Ionq results differ from quantinuum results with multiple measurements

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Describe the bug

The following test produces different results on Ionq emulation and Ionq simulation in CI due to mz instructions and extra mz-related registers we create in QIR.

Questions:

• Is this code valid?
  • should we emit an error on get_state on a kernel that contains a measurement?
• If the code is valid, what results do we expect for various platforms?

Steps to reproduce the bug

# ============================================================================ #
# Copyright (c) 2022 - 2025 NVIDIA Corporation & Affiliates.                   #
# All rights reserved.                                                         #
#                                                                              #
# This source code and the accompanying materials are made available under     #
# the terms of the Apache License 2.0 which accompanies this distribution.     #
# ============================================================================ #

def test_state_synthesis():
    
        @cudaq.kernel
        def init(n: int):
            q = cudaq.qvector(n)
            h(q[0]
            x(q[1])
            mz(q)
    
        @cudaq.kernel
        def kernel(s: cudaq.State):
            q = cudaq.qvector(s)
            x(q[1])
            mz(q)
    
        s = cudaq.get_state(init, 2)
        s = cudaq.get_state(kernel, s)
        print(counts)
        counts = cudaq.sample(kernel, s)

cudaq.set_target("ionq", emulate=True)
test_state_synthesis()

cudaq.set_target("ionq", emulate=False)
test_state_synthesis()

Tests with emulation enabled on a local simulator give following results:

{ 01:521 11:479 }

Tests against IonQ simulator in CI give different results:

   __global__ : { 000111:479 111111:521 }
   r00000 : { 0:479 1:521 }
   r00001 : { 1:1000 }
   r00002 : { 0:479 1:521 }
   r00003 : { 1:1000 }
   r00004 : { 0:479 1:521 }
   r00005 : { 1:1000 }
}
 =========================== short test summary info ============================
 FAILED python/tests/backends/test_IonQ.py::test_Ionq_state_synthesis - Assert...
 =================== 1 failed, 12 passed, 1 warning in 6.34s ====================

QIR for ionq (note that we create 6 registers)

; 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"

%Qubit = type opaque

define void @__nvqpp__mlirgen__kernel() local_unnamed_addr #0 {
"0":
  tail call void @__quantum__qis__h__body(%Qubit* null)
  tail call void @__quantum__qis__x__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*))
  tail call void @__quantum__qis__x__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*))
  tail call void @__quantum__qis__x__body(%Qubit* nonnull inttoptr (i64 1 to %Qubit*))
  ret void
}

declare void @__quantum__qis__h__body(%Qubit*) local_unnamed_addr

declare void @__quantum__qis__x__body(%Qubit*) local_unnamed_addr

attributes #0 = { "entry_point" "output_labeling_schema"="schema_id" "output_names"="[[[0,[0,\22r00000\22]],[1,[1,\22r00001\22]],[2,[0,\22r00002\22]],[3,[1,\22r00003\22]],[4,[0,\22r00004\22]],[5,[1,\22r00005\22]]]]" "qir_profiles"="base_profile" "requiredQubits"="2" "requiredResults"="6" }

!llvm.module.flags = !{!0, !1, !2, !3, !4}

!0 = !{i32 2, !"Debug Info Version", i32 3}
!1 = !{i32 1, !"qir_major_version", i32 1}
!2 = !{i32 7, !"qir_minor_version", i32 0}
!3 = !{i32 1, !"dynamic_qubit_management", i1 false}
!4 = !{i32 1, !"dynamic_result_management", i1 false}
WARNING: this kernel invocation produced 0 shots worth of results when executed. Exiting shot loop to avoid infinite loop.
{ }

Expected behavior

Same results in both executions (or an error if this code is invalid)

Is this a regression? If it is, put the last known working version (or commit) here.

Not a regression

Environment

• CUDA-Q version:
• Python version:
• C++ compiler:
• Operating system:

Suggestions

No response

Start with python/tests/backends/test_IonQ.py::test_Ionq_state_synthesis and run it with IonQ emulation and simulation enabled. Compare the get_state, measurement, and sample behavior with the shown QIR output. Done means both executions produce consistent results, or the API reports an explicit error for an invalid measured-state operation.