qamomile.optimization.qaoa

Overview¶

Functions¶

hubo_qaoa_state [source]¶

def hubo_qaoa_state(
    p_val: qmc.UInt,
    quad: qmc.Dict[qmc.Tuple[qmc.UInt, qmc.UInt], qmc.Float],
    linear: qmc.Dict[qmc.UInt, qmc.Float],
    higher: qmc.Dict[qmc.Vector[qmc.UInt], qmc.Float],
    n: qmc.UInt,
    gammas: qmc.Vector[qmc.Float],
    betas: qmc.Vector[qmc.Float],
) -> qmc.Vector[qmc.Qubit]

Generate HUBO QAOA state.

Creates a uniform superposition and applies p layers of the HUBO QAOA circuit.

Parameters:

Returns:

qmc.Vector[qmc.Qubit] — qmc.Vector[qmc.Qubit]: HUBO QAOA state vector.

is_close_zero [source]¶

def is_close_zero(value: float, abs_tol: float = 1e-15) -> bool

Check if a given floating-point value is close to zero within a small tolerance.

Parameters:

Returns:

bool — True if the value is close to zero, False otherwise.

qaoa_state [source]¶

def qaoa_state(
    p: qmc.UInt,
    quad: qmc.Dict[qmc.Tuple[qmc.UInt, qmc.UInt], qmc.Float],
    linear: qmc.Dict[qmc.UInt, qmc.Float],
    n: qmc.UInt,
    gammas: qmc.Vector[qmc.Float],
    betas: qmc.Vector[qmc.Float],
) -> qmc.Vector[qmc.Qubit]

Generate QAOA State for Ising model.

Parameters:

Returns:

qmc.Vector[qmc.Qubit] — qmc.Vector[qmc.Qubit]: QAOA state vector.

Classes¶

ExecutableProgram [source]¶

class ExecutableProgram(Generic[T])

A fully compiled program ready for execution.

Contains compiled quantum, classical, and expectation-value segments. Use sample() for multi-shot execution or run() for single execution.

Example:

executable = transpiler.compile(kernel)

# Sample: multiple shots, returns counts
job = executable.sample(executor, shots=1000)
result = job.result()  # SampleResult with counts

# Run: single shot, returns typed result
job = executable.run(executor)
result = job.result()  # Returns kernel's return type

Constructor¶

def __init__(
    self,
    plan: ProgramPlan | None = None,
    compiled_quantum: list[CompiledQuantumSegment[T]] = list(),
    compiled_classical: list[CompiledClassicalSegment] = list(),
    compiled_expval: list[CompiledExpvalSegment] = list(),
    output_values: list[ValueLike] = list(),
) -> None

Attributes¶

• compiled_classical: list[CompiledClassicalSegment]

• compiled_expval: list[CompiledExpvalSegment]

• compiled_quantum: list[CompiledQuantumSegment[T]]

• has_parameters: bool Check if this program has unbound parameters.

• output_values: list[ValueLike]

• parameter_names: list[str] Get list of parameter names that need binding.

• plan: ProgramPlan | None

• quantum_circuit: T Get the single quantum circuit.

Methods¶

get_circuits¶

def get_circuits(self) -> list[T]

Get all quantum circuits in execution order.

get_first_circuit¶

def get_first_circuit(self) -> T | None

Get the first quantum circuit, or None if no quantum segments.

run¶

def run(
    self,
    executor: QuantumExecutor[T],
    bindings: dict[str, Any] | None = None,
) -> RunJob[Any] | ExpvalJob

Execute once and return single result.

Parameters:

Returns:

RunJob[Any] | ExpvalJob — RunJob[Any] | ExpvalJob: A RunJob that resolves to the kernel’s return type, or an ExpvalJob when the program contains an expectation-value computation.

Raises:

• ExecutionError — If no quantum circuit to execute

• ValueError — If required parameters are missing

Example:

job = executable.run(executor, bindings={"gamma": [0.5]})
result = job.result()
print(result)  # 0.25 (for QFixed) or (0, 1) (for bits)

sample¶

def sample(
    self,
    executor: QuantumExecutor[T],
    shots: int = 1024,
    bindings: dict[str, Any] | None = None,
) -> SampleJob[Any]

Execute with multiple shots and return counts.

Parameters:

Returns:

SampleJob[Any] — SampleJob[Any]: A job that resolves to a SampleResult with the per-bitstring counts.

Raises:

• ExecutionError — If no quantum circuit to execute

• ValueError — If required parameters are missing

Example:

job = executable.sample(executor, shots=1000, bindings={"gamma": [0.5]})
result = job.result()
print(result.results)  # [(0.25, 500), (0.75, 500)]

MathematicalProblemConverter [source]¶

class MathematicalProblemConverter(abc.ABC)

Constructor¶

def __init__(
    self,
    instance: ommx.v1.Instance | BinaryModel,
    *,
    uniform_penalty_weight: float | None = None,
    penalty_weights: dict[int, float] | None = None,
) -> None

Initialize a converter from an OMMX instance or binary model.

Parameters:

Methods¶

decode¶

def decode(self, samples: SampleResult[list[int]]) -> BinarySampleSet | ommx.v1.SampleSet

Decode quantum measurement results.

The return type tracks the input that built this converter:

• Built from an :class:ommx.v1.Instance — returns an :class:ommx.v1.SampleSet evaluated against the original (un-penalized) instance, so feasibility, objective, and per-constraint violations are available through OMMX’s own API (.summary, .summary_with_constraints, .best_feasible, .feasible, .objectives).

• Built from a :class:BinaryModel — returns a :class:BinarySampleSet with samples in the model’s original vartype (BINARY 0/1 or SPIN ±1), energies, and shot counts.

Parameters:

Returns:

BinarySampleSet | ommx.v1.SampleSet — BinarySampleSet | ommx.v1.SampleSet: see method description.

See Also:

:meth:decode_to_binary_sampleset: always returns a :class:BinarySampleSet. Use it when you need the QUBO-domain (penalty-included) energy — e.g. to drive a classical optimizer that must penalize infeasibility.

Example:

>>> # OMMX in → OMMX out
>>> converter = QAOAConverter(ommx_instance)
>>> exe = converter.transpile(QiskitTranspiler(), p=2)
>>> result = exe.sample(QiskitTranspiler().executor(),
...                     shots=1024,
...                     bindings={"gammas": gs, "betas": bs}).result()
>>> sample_set = converter.decode(result)
>>> sample_set.best_feasible.objective

decode_to_binary_sampleset¶

def decode_to_binary_sampleset(self, samples: SampleResult[list[int]]) -> BinarySampleSet

Decode samples into a :class:BinarySampleSet.

Always returns a :class:BinarySampleSet, regardless of whether this converter was constructed with an :class:ommx.v1.Instance or a :class:BinaryModel. Use this when you need:

• The QUBO-domain energy (penalty-included), e.g. as the cost driving a classical optimizer like COBYLA — :meth:decode on OMMX-backed converters returns the un-penalized OMMX objective which won’t penalize infeasibility.

• The per-state samples / num_occurrences / vartype views from :class:BinarySampleSet.

For most usage — feasibility, original-objective evaluation, per-constraint diagnostics — prefer the polymorphic :meth:decode, which returns an :class:ommx.v1.SampleSet for OMMX-backed converters.

Parameters:

Returns:

BinarySampleSet — keyed by the SPIN model’s original variable BinarySampleSet — indices (the QUBO variable IDs for OMMX-backed converters) BinarySampleSet — in the converter’s original_vartype — BINARY for BinarySampleSet — OMMX-backed converters, the :class:BinaryModel’s declared BinarySampleSet — vartype otherwise.

get_cost_hamiltonian¶

def get_cost_hamiltonian(self) -> qm_o.Hamiltonian

Construct the cost Hamiltonian.

Subclasses must implement this method to build the appropriate Hamiltonian for their specific algorithm (e.g., Pauli-Z for QAOA, QRAC-encoded for QRAO). Oracle-based converters that do not use a cost Hamiltonian (e.g., GASConverter) should raise NotImplementedError.

Returns:

qm_o.Hamiltonian — qm_o.Hamiltonian: The cost Hamiltonian.

Raises:

• NotImplementedError — If the converter does not expose a cost Hamiltonian.

QAOAConverter [source]¶

class QAOAConverter(MathematicalProblemConverter)

Converter for Quantum Approximate Optimization Algorithm (QAOA).

Supports both standard quadratic (QUBO/Ising) models and higher-order binary optimization (HUBO) models. When higher-order terms are present, automatically uses phase-gadget decomposition for k-body Z-rotations.

Example:

>>> model = BinaryModel.from_hubo({(0, 1, 2): 1.0, (0,): -2.0})
>>> converter = QAOAConverter(model)
>>> executable = converter.transpile(QiskitTranspiler(), p=2)

Methods¶

get_cost_hamiltonian¶

def get_cost_hamiltonian(self) -> qm_o.Hamiltonian

Construct the Ising cost Hamiltonian from the spin model.

Builds a Pauli-Z Hamiltonian from the spin model’s linear, quadratic, and higher-order terms.

Returns:

qm_o.Hamiltonian — qm_o.Hamiltonian: The cost Hamiltonian.

transpile¶

def transpile(self, transpiler: Transpiler, *, p: int) -> ExecutableProgram

Transpile the model into an executable QAOA circuit.

Dispatches to the quadratic-only fast path when no higher-order terms are present, otherwise uses the HUBO path with phase-gadget decomposition.

Parameters:

Returns:

ExecutableProgram — The compiled circuit program.

Transpiler [source]¶

class Transpiler(ABC, Generic[T])

Base class for backend-specific transpilers.

Provides the full compilation pipeline from qkernel-like frontend objects to executable programs.

Example:

>>> from qamomile.circuit.transpiler import TranspilerConfig
>>> from qamomile.qiskit import QiskitTranspiler
>>> transpiler = QiskitTranspiler()
>>> executable = transpiler.transpile(kernel, bindings={"theta": 0.5})
>>> circuit = executable.get_first_circuit()
>>> config = TranspilerConfig.with_strategies({"qft": "approximate_k2"})
>>> transpiler.set_config(config)

Attributes¶

• MAX_UNROLL_DEPTH: int

• config: TranspilerConfig Get the transpiler configuration.

Methods¶

affine_validate¶

def affine_validate(self, block: Block) -> Block

Pass 1.5: Validate affine type semantics.

This is a safety net to catch affine type violations that may have bypassed frontend checks. Validates that quantum values are used at most once.

analyze¶

def analyze(self, block: Block) -> Block

Pass 2: Validate and analyze dependencies.

array_bounds_check¶

def array_bounds_check(self, block: Block) -> Block

Pass 1.85: Reject reachable accesses outside resolved array bounds.

Runs after :meth:partial_eval so binding-dependent view extents and indices are concrete where possible, and before declarative slice operations are stripped. Statically zero-trip loop bodies are skipped because their element accesses are unreachable.

Parameters:

Returns:

Block — The input block unchanged after successful validation.

Raises:

• ValidationError — If a reachable constant element index is outside a resolved root-array or view-local extent.

classical_lowering¶

def classical_lowering(self, block: Block) -> Block

Pass 2.25: Lower measurement-derived classical ops.

Identifies CompOp / CondOp / NotOp / BinOp instances whose operand dataflow traces back to a measurement and rewrites them to RuntimeClassicalExpr. Compile-time-foldable and emit-time-foldable (loop-bound, parameter-bound) classical ops are left unchanged.

Runs after analyze so the measurement-taint analysis has the full dependency graph available, and before validate_symbolic_shapes / plan / emit so downstream passes can rely on the cleaner IR (in particular: future segmentation work can dispatch on RuntimeClassicalExpr type instead of the BitType-only heuristic).

constant_fold¶

def constant_fold(self, block: Block, bindings: dict[str, Any] | None = None) -> Block

Pass 1.5: Fold constant expressions.

Evaluates BinOp operations when all operands are constants or bound parameters. This prevents quantum segment splitting from parametric expressions like phase * 2.

emit¶

def emit(
    self,
    separated: ProgramPlan,
    bindings: dict[str, Any] | None = None,
    parameters: list[str] | None = None,
) -> ExecutableProgram[T]

Pass 4: Generate backend-specific code.

Parameters:

Raises:

• ValueError — If a name appears in both bindings and parameters. This check also runs in transpile and to_block/build, but emit is a public step-by-step entry point that bypasses those, so the guard is repeated here to prevent a name from being silently baked in (its runtime parameter dropped) when the step-by-step API is driven directly.

executor¶

def executor(self, **kwargs: Any = {}) -> QuantumExecutor[T]

Create a quantum executor for this backend.

inline¶

def inline(self, block: Block) -> Block

Pass 1: Inline all inline-policy callable invocations.

lower_compile_time_ifs¶

def lower_compile_time_ifs(self, block: Block, bindings: dict[str, Any] | None = None) -> Block

Pass 1.75: Lower compile-time resolvable IfOperations.

Evaluates IfOperation conditions (including expression-derived conditions via CompOp/CondOp/NotOp) and replaces resolved ones with selected-branch operations. Merge outputs are substituted with selected-branch values throughout the block.

This prevents SegmentationPass from seeing classical-only compile-time IfOperations that would otherwise split quantum segments.

partial_eval¶

def partial_eval(self, block: Block, bindings: dict[str, Any] | None = None) -> Block

Pass 1.75: Fold constants and lower compile-time control flow.

plan¶

def plan(self, block: Block) -> ProgramPlan

Pass 3: Lower and split into a program plan.

Validates C→Q→C pattern with single quantum segment.

plan_circuit¶

def plan_circuit(
    self,
    prepared: PreparedModule,
    bindings: dict[str, Any] | None = None,
) -> ProgramPlan

Lower a prepared semantic module into the circuit execution model.

This is the destructive circuit-family path: inline-policy calls are flattened, compile-time structure is evaluated, affine and borrow invariants are checked, measurement-dependent classical expressions are classified, and the result is segmented into C-to-Q-to-C steps. Program-graph targets must compile :class:PreparedModule directly instead of invoking this method.

Parameters:

Returns:

ProgramPlan — Circuit-family host-orchestrated execution plan.

Raises:

• QamomileCompileError — If validation, partial evaluation, or segmentation rejects the program.

prepare¶

def prepare(
    self,
    kernel: QKernelLike,
    bindings: dict[str, Any] | None = None,
    parameters: list[str] | None = None,
) -> PreparedModule

Prepare a qkernel for target-specific planning and lowering.

This phase preserves callable boundaries. It performs tracing, entrypoint validation, configured substitutions, and parameter-shape resolution, then collects the reachable callable graph into a program-level semantic view.

Parameters:

Returns:

PreparedModule — Hierarchical entrypoint, reachable callables, call graph, and public ABI.

Raises:

• ValueError — If a name appears in both bindings and parameters.

• EntrypointValidationError — If the top-level kernel uses quantum inputs or outputs.

resolve_parameter_shapes¶

def resolve_parameter_shapes(self, block: Block, bindings: dict[str, Any] | None = None) -> Block

Pass 0.75: Resolve symbolic Vector parameter shape dims.

Qamomile circuits are compile-time fixed-structure. Parameter Vector[Float] / Vector[UInt] inputs carry symbolic {name}_dim{i} shape Values so frontend code like arr.shape[0] returns a usable handle. This pass looks at bindings and, for every parameter array that has a concrete binding, substitutes those symbolic dims with constants so that downstream loop-bound resolution sees fixed lengths.

Parameters without a concrete binding are left as-is; their symbolic dims are harmless as long as no compile-time structure decision depends on them (the library QAOA pattern).

set_config¶

def set_config(self, config: TranspilerConfig) -> None

Set the transpiler configuration.

Parameters:

slice_borrow_check¶

def slice_borrow_check(self, block: Block) -> Block

Pass 1.9: Post-fold slice-view linearity checker.

Runs after :meth:partial_eval has resolved slice bounds to concrete values. Catches the slice-view linearity violations that the trace-time frontend check cannot detect on its own — specifically, slices whose bounds were symbolic at trace time (so the frontend bulk-borrow tracker had to skip them) and aliasing scenarios that only become visible once those bounds are folded to constants:

1. A view whose newly-concrete coverage overlaps another live view of the same root parent.

2. A view whose newly-concrete coverage hits a slot that was consumed by a destructive operation earlier in the block.

3. Slice ownership changes that cannot be represented safely across control-flow boundaries.

Creating a direct element borrow (q[i]) emits no IR operation, so this pass cannot observe the borrow site itself. Later uses of that element do appear as operation operands and are checked for conflicts with live slice views. Trace-time validation in :func:qamomile.circuit.frontend.func_to_block._validate_returned_arrays covers unreturned direct-element borrows that have no observable operand use.

The pass is a pass-through for the IR — it only raises on violations and leaves the block unchanged on success.

Parameters:

Returns:

Block — The input block unchanged after successful validation.

Raises:

• QubitBorrowConflictError — If live slice ownership conflicts with another view or direct access.

• QubitConsumedError — If a slice or operand accesses a slot already destroyed by a destructive operation.

• ValidationError — If the block kind is invalid or ownership cannot be propagated safely through control flow.

strip_slice_ops¶

def strip_slice_ops(self, block: Block) -> Block

Pass 1.95: Remove SliceArrayOperation nodes from the block.

PartialEvaluationPass keeps these declarative ops through constant folding so :meth:slice_borrow_check can use them as view-declaration markers. Once the linearity check has run, segmentation and downstream passes expect a classical-op-free quantum stream — this pass performs that cleanup.

substitute¶

def substitute(self, block: Block) -> Block

Pass 0.5: Apply substitutions (optional).

This pass rewrites inline callable targets and sets strategy names on boxed InvokeOperations based on config.

Parameters:

Returns:

Block — Block with substitutions applied

to_block¶

def to_block(
    self,
    kernel: QKernelLike,
    bindings: dict[str, Any] | None = None,
    parameters: list[str] | None = None,
) -> Block

Convert a qkernel-like frontend object to a Block.

Parameters:

Returns:

Block — Hierarchical block for the frontend object.

Raises:

• ValueError — If a name appears in both bindings and parameters (propagated from kernel.build), violating the bindings/parameters disjointness rule.

Always uses kernel.build() so Python defaults, required arguments, runtime parameters, and array shapes follow one validated entry path.

to_circuit¶

def to_circuit(self, kernel: QKernelLike, bindings: dict[str, Any] | None = None) -> T

Compile and extract just the quantum circuit.

This is a convenience method for when you just want the backend circuit without the full executable.

Parameters:

Returns:

T — Backend-specific quantum circuit.

transpile¶

def transpile(
    self,
    kernel: QKernelLike,
    bindings: dict[str, Any] | None = None,
    parameters: list[str] | None = None,
) -> ExecutableProgram[T]

Full compilation pipeline from a qkernel-like object to executable.

Parameters:

Returns:

ExecutableProgram[T] — ExecutableProgram[T]: Executable wrapping the backend circuit and the parameter metadata needed to re-bind runtime parameters, ready for execution.

Raises:

• ValueError — If a name appears in both bindings and parameters. A name being in both is ambiguous (placeholder value vs runtime symbol) and used to silently miscompile control-flow predicates that depended on parameter-array elements; rejecting the overlap up front keeps the contract unambiguous.

• QamomileCompileError — If compilation fails (validation, dependency errors)

Pipeline:

1. prepare: Trace and validate the entrypoint, apply configured substitutions, resolve parameter shapes, and preserve the reachable callable graph.

2. plan_circuit: Inline inline-policy calls, unroll recursion, validate affine and borrow rules, partially evaluate compile-time structure, analyze dependencies, and segment the program into the host-orchestrated C-to-Q-to-C model.

3. lower: Convert each quantum segment to immutable, backend-neutral CircuitProgram IR.

4. legalize: Select native intrinsics and Pauli-evolution realizations from target capabilities and compilation policy.

5. verify: Prove circuit structure and target legality before constructing backend objects.

6. materialize: Convert the legalized circuit IR to backend-native artifacts and preserve the executable ABI.

unroll_recursion¶

def unroll_recursion(self, block: Block, bindings: dict[str, Any] | None = None) -> Block

Fixed-point loop of inline and branch lowering for recursion.

Each iteration unrolls one layer of self-referential inline callable invocation and then lowers its compile-time base-case IfOperation. Loop-carried Bit conditions remain visible until the final validation pass so first-iteration constants cannot erase a real backedge read. Terminates when no inline callable invocation remains (success), when every residual call is trapped inside an operation-owned block whose recursive callable contract is unsupported (control / inverse / select over a recursive kernel — raises a targeted error, see below), or when MAX_UNROLL_DEPTH is reached (genuinely non-terminating top-level recursion — raises).

Parameters:

Returns:

Block — The fully unrolled, AFFINE block once no inline callable invocation remains. Returned unchanged when the input already has no calls.

Raises:

• FrontendTransformError — If every remaining inline callable invocation is trapped inside a ControlledUOperation.block, an InverseBlockOperation block, or a SelectOperation.case_blocks entry (a self-recursive kernel was passed to qmc.control, qmc.inverse, or qmc.select), or if a genuinely non-terminating top-level recursion does not converge within MAX_UNROLL_DEPTH iterations. The two cases carry distinct, cause-specific messages.

validate_symbolic_shapes¶

def validate_symbolic_shapes(self, block: Block) -> Block

Pass 2.5: Reject unresolvable ForOperation loop bounds.

Runs after analyze so dependency info is complete. Raises QamomileCompileError with an actionable message when a gamma_dim0-style symbolic Value reaches a ForOperation bound without being folded to a constant by ParameterShapeResolutionPass, or when a loop bound depends (directly or through classical arithmetic) on a runtime parameter — loop bounds are compile-time structure and must be provided via bindings, not parameters.

Parameters:

Returns:

Block — block, unchanged, when validation succeeds.

Raises:

• QamomileCompileError — If a loop bound is an unresolved parameter shape dim or depends on a runtime parameter.