Working with the CUDA-Q IR

Let’s see the output of nvq++ in verbose mode. Consider a simple code like the one below, saved to file simple.cpp.

   #include <cudaq.h>

   struct ghz {
     void operator()(int N) __qpu__ {
       cudaq::qvector q(N);
       for (int i = 0; i < N - 1; i++) {
         x<cudaq::ctrl>(q[i], q[i + 1]);

   int main() { ... }

We see the following output from :code:`nvq++` verbose mode (up to some absolute paths).
$ nvq++ simple.cpp -v --save-temps

cudaq-quake --emit-llvm-file simple.cpp -o simple.qke
cudaq-opt --pass-pipeline=builtin.module(canonicalize,lambda-lifting,canonicalize,apply-op-specialization,kernel-execution,inline{default-pipeline=func.func(indirect-to-direct-calls)},func.func(quake-add-metadata),device-code-loader{use-quake=1},expand-measurements,func.func(lower-to-cfg),canonicalize,cse) simple.qke -o simple.qke.LpsXpu
cudaq-translate --convert-to=qir simple.qke.LpsXpu -o simple.ll.p3De4L simple.qke simple.ll
llc --relocation-model=pic --filetype=obj -O2 simple.ll.p3De4L -o simple.qke.o
llc --relocation-model=pic --filetype=obj -O2 simple.ll -o simple.classic.o
clang++ -L/usr/lib/gcc/x86_64-linux-gnu/12 -L/usr/lib64 -L/lib/x86_64-linux-gnu -L/lib64 -L/usr/lib/x86_64-linux-gnu -L/lib -L/usr/lib -L/usr/local/cuda/lib64/stubs -r simple.qke.o simple.classic.o -o simple.o
clang++ -Wl,-rpath,lib -Llib -L/usr/lib/gcc/x86_64-linux-gnu/12 -L/usr/lib64 -L/lib/x86_64-linux-gnu -L/lib64 -L/usr/lib/x86_64-linux-gnu -L/lib -L/usr/lib -L/usr/local/cuda/lib64/stubs simple.o -lcudaq -lcudaq-common -lcudaq-mlir-runtime -lcudaq-builder -lcudaq-ensmallen -lcudaq-nlopt -lcudaq-spin -lcudaq-em-default -lcudaq-platform-default -lnvqir -lnvqir-qpp

This workflow orchestration is represented in the figure below:


We start by mapping CUDA-Q C++ kernel representations (structs, lambdas, and free functions) to the Quake dialect. Since we added --save-temps, we can look at the IR code that was produced. The base Quake file, simple.qke, contains the following:

module attributes {qtx.mangled_name_map = {__nvqpp__mlirgen__ghz = "_ZN3ghzclEi"}} {
    func.func @__nvqpp__mlirgen__ghz(%arg0: i32) attributes {"cudaq-entrypoint", "cudaq-kernel"} {
       %alloca = memref.alloca() : memref<i32> %arg0, %alloca[] : memref<i32>
       %0 = memref.load %alloca[] : memref<i32>
       %1 = arith.extsi %0 : i32 to i64
       %2 = quake.alloca(%1 : i64) !quake.veq<?>
       %c0_i32 = arith.constant 0 : i32
       %3 = arith.extsi %c0_i32 : i32 to i64
       %4 = quake.extract_ref %2[%3] : (!quake.veq<?>, i64) -> !quake.ref
       quake.h %4 : (!quake.ref) -> ()
       cc.scope {
        %c0_i32_0 = arith.constant 0 : i32
        %alloca_1 = memref.alloca() : memref<i32> %c0_i32_0, %alloca_1[] : memref<i32>
        cc.loop while {
            %6 = memref.load %alloca_1[] : memref<i32>
            %7 = memref.load %alloca[] : memref<i32>
            %c1_i32 = arith.constant 1 : i32
            %8 = arith.subi %7, %c1_i32 : i32
            %9 = arith.cmpi slt, %6, %8 : i32
            cc.condition %9
        } do {
          cc.scope {
            %6 = memref.load %alloca_1[] : memref<i32>
            %7 = arith.extsi %6 : i32 to i64
            %8 = quake.extract_ref %2[%7] : (!quake.veq<?>, i64) -> !quake.ref
            %9 = memref.load %alloca_1[] : memref<i32>
            %c1_i32 = arith.constant 1 : i32
            %10 = arith.addi %9, %c1_i32 : i32
            %11 = arith.extsi %10 : i32 to i64
            %12 = quake.extract_ref %2[%11] : (!quake.veq<?>, i64) -> !quake.ref
            quake.x [%8] %12 : (!quake.ref, !quake.ref) -> ()
        } step {
            %6 = memref.load %alloca_1[] : memref<i32>
            %c1_i32 = arith.constant 1 : i32
            %7 = arith.addi %6, %c1_i32 : i32
   %7, %alloca_1[] : memref<i32>
        %5 = %2 : (!quake.veq<?>) -> !cc.stdvec<i1>

This base Quake file is unoptimized and unchanged. It is produced by the cudaq-quake tool, which also allows us to output the full LLVM IR representation for the code. This LLVM IR is classical-only, and is directly produced by clang++ code-generation. The LLVM IR file simple.ll contains the CUDA-Q kernel operator()(Args...) LLVM function, with a mangled name. Ultimately, we want to replace this function with our own MLIR-generated function.

Next, the cudaq-opt tool is invoked on the simple.qke file. This runs an MLIR pass pipeline that canonicalizes and optimizes the code. It will also process quantum lambdas, lift those lambdas to functions, and synthesis adjoint and controlled versions of CUDA-Q kernel functions if necessary. The most important pass that this step applies is the kernel-execution pass, which synthesizes a new entry point LLVM function with the same name and signature as the original operator()(Args...) call function in the classical simple.ll file. We also extract all Quake code representations as strings and register them with the CUDA-Q runtime for runtime IR introspection.

After cudaq-opt, the cudaq-translate tool is used to lower the transformed Quake representation to an LLVM IR representation, specifically the QIR. We finish by lowering this representation to object code via standard LLVM tools (e.g. llc), and merge all object files into a single object file, ensuring that our new mangled operator()(Args...) call is injected first, thereby overwriting the original. Finally, based on user compile flags, we configure the link line with specific libraries that implement the quantum_platform (here the and NVQIR circuit simulator backend (the Q++ CPU-only simulation backend). These latter libraries are controlled via the --platform and --target compiler flags.


The above figure demonstrate the MLIR dialects involved and the overall workflow mapping high-level language constructs to lower-level MLIR dialect code, and ultimately LLVM IR.

CUDA-Q also provides value-semantics form of Quake for static circuit representation. This dialect directly enables robust circuit optimizations via data-flow analysis of the representative circuit. This dialect is typically produced just-in-time when the structure of the circuit is fully known.

You will notice that there are a number of CUDA-Q executable tools installed as part of this open beta release. These tools are directly related to the generation, processing, optimization, and lowering of the core nvq++ compiler representations. The tools available are

  1. cudaq-quake - Lower C++ to Quake, can also output classical LLVM IR file

  2. cudaq-opt - Process Quake with various MLIR Passes

  3. cudaq-translate - Lower Quake to external representations like QIR

CUDA-Q and nvq++ rely on Quake for the core quantum intermediate representation. Quake represents an IR closer to the CUDA-Q source language and models qubits and quantum instructions via memory semantics. Quake can be fully dynamic and in that sense represents a quantum circuit template or generator. With runtime arguments fully specified, Quake code can be used to generate or synthesize a fully known quantum circuit. The value semantics form of Quake can thus be used as a representation for fully known or synthesized quantum circuits. Its utility, therefore, lies in its ability to optimize quantum code. It departs from the memory semantics model of Quake and expresses the flow of quantum information explicitly as MLIR values. This approach makes it easier for finding circuit patterns and leveraging it for common optimization tasks.

To demonstrate how these tools work together, let’s take the simple GHZ CUDA-Q program and lower the kernel from C++ to Quake, synthesize that Quake code, and produce QIR. Recall the code snippet for the kernel

// Define a quantum kernel
struct ghz {
  auto operator()() __qpu__ {
    cudaq::qarray<5> q;
    for (int i = 0; i < 4; i++)
      x<cudaq::ctrl>(q[i], q[i + 1]);

Using the toolchain, we can lower this directly to QIR,

cudaq-quake simple.cpp | cudaq-opt --canonicalize | cudaq-translate --convert-to=qir

which prints:

; ModuleID = 'LLVMDialectModule'
source_filename = "LLVMDialectModule"
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

%Array = type opaque
%Qubit = type opaque
%Result = type opaque

declare void @invokeWithControlQubits(i64, void (%Array*, %Qubit*)*, ...) local_unnamed_addr

declare void @__quantum__qis__x__ctl(%Array*, %Qubit*)

declare %Result* @__quantum__qis__mz(%Qubit*) local_unnamed_addr

declare void @__quantum__rt__qubit_release_array(%Array*) local_unnamed_addr

declare i64 @__quantum__rt__array_get_size_1d(%Array*) local_unnamed_addr

declare void @__quantum__qis__h(%Qubit*) local_unnamed_addr

declare i8* @__quantum__rt__array_get_element_ptr_1d(%Array*, i64) local_unnamed_addr

declare %Array* @__quantum__rt__qubit_allocate_array(i64) local_unnamed_addr

define void @__nvqpp__mlirgen__ghz(i32 %0) local_unnamed_addr {
  %2 = sext i32 %0 to i64
  %3 = tail call %Array* @__quantum__rt__qubit_allocate_array(i64 %2)
  %4 = tail call i8* @__quantum__rt__array_get_element_ptr_1d(%Array* %3, i64 0)
  %5 = bitcast i8* %4 to %Qubit**
  %6 = load %Qubit*, %Qubit** %5, align 8
  tail call void @__quantum__qis__h(%Qubit* %6)
  %7 = add i32 %0, -1
  %8 = icmp sgt i32 %7, 0
  br i1 %8, label, label %._crit_edge                                 ; preds = %1
  %wide.trip.count = zext i32 %7 to i64
  br label                                           ; preds =,
  %indvars.iv = phi i64 [ 0, ], [, ]
  %9 = tail call i8* @__quantum__rt__array_get_element_ptr_1d(%Array* %3, i64 %indvars.iv)
  %10 = bitcast i8* %9 to %Qubit**
  %11 = load %Qubit*, %Qubit** %10, align 8 = add nuw nsw i64 %indvars.iv, 1
  %12 = tail call i8* @__quantum__rt__array_get_element_ptr_1d(%Array* %3, i64
  %13 = bitcast i8* %12 to %Qubit**
  %14 = load %Qubit*, %Qubit** %13, align 8
  tail call void (i64, void (%Array*, %Qubit*)*, ...) @invokeWithControlQubits(i64 1, void (%Array*, %Qubit*)* nonnull @__quantum__qis__x__ctl, %Qubit* %11, %Qubit* %14)
  %exitcond.not = icmp eq i64, %wide.trip.count
  br i1 %exitcond.not, label %._crit_edge, label

._crit_edge:                                      ; preds =, %1
  %15 = tail call i64 @__quantum__rt__array_get_size_1d(%Array* %3)
  %16 = icmp sgt i64 %15, 0
  br i1 %16, label, label %._crit_edge4

.lr.ph3:                                          ; preds = %._crit_edge,
  %17 = phi i64 [ %22, ], [ 0, %._crit_edge ]
  %18 = tail call i8* @__quantum__rt__array_get_element_ptr_1d(%Array* %3, i64 %17)
  %19 = bitcast i8* %18 to %Qubit**
  %20 = load %Qubit*, %Qubit** %19, align 8
  %21 = tail call %Result* @__quantum__qis__mz(%Qubit* %20)
  %22 = add nuw nsw i64 %17, 1
  %exitcond5.not = icmp eq i64 %22, %15
  br i1 %exitcond5.not, label %._crit_edge4, label

._crit_edge4:                                     ; preds =, %._crit_edge
  tail call void @__quantum__rt__qubit_release_array(%Array* %3)
  ret void

!llvm.module.flags = !{!0}

!0 = !{i32 2, !"Debug Info Version", i32 3}

Note that the results of each tool can be piped to further tools, creating a composable pipeline of compiler lowering tools.