this is defined in the section on [output
+recording](#output-recording).
+
+The defined [output schemas](../output_schemas/) provide different options for
+how a backend may express the computed value(s). The exact schema can be freely
+chosen by the backend and is identified by a string label in the produced
+schema. Each output schema contains sufficient information to allow quantum
+programming frameworks to generate a user-friendly presentation of the returned
+values in the requested order, such as, e.g., a histogram of all results when
+running the program multiple times.
+
+While the general output recording mechanism and the output schemas are the same
+for all profiles, the Adaptive Profile makes it possible to output classical
+values, if - and only if - computations on classical data types are supported
+(see the section on [output recording](#output-recording) for more details). If
+computations on classical data types are supported, the program may furthermore
+produce a non-zero exit codes indicating a runtime failure (e.g. for division by
+zero). Injecting suitable logic to produce a non-zero exit code in the case of
+classical computations that lead to an incorrect program output is generally up
+to the compiler, and the backend is not required to detect runtime failures.
+Unless the backend supports the optional capability of having multiple return
+statements in a program, it is up to the compiler to make use of `phi`-nodes to
+propagate any error code to the single final return statement at the end of the
+entry-point function.
+
+## Optional Capabilities
+
+### Bullet 5: Classical Computations
+
+A backend can choose to support an extended Adaptive Profile that may include
+instructions for classical computations on atomic data types, including integer
+and floating-point arithmetics. The behavior in the case of an overflow or
+underflow may be undefined. All LLVM instructions that must be available to
+support an extended Adaptive Profile including classical computations are listed
+in the section on [classical instructions](#classical-instructions).
+
+Which data types are used in classical computations as part of an extended
+Adaptive Profile must be indicated in the form of [module
+flags](#module-flags-metadata). The module flag(s) specifically also include
+information about the bitwidth(s) of the used data type(s). It is the
+responsibility of the backend to reject the program if any of the used data
+types or widths thereof are not supported.
+
+Support for a classical data type implies that local variables of that data type
+may exist at any point in the program. Specifically, it is then also permitted
+to pass such variables as arguments to QIS functions, runtime functions, or
+IR-defined functions (**Bullet 6**) if available, as illustrated in the
+[examples](#examples) section. Passing constant values of any data type as
+arguments to QIS and runtime functions is always permitted, regardless of
+whether classical computations on that data type are supported.
+
+In addition to local variables, global constants may be defined for any of the
+supported classical data types. Such global constants may be used anywhere in
+the program where a value of this type can be used.
+
+### Bullet 6: IR-defined functions and function calls
+
+A backend can choose to support an extended Adaptive Profile that includes
+IR-defined functions, that is functions whose implementation is defined as part
+of the program IR. An Adaptive Profile program that includes IR-defined
+functions must indicate this in the form of a [module
+flag](#module-flags-metadata).
+
+IR-defined functions may take arguments of type `%Qubit*` and `%Result*`, and it
+must have `void` return
+type. If [classical computations](#bullet-5-classical-computations) are
+supported in addition to IR-defined functions, then values of the supported data
+type(s) may also be passed as arguments to, and returned from, an IR-defined
+function. Since the adaptive profile does not include support for composite data
+types, such as tuples and arrays, they cannot be passed to or returned from
+IR-defined functions.
+
+The body of an IR-defined function may use any of the available [classical
+instructions](#classical-instructions). It may call QIS functions and other
+IR-defined functions. However, any form of direct or indirect recursion is
+forbidden. In contrast to the [entry point function](#entry-point-definition),
+an IR-defined function may *not* contain any calls to [output
+recording](#output-recording) or initialization functions, but it may call other
+runtime functions. Just like for the entry point function, values of type
+`%Qubit*` and `%Result*` may only occur in calls to other functions; qubit
+values of these types that are passed as arguments cannot be assigned to local
+variables, that is they cannot be aliased.
+
+### Bullet 7: Backwards branching
+
+Opting into this capability relieves the restriction on backwards branching so
+that a more compact representation of loops can be expressed in programs. Any
+use of this optional capability must be indicated in the form of [module
+flags](#module-flags-metadata) in the program IR.
+
+The Adaptive Profile distinguishes two kinds of loops; iterations over sequences
+of known length, and conditionally terminating loops.
+
+**Iterations** are primarily useful for a more compact representation of the
+code, since code size may be a limiting factor. Since the Adaptive Profile does
+not allow for any composite data types, supporting iterations necessarily
+requires supporting the use of `phi`-nodes to identify a qubit or result value.
+For example, the following IR expresses a loop that flips the state of qubit 1
+to 4, if qubit 0 is in a non-zero state:
+
+```llvm
+...
+define void @simple_loop() {
+entry:
+ br label %loop_body
+loop_body: ; preds = %loop_body, %entry
+ %0 = phi i64 [ 1, %entry ], [ %1, %loop_body ]
+ call void @__quantum__qis__cnot__body(%Qubit* null, %Qubit* nonnull inttoptr (i64 %0 to %Qubit*))
+ %1 = add i64 %0, 1
+ %2 = icmp sle i64 %1, 4
+ br i1 %2, label %loop_body, label %loop_exit
+loop_exit: ; preds = %loop_body
+ ...
+}
+...
+```
+
+In the case of an iteration, the value of a phi-node used to identify a qubit or
+result value must never depend on any quantum measurements. The same requirement
+exists for the condition for exiting the loop. This means that iterations can
+always be unrolled at compile time, and upon unrolling, all values used to
+identify a qubit or result value can be replaced by a constant. A static
+analysis tool can accurately enforce both of these requirements.
+
+**Conditionally terminating loops** may be used if indicated by the appropriate
+[module flag](#module-flags-metadata). These loops may break or continue
+depending on values that depend on a quantum measurement, as illustrated by the
+following code snippet.
+
+```llvm
+ ...
+ br label %loop
+loop:
+ call void @__quantum__qis__h__body(%Qubit* null)
+ call void @__quantum__qis__mz__body(%Qubit* null, %Result* writeonly null)
+ %0 = call i1 @__quantum__rt__read_result(%Result* readonly null)
+ br i1 %0, label %cont, label %loop
+cont:
+ ...
+```
+
+In contrast to iterations, they cannot be eliminated at compile time without
+assuming a hard limit for the number of iterations after which the execution is
+terminated with an error. If a backend supports the use of conditionally
+terminating loops, it is up to backend to force the termination of programs that
+would otherwise run indefinitely.
+
+### Bullet 8: Multiple Target Branching
+
+It can be desirable to support control flow constructs that indicate how a
+computation can lead to branching to one of *many* different execution paths.
+Having such a construct exposed in the IR allows for more aggressive
+optimizations across different blocks without any dependencies between them. A
+backend may hence opt into supporting `switch` instructions to facilitate such
+optimizations. An Adaptive Profile program that includes `switch` instructions
+must indicate this in the form of a [module flag](#module-flags-metadata).
+
+For this capability to be practically useful, integer computations must be
+supported as well (**Bullet 5**). For example, the snippet below causes a jump
+to a block `onzero`, `onone`, `ontwo`, or `otherwise` respectively, depending on
+the value of an integer variable `%val`:
+
+```llvm
+switch i32 %val, label %otherwise [ i32 0, label %onzero
+ i32 1, label %onone
+ i32 2, label %ontwo ]
+```
+
+The variable `%val` may, for example, depend on measurement results or a global
+constant. We refer to the [LLVM language
+reference](https://llvm.org/docs/LangRef.html#switch-instruction) for more
+information about the switch instruction.
+
+
+
+### Bullet 9: Multiple Return Points
+
+A backend my choose to support multiple return points in an entry point
+function, and IR-defined functions if the optional capability in **Bullet 6** is
+supported. This eliminates the need to create `phi` nodes for the purpose of
+propagating the computed output to a single final block. Any use of this
+optional capability must be indicated in the form of [module
+flags](#module-flags-metadata) in the program IR.
+
+A return statement is necessarily always the last statement in a block. For each
+block that contains returns a zero exit code in the entry point function, that
+same block must also contain the necessary calls to [output recording
+functions](#output-recording) to ensure the correct program output is recorded.
+If the block returns a non-zero exit code, calls to these functions may be
+omitted, implying that no output will be recorded in this case.
+
+For example, an Adaptive Profile program that uses this optional capability may
+contain a logic like this:
+
+```llvm
+@0 = internal constant [2 x i8] c"0\00"
+
+define i64 @main() local_unnamed_addr #0 {
+entry:
+ tail call void @__quantum__qis__mz__body(%Qubit* null, %Result* writeonly null)
+ %0 = tail call i1 @__quantum__rt__read_result(%Result* readonly null)
+ br i1 %0, label %error, label %exit
+error:
+ ; qubits should be in a zero state at the end of the program
+ ret i64 1
+exit:
+ call void @__quantum__rt__result_record_output(%Result* null, i8* getelementptr inbounds ([2 x i8], [2 x i8]* @0, i32 0, i32 0))
+ ret i64 0
+}
+```
+
+## Program Structure
+
+An Adaptive Profile-compliant program is defined in the form of a single LLVM
+bitcode file that contains the following:
+
+- the definitions of the opaque `Qubit` and `Result` types
+- global constants that store [string labels](#output-recording) needed for
+ certain output schemas that may be ignored if the [output
+ schema](../output_schemas/) does not make use of them
+- optionally, and only if classical computations (**Bullet 5**) are supported,
+ global constants of the supported classical data types
+- the [entry point definition](#entry-point-definition) that contains the
+ program logic
+- optionally, and only if IR-defined functions (**Bullet 6**) are supported,
+ additional functions that are called from the entry point function
+- declarations of the [QIS functions](#quantum-instruction-set) used by the
+ program
+- declarations of [runtime functions](#runtime-functions) used for
+ initialization and output recording
+- one or more [attribute groups](#attributes) used to store information about
+ the entry point, and optionally additional information about other function
+ declarations
+- [module flags](#module-flags-metadata) that contain information that a
+ compiler or backend may need to process the bitcode, including module flags
+ that indicate which features of the Adaptive Profile are used
+
+The human-readable LLVM IR for the bitcode can be obtained using standard [LLVM
+tools](https://llvm.org/docs/CommandGuide/llvm-dis.html). For clarity, this
+specification contains examples of the human-readable IR emitted by [LLVM
+13](https://releases.llvm.org/13.0.1/docs/LangRef.html). While the bitcode
+representation is portable and usually backward compatible, there may be visual
+differences in the human-readable format depending on the LLVM version. These
+differences are irrelevant when using standard tools to load, manipulate, and/or
+execute bitcode.
+
+The code below illustrates how a simple program implementing a teleport chain
+looks within a minimal Adaptive Profile representation:
+
+```llvm
+; type definitions
+
+%Result = type opaque
+%Qubit = type opaque
+
+; global constants (labels for output recording)
+
+@0 = internal constant [5 x i8] c"0_t0\00"
+@1 = internal constant [5 x i8] c"0_t1\00"
+
+; entry point definition
+
+define i64 @TeleportChain() local_unnamed_addr #0 {
+entry:
+ ; calls to initialize the execution environment
+ call void @__quantum__rt__initialize(i8* null)
+ br label %body
+
+body: ; preds = %entry
+ tail call void @__quantum__qis__h__body(%Qubit* null)
+ tail call void @__quantum__qis__cnot__body(%Qubit* null, %Qubit* nonnull inttoptr (i64 1 to %Qubit*))
+ tail call void @__quantum__qis__h__body(%Qubit* nonnull inttoptr (i64 2 to %Qubit*))
+ tail call void @__quantum__qis__cnot__body(%Qubit* nonnull inttoptr (i64 2 to %Qubit*), %Qubit* nonnull inttoptr (i64 4 to %Qubit*))
+ tail call void @__quantum__qis__h__body(%Qubit* nonnull inttoptr (i64 3 to %Qubit*))
+ tail call void @__quantum__qis__cnot__body(%Qubit* nonnull inttoptr (i64 3 to %Qubit*), %Qubit* nonnull inttoptr (i64 5 to %Qubit*))
+ tail call void @__quantum__qis__cnot__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*), %Qubit* nonnull inttoptr (i64 2 to %Qubit*))
+ tail call void @__quantum__qis__h__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*))
+ tail call void @__quantum__qis__mz__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*), %Result* writeonly null)
+ tail call void @__quantum__qis__reset__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*))
+ %0 = tail call i1 @__quantum__rt__read_result(%Result* readonly null)
+ br i1 %0, label %then__1, label %continue__1
+
+; conditional quantum gate (only one in this block, but many can appear and the full quantum instruction set should be usable)
+then__1: ; preds = %body
+ tail call void @__quantum__qis__z__body(%Qubit* nonnull inttoptr (i64 4 to %Qubit*))
+ br label %continue__1
+
+continue__1: ; preds = %then__1, %body
+ tail call void @__quantum__qis__mz__body(%Qubit* nonnull inttoptr (i64 2 to %Qubit*), %Result* writeonly nonnull inttoptr (i64 1 to %Result*))
+ tail call void @__quantum__qis__reset__body(%Qubit* nonnull inttoptr (i64 2 to %Qubit*))
+ %1 = tail call i1 @__quantum__rt__read_result(%Result* readonly nonnull inttoptr (i64 1 to %Result*))
+ br i1 %1, label %then__2, label %continue__2
+
+then__2: ; preds = %continue__1
+ tail call void @__quantum__qis__x__body(%Qubit* nonnull inttoptr (i64 4 to %Qubit*))
+ br label %continue__2
+
+continue__2: ; preds = %then__2, %continue__1
+ tail call void @__quantum__qis__cnot__body(%Qubit* nonnull inttoptr (i64 4 to %Qubit*), %Qubit* nonnull inttoptr (i64 3 to %Qubit*))
+ tail call void @__quantum__qis__h__body(%Qubit* nonnull inttoptr (i64 4 to %Qubit*))
+ tail call void @__quantum__qis__mz__body(%Qubit* nonnull inttoptr (i64 4 to %Qubit*), %Result* writeonly nonnull inttoptr (i64 2 to %Result*))
+ tail call void @__quantum__qis__reset__body(%Qubit* nonnull inttoptr (i64 4 to %Qubit*))
+ %2 = tail call i1 @__quantum__rt__read_result(%Result* readonly nonnull inttoptr (i64 2 to %Result*))
+ br i1 %2, label %then__3, label %continue__3
+
+then__3: ; preds = %continue__2
+ tail call void @__quantum__qis__z__body(%Qubit* nonnull inttoptr (i64 5 to %Qubit*))
+ br label %continue__3
+
+continue__3: ; preds = %then__3, %continue__2
+ tail call void @__quantum__qis__mz__body(%Qubit* nonnull inttoptr (i64 3 to %Qubit*), %Result* writeonly nonnull inttoptr (i64 3 to %Result*))
+ tail call void @__quantum__qis__reset__body(%Qubit* nonnull inttoptr (i64 3 to %Qubit*))
+ %3 = tail call i1 @__quantum__rt__read_result(%Result* readonly nonnull inttoptr (i64 3 to %Result*))
+ br i1 %3, label %then__4, label %continue__4
+
+then__4: ; preds = %continue__3
+ tail call void @__quantum__qis__x__body(%Qubit* nonnull inttoptr (i64 5 to %Qubit*))
+ br label %continue__4
+
+continue__4: ; preds = %continue__3, %then__4
+ tail call void @__quantum__qis__mz__body(%Qubit* null, %Result* writeonly nonnull inttoptr (i64 4 to %Result*))
+ tail call void @__quantum__qis__reset__body(%Qubit* null)
+ tail call void @__quantum__qis__mz__body(%Qubit* nonnull inttoptr (i64 5 to %Qubit*), %Result* writeonly nonnull inttoptr (i64 5 to %Result*))
+ tail call void @__quantum__qis__reset__body(%Qubit* nonnull inttoptr (i64 5 to %Qubit*))
+ br label %exit
+
+exit:
+ call void @__quantum__rt__result_record_output(%Result* nonnull inttoptr (i64 4 to %Result*), i8* getelementptr inbounds ([5 x i8], [5 x i8]* @0, i32 0, i32 0))
+ call void @__quantum__rt__result_record_output(%Result* nonnull inttoptr (i64 5 to %Result*), i8* getelementptr inbounds ([5 x i8], [5 x i8]* @1, i32 0, i32 0))
+ ret i64 0
+}
+
+; declarations of QIS functions
+
+declare void @__quantum__qis__cnot__body(%Qubit*, %Qubit*) local_unnamed_addr
+
+declare void @__quantum__qis__h__body(%Qubit*) local_unnamed_addr
+
+declare void @__quantum__qis__x__body(%Qubit*) local_unnamed_addr
+
+declare void @__quantum__qis__z__body(%Qubit*) local_unnamed_addr
+
+declare void @__quantum__qis__reset__body(%Qubit*) local_unnamed_addr
+
+declare void @__quantum__qis__mz__body(%Qubit*, %Result* writeonly) #1
+
+; declarations of runtime functions
+
+declare void @__quantum__rt__initialize(i8*)
+
+declare i1 @__quantum__rt__read_result(%Result* readonly)
+
+declare void @__quantum__rt__result_record_output(%Result*, i8*)
+
+; attributes
+
+attributes #0 = { "entry_point" "qir_profiles"="adaptive_profile" "output_labeling_schema"="schema_id" "required_num_qubits"="6" "required_num_results"="6" }
+
+attributes #1 = { "irreversible" }
+
+; module flags
+
+!llvm.module.flags = !{!0, !1, !2, !3, !4, !5, !6, !7, !8, !9}
+
+!0 = !{i32 1, !"qir_major_version", i32 1}
+!1 = !{i32 7, !"qir_minor_version", i32 0}
+!2 = !{i32 1, !"dynamic_qubit_management", i1 false}
+!3 = !{i32 1, !"dynamic_result_management", i1 false}
+!4 = !{i32 5, !"int_computations", !""}
+!5 = !{i32 5, !"float_computations", !""}
+!6 = !{i32 1, !"ir_functions", i1 false}
+!7 = !{i32 1, !"backwards_branching", i2 0}
+!8 = !{i32 1, !"multiple_target_branching", i1 false}
+!9 = !{i32 1, !"multiple_return_points", i1 false}
+```
+
+The program performs gate teleportation involving mid-circuit measurements and
+conditionally applied quantum instructions.
+
+For the sake of clarity, the code above does not contain any [debug
+symbols](https://releases.llvm.org/13.0.0/docs/tutorial/MyFirstLanguageFrontend/LangImpl09.html?highlight=debug%20symbols).
+Debug symbols contain information that is used by a debugger to relate failures
+during execution back to the original source code. While we expect this to be
+primarily useful for execution on simulators, debug symbols are both easy to
+ignore and may be useful to generate helpful error messages for compilation
+failures that happen only late in the process. We hence see no reason to
+disallow them from occurring in the bitcode but will not detail their use any
+further. We defer to existing resources for more information about how to
+generate and use debug symbols.
+
+## Entry Point Definition
+
+The bitcode contains the definition of the LLVM function that should be invoked
+when the program is executed, referred to as "entry point" in the rest of this
+profile specification. The name of this function may be chosen freely, as long
+as it is a valid [global
+identifier](https://llvm.org/docs/LangRef.html#identifiers) according to the
+LLVM standard. The entry point is identified by a custom function attribute;
+as mentioned in the section on [attributes](#attributes), this is the same
+set of attributes as in the base profile.
+
+An entry point function may not take any parameters and must must return an
+exit code in the form of a 64-bit integer. The exit code `0` must be used to
+indicate a successful execution of the quantum program. Any other value of the
+exit code indicates a failure during execution. The program IR must use exit
+codes within the range `1` to `63` to indicate a failure; exit codes that are
+larger than `63` are reserved for execution failures detected by the executing
+backend. The recorded output always contains the exit code for each shot. If a
+shot fails, no other output values may be recorded. See the [output
+schemas](../output_schemas/) for more detail.
+
+The Adaptive Profile program makes no restrictions on the structure of [basic
+blocks](https://en.wikipedia.org/wiki/Basic_block) within the entry point
+function, other than that a block cannot jump to a previously encountered block
+in the control flow graph unless it makes use of the optionally supported
+capability in **Bullet 7**. Execution starts at the entry block and follows the
+[control flow graph](https://en.wikipedia.org/wiki/Control-flow_graph) defined
+by the block terminators ending when a block terminates in a return (`ret`)
+statement. Block names/block identifiers may be chosen arbitrarily, and the
+order in which blocks are listed in the function definition is irrelevant for
+execution.
+
+The entry block contains the necessary call to initialize the execution
+environment as the first instruction to ensure that all used qubits are set to a
+zero-state. Calls to runtime functions for initialization may only appear at the
+beginning of the program. All subsequent instructions are either function calls,
+or any of the supported [LLVM instructions](#classical-instructions). Calls to
+[output recording functions](#output-recording) may only be followed by calls to
+other output recording functions and the return statement. Calls to QIS
+functions, other runtime functions, or IR-defined functions (**Bullet 6**) if
+available, can occur at any point after initialization and before output
+recording.
+
+## Quantum Instruction Set
+
+For a quantum instruction set to be fully compatible with the Adaptive Profile,
+it must satisfy the following three requirements:
+
+- All functions must return `void`, or any of the supported classical data types
+ (**Bullet 5**).
+- Functions may take values of any type as arguments. Functions that measure
+ qubits must take the qubit pointer(s) as well as the result pointer(s) as
+ arguments and return `void`.
+- Functions that perform a measurement of one or more qubit(s) must be marked
+ with a custom function attribute named `irreversible`. The use of
+ [attributes](#attributes) in general is outlined in the corresponding section.
+
+For more information about the relationship between a profile specification and
+the quantum instruction set, we refer to the paragraph on [Bullet
+1](#adaptive-profile) in the introduction of this document. For more information
+about how and when the QIS is resolved, as well as recommendations for front-
+and backend developers, we refer to the document on [compilation stages and
+targeting](../Compilation_And_Targeting.md).
+
+## Classical Instructions
+
+The following table lists all classical instructions the must be supported to
+execute a minimal Adaptive Profile program, that is a program that does not make
+use of any optional capabilities:
+
+| LLVM Instruction | Context and Purpose | Rules for Usage |
+| :----------------------- | :----------------------------------------------------------------------------------------------- | :---------------------------------------------------------------------------------------------------------- |
+| `call` | Used within a basic block to invoke any one of the QIS-, IR-, and runtime functions. | May optionally be preceded by a [`tail` marker](https://llvm.org/docs/LangRef.html#call-instruction). |
+| `br` | Used to branch from one basic block to another. | The branching is the final instruction in any basic block and may conditionally jump to different blocks depending on an `i1` value. |
+| `ret` | Used to return the exit code of the program. | Must occur (only) as the last instruction of the final block in an entry point, unless multiple return statements (optional capability) are supported. |
+| `inttoptr` | Used to cast an `i64` integer value to either a `%Qubit*` or a `%Result*`. | May be used as part of a function call only. |
+| `getelementptr inbounds` | Used to create an `i8*` to pass a constant string for the purpose of labeling an output value. | May be used as part of a call to an output recording function only. |
+
+See also the section on [data types and values](#data-types-and-values) for more
+information about the creation and usage of LLVM values.
+
+Additional LLVM instructions, as listed below, must be supported to enable
+classical computations (**Bullet 4**) and multiple target branching (**Bullet
+8**).
+
+If a backend chooses to support integer computations, then the following LLVM
+instructions must be supported:
+
+| LLVM Instruction | Context and Purpose | Note |
+|:-----------------|:----------------------------------------------------------------------|:-------------------------------------------------------------------------------------------|
+| `add` | Adds two signed or unsigned integers. | Overflow behavior is undefined, no support for `nuw` and/or `nsw`. |
+| `sub` | Subtracts two signed or unsigned integers. | Underflow behavior is undefined, no support for `nuw` and/or `nsw`. |
+| `mul` | Multiplies two integers. | Overflow/underflow behavior is undefined, no support for `nuw` and/or `nsw`. |
+| `udiv` | Divides two unsigned integers. | Division by zero leads to undefined behavior. |
+| `sdiv` | Divides two signed integers. | Division by zero and overflow leads to undefined behavior. |
+| `urem` | Computes the remainder of a division of two unsigned integers. | Division by zero leads to undefined behavior. |
+| `srem` | Computes the remainder of a division of two signed integers. | Division by zero and overflow leads to undefined behavior. |
+| `and` | Computes the bitwise logical AND of two integers. | |
+| `or` | Computes the bitwise logical OR of two integers. | |
+| `xor` | Computes the bitwise logical exclusive OR (XOR) of two integers. | |
+| `shl` | Computes a bitwise left shift of an integer. | Behavior when shifting more bits that the bitwidth of the integer is undefined, no support for `nuw`. |
+| `lshr` | Computes a bitwise right shift of an unsigned integer. | Behavior when shifting more bits that the bitwidth of the integer is undefined, no support for `exact`. |
+| `ashr` | Computes a bitwise right shift of a signed integer. | Behavior when shifting more bits that the bitwidth of the integer is undefined, no support for `exact`. |
+| `icmp` | Compares two signed or unsigned integers. | All condition codes as listed in the [LLVM Language Reference](https://llvm.org/docs/LangRef.html#icmp-instruction) must be supported. |
+| `zext .. to` | Extends an integer value to create an integer of greater bitwidth by filling the added bits with zero. | May be used at any point in the program if classical computations on both the input and the output type are supported. May only be used as part of a call to an output recording function if computations on the output type are not supported. |
+| `sext .. to` | Extends an integer value to create an integer of greater bitwidth by filling the added bits with the sign bit of the integer. | May be used at any point in the program if classical computations on both the input and the output type are supported. May only be used as part of a call to an output recording function if computations on the output type are not supported. |
+| `trunc .. to` | Truncates the highest order bits of an integer to create an integer of smaller bitwidth. | Behavior if the truncation changes the value of the integer is undefined, no support for `nuw` and/or `nsw`. May be used at any point in the program if classical computations on both the input and the output type are supported. May only be used as part of a call to an output recording function if computations on the output type are not supported. |
+| `select` | Evaluates to one of two integer values depending on a boolean condition. | |
+| `phi` | Implement the φ node in the SSA graph representing the function. | Must be at the start of a basic block, or preceded by other `phi` instructions. |
+
+For more information about any of these instructions, we refer to the
+corresponding section in the [LLVM Language
+Reference](https://llvm.org/docs/LangRef.html).
+
+If a backend chooses to support floating point computations, then the following
+LLVM instructions must be supported:
+
+| LLVM Instruction | Context and Purpose | Note |
+| :--------------- | :-------------------------------- | :-------------------------- |
+| `fadd` | Adds two floating-point values. | |
+| `fsub` | Subtracts two floating-point values. | |
+| `fmul` | Multiplies two floating-point values. | |
+| `fdiv` | Divides two floating-point values. | Division by zero leads to undefined behavior, no support for `NaN`. |
+| `fpext .. to` | Casts a value of floating-point type to a larger floating-point type. | May be used at any point in the program if classical computations on both the input and the output type are supported. May only be used as part of a call to an output recording function if computations on the output type are not supported. |
+| `fptrunc .. to` | Casts a value of floating-point type to a smaller floating-point type. | May be used at any point in the program if classical computations on both the input and the output type are supported. May only be used as part of a call to an output recording function if computations on the output type are not supported. |
+
+If the backend chooses to support multiple target branching, the following LLVM
+instruction must be supported:
+
+| LLVM Instruction | Context and Purpose | Note |
+| :--------------- | :-------------------------------- | :-------------------------- |
+| `switch` | Transfers control flow to one of several different blocks depending on an integer value. | The integer value that determines the block to jump to must be a constant value unless integer computations are supported. |
+
+See also the [LLVM Language
+Reference](https://llvm.org/docs/LangRef.html#switch-instruction) for more
+information about the `switch` instruction.
+
+## Runtime Functions
+
+The following runtime functions must be supported by all backends:
+
+| Function | Signature | Description |
+| :---------------------------------- | :------------------- | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| __quantum__rt__initialize | `void(i8*)` | Initializes the execution environment. Sets all qubits to a zero-state if they are not dynamically managed. |
+| __quantum__rt__read_result | `i1(%Result* readonly)` | Reads the value of the given measurement result and converts it to a boolean value. |
+| __quantum__rt__tuple_record_output | `void(i64,i8*)` | Inserts a marker in the generated output that indicates the start of a tuple and how many tuple elements it has. The second parameter defines a string label for the tuple. Depending on the output schema, the label is included in the output or omitted. |
+| __quantum__rt__array_record_output | `void(i64,i8*)` | Inserts a marker in the generated output that indicates the start of an array and how many array elements it has. The second parameter defines a string label for the array. Depending on the output schema, the label is included in the output or omitted. |
+| __quantum__rt__result_record_output | `void(%Result*,i8*)` | Adds a measurement result to the generated output. The second parameter defines a string label for the result value. Depending on the output schema, the label is included in the output or omitted. |
+| __quantum__rt__bool_record_output | `void(i1,i8*)` | Adds a boolean value to the generated output. The second parameter defines a string label for the result value. Depending on the output schema, the label is included in the output or omitted. |
+
+If a backend chooses to support integer computations, then the following
+additional runtime function must be available:
+
+| Function | Signature | Description |
+| :------------------------------- | :-------------- | :------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| __quantum__rt__int_record_output | `void(i64,i8*)` | Records an integer value in the generated output. The second parameter defines the string label for the value. Depending on the output schema, the label is included in the output or omitted. |
+
+If a backend chooses to support floating-point computations, then the following
+additional runtime function must be available:
+
+| Function | Signature | Description |
+| :---------------------------------- | :-------------- | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
+| __quantum__rt__float_record_output | `void(f64,i8*)` | Records a floating-point value in the generated output. The second parameter defines the string label for the value. Depending on the output schema, the label is included in the output or omitted. |
+
+### Output Recording
+
+The program output of a quantum application is defined by a sequence of calls to
+runtime functions that record the values produced by the computation,
+specifically calls to the runtime functions ending in `record_output` listed in
+the tables [above](#runtime-functions). In the case of the Adaptive Profile,
+these calls are contained within each block terminating in a return (`ret`)
+statement in the entry point function. Unless the backend supports multiple
+return points (**Bullet 9**), there is a single block that contains all calls to
+output recording functions followed by the final return statements. Multiple
+return statements in the application code can be replaced with suitable `phi`
+nodes by the compiler to propagate the data into that block.
+
+For all output recording functions, the `i8*` argument must be a non-null
+pointer to a global constant that contains a null-terminated string. A backend
+may ignore that argument if it guarantees that the order of the recorded output
+matches the order defined by the entry point. Conversely, certain output schemas
+do not require the recorded output to be listed in a particular order. For those
+schemas, the `i8*` argument serves as a label that permits the compiler or tool
+that generated the labels to reconstruct the order intended by the program.
+[Compiler frontends](https://en.wikipedia.org/wiki/Compiler#Front_end) must
+always generate these labels in such a way that the bitcode does not depend on
+the output schema; while choosing how to best label the program output is up to
+the frontend, the choice of output schema, on the other hand, is up to the
+backend. A backend may reject a program as invalid or fail execution if a label
+is missing.
+
+Both the labeling schema and the output schema are identified by a metadata
+entry in the produced output. For the [output schema](../output_schemas/), that
+identifier matches the one listed in the corresponding specification. The
+identifier for the labeling schema, on the other hand, is defined by the value
+of the `"output_labeling_schema"` attribute attached to the entry point.
+
+## Data Types and Values
+
+Within the Adaptive Profile, local variables are created when reading
+mid-circuit measurements (**Bullet 2**) or to store classical computations
+(**Bullet 5**) if supported. This implies the following:
+
+- Variables of boolean type may be defined, even if the backend supports none of
+ the optional extensions to the Adaptive Profile.
+- Values of type `%Qubit*` and `%Result*` may only occur in function calls;
+ specifically, local variables of these types cannot be created regardless of
+ which optional extensions are supported by the targeted backend. See also the
+ subsequent paragraphs for more detail.
+- Variables of numeric data types may be defined if the backend supports the
+ extension in **Bullet 5**. Such variables may be used in the supported [LLVM
+ instructions](#classical-instructions) acting on that data type, or in
+ function calls.
+- Call arguments can be constant values, classical variables, as well as
+ `inttoptr` casts or `getelementptr` instructions that are inlined into a call
+ instruction.
+
+Constants of any type are permitted as arguments to QIS and runtime functions.
+Constant values of type `i64`, for example, are used and permitted as part of
+calls to output recording functions regardless of whether integer computations
+are supported; see the section on [output recording](#output-recording) for more
+details.
+
+### Qubit and Result Usage
+
+The `%Qubit*` and `%Result*` data types must be supported by all backends.
+Qubits and results can occur only as arguments in function calls and are
+represented as a pointer of type `%Qubit*` and `%Result*` respectively. To be
+compliant with the Adaptive Profile specification, the program must not make use
+of dynamic qubit or result management, meaning qubits and results must be
+identified by an integer value that is bitcast to a pointer to match the
+expected type. How such an integer value is interpreted and specifically how it
+relates to hardware resources is ultimately up to the executing backend.
+
+
+
+The integer value that is cast must be either a constant, or a phi node of
+integer type if [iterations](#bullet-7-backwards-branching) are used/supported.
+If the cast value is a phi node, it must not directly or indirectly depend on
+any quantum measurements. The integer constant that is cast must be in the
+interval `[0, numQubits)` for `%Qubit*` and `[0,numResults)` for `%Result*`,
+where `numQubits` and `numResults` are the required number of qubits and results
+defined by the corresponding [entry point attributes](#attributes). Since
+backends may look at the values of the `required_num_qubits` and
+`required_num_results` attributes to determine whether a program can be
+executed, it is recommended to index qubits and results consecutively so that
+there are no unused values within these ranges.
+
+## Attributes
+
+The attribute usage and requirements of the Adaptive Profile remain the same as
+defined in the [Base Profile](./Base_Profile.md#attributes). The one change
+from base profile is that there are additional relevant attributes (the base
+profile only included `inlinehint`, `nofree`, `norecurse`, `readnone`,
+`readonly`, `writeonly`, and `argmemonly`) that can be used on functions,
+depending on the exact instructions supported via using the extensions in the
+Adaptive Profile.
+
+## Module Flags Metadata
+
+The Adaptive Profile requires the same mandatory module flags as specified in
+the [Base Profile](./Base_Profile.md#module-flags-metadata). Additionally, the
+following [module
+flags](https://llvm.org/docs/LangRef.html#module-flags-metadata) may be defined
+to indicate the use of optional capabilities. A lack of these module flags
+indicates that these capabilities are not used in the program.
+
+- a flag with the string identifier `"int_computations"` that contains a string
+ value where the string value is a comma-separated list of the supported/used
+ integer precision(s). For example, `!0 = !{i32 5, !"int_computations",
+ !"i32,i64"}`. Classical computations on integers of all listed precisions must
+ be supported by the executing backend. An empty value indicates that no
+ integer computations are supported/used.
+- a flag with the string identifier `"float_computations"` that contains a
+ string value where the string value is a comma-separated list of the
+ supported/used floating-point precision(s). For example, `!0 = !{i32 5,
+ !"float_computations", !"f32,f64"}`. The precision must be one of the LLVM
+ recognized values (f16, f32, f64, f80, or f128), and classical computations on
+ floating point numbers of all listed precisions must be supported by the
+ executing backend. An empty value indicates that no floating-point
+ computations are supported/used.
+- A flag named `"ir_functions"` that contains a constant `true` or `false` value
+ of type `i1` value indicating if subroutines may be expressed a functions
+ which can be called from the entry-point.
+- A flag named `"backwards_branching"` with an `i2` value indicating which
+ kinds of loops are supported. A value of `0` indicates that the control flow
+ graph does not contain any loops. A value of `1` indicates that iterations as
+ defined [here](#bullet-7-backwards-branching) are used. A value of `2`
+ indicates that conditionally terminating loops as described
+ [here](#bullet-7-backwards-branching) may occur. A value of `3` indicates that
+ both iterations and conditional loops may occur.
+- A flag named `"multiple_target_branching"` with a constant `true` or `false`
+ value of type `i1` indicating if the program uses the `switch` instruction in
+ llvm.
+- A flag named `"multiple_return_points"` with a constant `true` or `false`
+ value of type `i1` indicating whether multiple return statements can apper in
+ a function within the IR as defined [here](#bullet-9-multiple-return-points).
+
+## Error Messages
+
+Two forms of error messages can occur as a result of the submission of adaptive
+profile programs to a backend:
+
+1. Compile-time error messages.
+2. runtime error messages.
+
+The compile-time error messages can occur when a backend doesn't support some of
+the optional features from **Bullets 5-9**. If upon inspecting a module flag,
+the backend determines that the Adaptive Profile program uses features not
+supported by the backend, then a compile-time error message should be provided.
+
+The runtime error messages can occur when opting into features such as the
+classical computations in **Bullets 5**. An Adaptive Profile program that
+undergoes a real-time classical error (for example unchecked division by zero)
+has undefined behavior, and a backend is free to execute an undefined behavior.
+Programs can also check computations and provide error code by returning a value
+supported by a classical data type in a program, assuming a classical type
+specified in **Bullet 5** is supported.
+
+## Examples
+
+For example, consider a backend that supports integer computations and provides
+a runtime function for random number generation. Then an Adaptive Profile
+program may contain code like the following to do randomized benchmarking:
+
+```llvm
+%0 = call i64 @__quantum__rt__rand_range(i64 0, i64 2)
+%1 = icmp eq i64 %0, 0
+br i1 %1, label %zero_rand_sequence, label %one_rand_sequence
+```
+
+By combining mid-circuit measurements with instructions on classical data types,
+you can conditionally apply gates based on logic using multiple mid-circuit
+measurements and boolean computations:
+
+```llvm
+ tail call void @__quantum__qis__h__body(%Qubit* null)
+ tail call void @__quantum__qis__mz__body(%Qubit* null, %Result* writeonly null)
+ tail call void @__quantum__qis__reset__body(%Qubit* null)
+ %0 = tail call i1 @__quantum__rt__read_result(%Result* readonly null)
+ tail call void @__quantum__qis__h__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*))
+ tail call void @__quantum__qis__mz__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*), %Result* writeonly nonnull inttoptr (i64 1 to %Result*))
+ tail call void @__quantum__qis__reset__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*))
+ %1 = tail call i1 @__quantum__rt__read_result(%Result* readonly nonnull inttoptr (i64 1 to %Result*))
+ %2 = and i1 %0, %1
+ br i1 %2, label %then, label %continue
+
+then:
+ tail call void @__quantum__qis__x__body(%Qubit* nonnull inttoptr (i64 2 to %Qubit*))
+ br label %continue
+
+continue:
+...
+```
+
+Consider a backend that supports IR-defined functions and provides a `cnot`
+instruction as part of the QIS, but not `swap`. Defining and calling a `swap`
+function may then greatly reduce code size for a program that involves frequent
+use of swaps between qubits:
+
+```llvm
+define void @swap(%Qubit* %arg1, %Qubit* %arg2) {
+call void __quantum__qis__cnot__body(%Qubit* %arg1, %Qubit* %arg2)
+call void __quantum__qis__cnot__body(%Qubit* %arg2, %Qubit* %arg1)
+call void __quantum__qis__cnot__body(%Qubit* %arg1, %Qubit* %arg2)
+}
+
+define void @main() {
+...
+call void @swap(%Qubit* null, %Qubit* nonnull inttoptr (1 to %Qubit*))
+...
+}
+```
+
+Moreover, classical functions can be defined in the IR assuming that a backend
+has opted into supporting classical computations:
+
+```llvm
+define i64 @triple(i64 %0) {
+%1 = mul i64 %0, 3
+ret i64 %1
+}
+
+define void @main() {
+...
+%0 = call void @triple(i64 2)
+...
+}
+```
diff --git a/specification/under_development/profiles/Base_Profile.md b/specification/under_development/profiles/Base_Profile.md
index 7f37007..5867156 100644
--- a/specification/under_development/profiles/Base_Profile.md
+++ b/specification/under_development/profiles/Base_Profile.md
@@ -65,9 +65,9 @@ express this is defined in the section on [output recording](#output-recording).
While it is sufficient for the QPU to do a final measurement of all qubits in a
predefined order at the end of the program, only the selected subset will be
reflected in the produced output schema. A suitable output schema can be
-generated in a post-processing step after the computation on the quantum
-processor itself has completed; customization of the program output hence does
-not require support on the QPU itself.
+generated during execution or in a post-processing step after the computation on
+the quantum processor itself has completed; customization of the program output
+hence does not require support on the QPU itself.
The defined [output schemas](../output_schemas/) provide different options for
how a backend may express the computed value(s). The exact schema can be freely
@@ -489,10 +489,10 @@ These flags are attached as `llvm.module.flags` metadata to the module. They can
be queried using the standard LLVM tools and follow the LLVM specification in
behavior and purpose. Since module flags impact whether different modules can be
merged and how, additional module flags may be added to the bitcode only if
-their behavior is set to `Warning`, `Append`, `AppendUnique`, or `Max`.
-It is at the discretion of the maintainers for various components in the QIR
-stack to discard module flags that are not explicitly required or listed as
-optional flags in the QIR specification.
+their behavior is set to `Warning`, `Append`, `AppendUnique`, or `Max`. It is at
+the discretion of the maintainers for various components in the QIR stack to
+discard module flags that are not explicitly required or listed as optional
+flags in the QIR specification.
### Specification Version
diff --git a/specification/v0.1/1_Data_Types.md b/specification/v0.1/1_Data_Types.md
index 3854b1b..118c1ed 100644
--- a/specification/v0.1/1_Data_Types.md
+++ b/specification/v0.1/1_Data_Types.md
@@ -68,8 +68,8 @@ with values of type `%Result*`:
| Function | Signature | Description |
|-----------------------------------|--------------------------|-------------|
-| __quantum__rt__result_get_zero | `%Result*()` | Returns a constant representing a measurement result zero.
-| __quantum__rt__result_get_one | `%Result*()` | Returns a constant representing a measurement result one.
+| __quantum__rt__result_get_zero | `%Result*()` | Returns a constant representing a measurement result zero. |
+| __quantum__rt__result_get_one | `%Result*()` | Returns a constant representing a measurement result one. |
| __quantum__rt__result_equal | `i1(%Result*, %Result*)` | Returns true if the two results are the same, and false if they are different. If a `%Result*` parameter is null, a runtime failure should occur. |
| __quantum__rt__result_update_reference_count | `void(%Result*, i32)` | Adds the given integer value to the reference count for the result. Deallocates the result if the reference count becomes 0. The behavior is undefined if the reference count becomes negative. The call should be ignored if the given `%Result*` is a null pointer. |
@@ -322,4 +322,4 @@ For all of these functions, if an `%Array*` pointer is null, a runtime failure
should occur.
---
-_[Back to index](README.md)_
+*[Back to index](README.md)*
diff --git a/specification/v0.1/2_Callables.md b/specification/v0.1/2_Callables.md
index bbae07c..8009716 100644
--- a/specification/v0.1/2_Callables.md
+++ b/specification/v0.1/2_Callables.md
@@ -3,8 +3,8 @@
We use the term _callable_ to mean a subroutine in the source language.
Different source languages use different names for this concept.
-> *Note:*
-The QIR specification permits the usage of subroutines as first class values,
+> [!NOTE]
+> The QIR specification permits the usage of subroutines as first class values,
and includes the necessary expressiveness to e.g. provide runtime support for
functor application. This introduces the need to define a common structure to
represent callable values and their arguments. If the source language does not
@@ -389,4 +389,4 @@ callable values:
| __quantum__rt__capture_update_alias_count | `void(%Callable*, i32)` | Invokes the function at index 1 in the memory management table of the callable with the capture tuple and the given 32-bit integer. Does nothing if the memory management table pointer or the function pointer at that index is null, or if the given `%Callable*` is a null pointer. |
---
-_[Back to index](README.md)_
+*[Back to index](README.md)*
diff --git a/specification/v0.1/3_Classical_Runtime.md b/specification/v0.1/3_Classical_Runtime.md
index ce5a938..886e5eb 100644
--- a/specification/v0.1/3_Classical_Runtime.md
+++ b/specification/v0.1/3_Classical_Runtime.md
@@ -68,4 +68,4 @@ reference counts as hints or as simple no-ops.
instance pointer and simply ignore the call if the pointer is null.
---
-_[Back to index](README.md)_
+*[Back to index](README.md)*
diff --git a/specification/v0.1/5_Metadata.md b/specification/v0.1/5_Metadata.md
index c0fc348..286acf4 100644
--- a/specification/v0.1/5_Metadata.md
+++ b/specification/v0.1/5_Metadata.md
@@ -75,4 +75,4 @@ marked with an LLVM "EntryPoint" attribute.
>use.
---
-_[Back to index](README.md)_
+*[Back to index](README.md)*
diff --git a/specification/v0.1/7_Profiles.md b/specification/v0.1/7_Profiles.md
index 91ddc67..f08e4db 100644
--- a/specification/v0.1/7_Profiles.md
+++ b/specification/v0.1/7_Profiles.md
@@ -82,4 +82,4 @@ restrictions:
appear as literals.
---
-_[Back to index](README.md)_
+*[Back to index](README.md)*
diff --git a/specification/v0.1/8_Library_Reference.md b/specification/v0.1/8_Library_Reference.md
index eaee306..b18d20e 100644
--- a/specification/v0.1/8_Library_Reference.md
+++ b/specification/v0.1/8_Library_Reference.md
@@ -62,8 +62,8 @@ This table lists all of the runtime functions specified by QIR:
| __quantum__rt__qubit_to_string | `%String*(%Qubit*)` | Returns a string representation of the qubit. |
| __quantum__rt__range_to_string | `%String*(%Range)` | Returns a string representation of the range. |
| __quantum__rt__result_equal | `i1(%Result*, %Result*)` | Returns true if the two results are the same, and false if they are different. If a `%Result*` parameter is null, a runtime failure should occur. |
-| __quantum__rt__result_get_one | `%Result*()` | Returns a constant representing a measurement result one.
-| __quantum__rt__result_get_zero | `%Result*()` | Returns a constant representing a measurement result zero.
+| __quantum__rt__result_get_one | `%Result*()` | Returns a constant representing a measurement result one. |
+| __quantum__rt__result_get_zero | `%Result*()` | Returns a constant representing a measurement result zero. |
| __quantum__rt__result_to_string | `%String*(%Result*)` | Returns a string representation of the result. |
| __quantum__rt__result_update_reference_count | `void(%Result*, i32)` | Adds the given integer value to the reference count for the result. Deallocates the result if the reference count becomes 0. The behavior is undefined if the reference count becomes negative. The call should be ignored if the given `%Result*` is a null pointer. |
| __quantum__rt__string_concatenate | `%String*(%String*, %String*)` | Creates a new string that is the concatenation of the two argument strings. If a `%String*` parameter is null, a runtime failure should occur. |
@@ -77,4 +77,4 @@ This table lists all of the runtime functions specified by QIR:
| __quantum__rt__tuple_update_alias_count | `void(%Tuple*, i32)` | Adds the given integer value to the alias count for the tuple. Fails if the count becomes negative. The call should be ignored if the given `%Tuple*` is a null pointer. |
| __quantum__rt__tuple_update_reference_count | `void(%Tuple*, i32)` | Adds the given integer value to the reference count for the tuple. Deallocates the tuple if the reference count becomes 0. The behavior is undefined if the reference count becomes negative. The call should be ignored if the given `%Tuple*` is a null pointer. |
---
-_[Back to index](README.md)_
+*[Back to index](README.md)*