diff --git a/CHANGELOG.md b/CHANGELOG.md
index c655fdb..baadf25 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.1.0/),
 
 ### Added
 
+- `examples/` with a Hamiltonian-energy Quantum Function workload and client-side parameter optimization.
 - `QctrlQaoaJobCreationPayload` and `QctrlQaoaJobInput` for submitting Q-CTRL QAOA maxcut combinatorial-optimization jobs via `create_job`. The `create_job` body union now also accepts `QctrlQaoaJobCreationPayload`.
 - `cost_model` optional field on `BaseJob`, `GetCircuitJobResponse`, and `GetJobResponse`, typed as `CostModel` (`"quantum_compute_time"` or `"execution_time"`).
 
diff --git a/README.md b/README.md
index 992bbde..5f63819 100644
--- a/README.md
+++ b/README.md
@@ -65,6 +65,10 @@ Each generated endpoint module exposes four callables: `sync`, `sync_detailed`,
 
 For options (`api_key`, `base_url`, `max_retries`, `timeout`, `extension`), error classes, retry behavior, pagination, polling, sessions, and downstream-SDK extension hooks, see the [API reference](https://ionq.github.io/ionq-core-python/).
 
+## Examples
+
+See [examples/README.md](examples/README.md) for runnable examples, including a Hamiltonian-energy Quantum Function workload with client-side parameter optimization.
+
 ## Versioning
 
 This package follows [SemVer 2.0](https://semver.org/spec/v2.0.0.html), independent of the upstream REST API version - pass an explicit `base_url` to `IonQClient` to pin against a different API. Print the installed version with:
diff --git a/examples/README.md b/examples/README.md
new file mode 100644
index 0000000..94f0ddf
--- /dev/null
+++ b/examples/README.md
@@ -0,0 +1,20 @@
+# ionq-core Examples
+
+## Hamiltonian Energy Optimization
+
+`hamiltonian_energy_optimization.py` demonstrates a Hamiltonian-energy Quantum Function using only the public `ionq-core` API:
+
+- `IonQClient`
+- `create_job.sync`
+- `wait_for_job`
+- typed models under `ionq_core.models`
+
+It minimizes the one-qubit Hamiltonian `H = -Z` with a parameterized OpenQASM 3 `RY(theta)` ansatz and a small dependency-free coordinate search optimizer.
+
+```sh
+pip install ionq-core
+export IONQ_API_KEY=...
+python examples/hamiltonian_energy_optimization.py --iterations 4
+```
+
+The script targets the free `simulator` backend by default and prints each optimization iteration plus the final energy and parameters.
diff --git a/examples/__init__.py b/examples/__init__.py
new file mode 100644
index 0000000..8a56161
--- /dev/null
+++ b/examples/__init__.py
@@ -0,0 +1,4 @@
+# SPDX-FileCopyrightText: 2026 IonQ, Inc.
+# SPDX-License-Identifier: Apache-2.0
+
+"""Runnable ionq-core examples."""
diff --git a/examples/hamiltonian_energy_optimization.py b/examples/hamiltonian_energy_optimization.py
new file mode 100644
index 0000000..0fec5ff
--- /dev/null
+++ b/examples/hamiltonian_energy_optimization.py
@@ -0,0 +1,189 @@
+# SPDX-FileCopyrightText: 2026 IonQ, Inc.
+# SPDX-License-Identifier: Apache-2.0
+
+"""Hamiltonian-energy Quantum Function example with client-side optimization.
+
+This example minimizes the one-qubit Hamiltonian ``H = -Z`` with a
+parameterized OpenQASM 3 ansatz, ``RY(theta) |0>``. The optimizer is a small
+dependency-free coordinate search that repeatedly submits Hamiltonian-energy
+Quantum Function jobs through `ionq-core`.
+"""
+
+from __future__ import annotations
+
+import argparse
+from collections.abc import Callable, Sequence
+from dataclasses import dataclass
+from typing import Any
+
+from ionq_core import AuthenticatedClient, IonQClient, wait_for_job
+from ionq_core.api.default import create_job
+from ionq_core.models.ansatz import Ansatz
+from ionq_core.models.hamiltonian_energy_data import HamiltonianEnergyData
+from ionq_core.models.hamiltonian_energy_input import HamiltonianEnergyInput
+from ionq_core.models.hamiltonian_energy_input_data import HamiltonianEnergyInputData
+from ionq_core.models.hamiltonian_pauli_term import HamiltonianPauliTerm
+from ionq_core.models.quantum_function_job_creation_payload import QuantumFunctionJobCreationPayload
+
+ANSATZ_OPENQASM = """OPENQASM 3.0;
+input float theta;
+qubit[1] q;
+ry(theta) q[0];
+"""
+
+
+@dataclass(frozen=True)
+class OptimizationResult:
+    """Result from the client-side coordinate-search loop."""
+
+    parameters: list[float]
+    energy: float
+    history: list[tuple[int, list[float], float]]
+
+
+def build_hamiltonian_energy_payload(
+    params: Sequence[float],
+    *,
+    backend: str = "simulator",
+    shots: int = 100,
+    name: str = "ionq-core hamiltonian energy example",
+) -> QuantumFunctionJobCreationPayload:
+    """Build a typed Hamiltonian-energy Quantum Function payload."""
+    return QuantumFunctionJobCreationPayload(
+        backend=backend,
+        type_="quantum-function",
+        input_=HamiltonianEnergyInput(
+            data=HamiltonianEnergyInputData(
+                type_="hamiltonian-energy",
+                data=HamiltonianEnergyData(
+                    hamiltonian=[HamiltonianPauliTerm(pauli_string="Z", coefficient=-1.0)],
+                    ansatz=Ansatz(data=ANSATZ_OPENQASM),
+                ),
+            ),
+            params=list(params),
+        ),
+        name=name,
+        shots=shots,
+    )
+
+
+def evaluate_energy(
+    client: AuthenticatedClient,
+    params: Sequence[float],
+    *,
+    backend: str = "simulator",
+    shots: int = 100,
+    poll_interval: float = 1.0,
+    timeout: float = 300.0,
+    create_job_sync: Callable[..., Any] = create_job.sync,
+    wait_for_job_fn: Callable[..., Any] = wait_for_job,
+) -> float:
+    """Submit a Hamiltonian-energy job and return its completed energy."""
+    payload = build_hamiltonian_energy_payload(params, backend=backend, shots=shots)
+    created = create_job_sync(client=client, body=payload)
+    if created is None:
+        raise RuntimeError("IonQ API did not return a job creation response")
+
+    completed = wait_for_job_fn(client, created.id, poll_interval=poll_interval, timeout=timeout)
+    return extract_energy(completed)
+
+
+def extract_energy(completed_job: Any) -> float:
+    """Extract an energy value from a completed Quantum Function job response."""
+    output = completed_job.output.to_dict()
+    candidates = [output.get("energy"), output.get("value")]
+
+    result = output.get("result")
+    if isinstance(result, dict):
+        candidates.append(result.get("energy"))
+
+    solution = output.get("solution")
+    if isinstance(solution, dict):
+        candidates.append(solution.get("minimum_value"))
+
+    for candidate in candidates:
+        if isinstance(candidate, (int, float)):
+            return float(candidate)
+
+    raise KeyError("completed job output did not contain an energy value")
+
+
+def coordinate_search(
+    energy_fn: Callable[[list[float]], float],
+    initial_params: Sequence[float],
+    *,
+    step_size: float = 0.4,
+    min_step: float = 0.025,
+    max_iterations: int = 8,
+    log: Callable[[str], None] = print,
+) -> OptimizationResult:
+    """Minimize ``energy_fn`` with a small deterministic coordinate search."""
+    params = list(initial_params)
+    energy = energy_fn(params)
+    history = [(0, params.copy(), energy)]
+    log(f"iteration 0: energy={energy:.12g}, params={params}")
+
+    step = step_size
+    for iteration in range(1, max_iterations + 1):
+        improved = False
+
+        for index in range(len(params)):
+            for direction in (1.0, -1.0):
+                candidate = params.copy()
+                candidate[index] += direction * step
+                candidate_energy = energy_fn(candidate)
+                if candidate_energy < energy:
+                    params = candidate
+                    energy = candidate_energy
+                    improved = True
+
+        if improved:
+            history.append((iteration, params.copy(), energy))
+        else:
+            step *= 0.5
+
+        log(f"iteration {iteration}: energy={energy:.12g}, params={params}, step={step:.12g}")
+
+        if not improved and step < min_step:
+            break
+
+    return OptimizationResult(parameters=params, energy=energy, history=history)
+
+
+def main(argv: Sequence[str] | None = None) -> int:
+    """Run the Hamiltonian-energy example from the command line."""
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--backend", default="simulator", help="IonQ backend to target")
+    parser.add_argument("--shots", type=int, default=100, help="Shots per energy evaluation")
+    parser.add_argument("--initial-theta", type=float, default=1.2, help="Initial RY angle")
+    parser.add_argument("--iterations", type=int, default=4, help="Maximum coordinate-search iterations")
+    parser.add_argument("--step", type=float, default=0.4, help="Initial coordinate-search step")
+    parser.add_argument("--poll-interval", type=float, default=1.0, help="Initial polling interval in seconds")
+    parser.add_argument("--timeout", type=float, default=300.0, help="Polling timeout per submitted job")
+    args = parser.parse_args(argv)
+
+    client = IonQClient()
+
+    def energy_fn(params: list[float]) -> float:
+        return evaluate_energy(
+            client,
+            params,
+            backend=args.backend,
+            shots=args.shots,
+            poll_interval=args.poll_interval,
+            timeout=args.timeout,
+        )
+
+    result = coordinate_search(
+        energy_fn,
+        [args.initial_theta],
+        step_size=args.step,
+        max_iterations=args.iterations,
+    )
+    print(f"final_energy={result.energy:.12g}")
+    print(f"optimal_parameters={result.parameters}")
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/tests/test_examples.py b/tests/test_examples.py
new file mode 100644
index 0000000..adbe97f
--- /dev/null
+++ b/tests/test_examples.py
@@ -0,0 +1,86 @@
+# SPDX-FileCopyrightText: 2026 IonQ, Inc.
+# SPDX-License-Identifier: Apache-2.0
+
+import pytest
+
+from examples import hamiltonian_energy_optimization as example
+
+
+def test_hamiltonian_energy_payload_uses_typed_models():
+    payload = example.build_hamiltonian_energy_payload([0.25], shots=200)
+
+    assert payload.to_dict() == {
+        "backend": "simulator",
+        "type": "quantum-function",
+        "input": {
+            "data": {
+                "type": "hamiltonian-energy",
+                "data": {
+                    "hamiltonian": [{"pauli_string": "Z", "coefficient": -1.0}],
+                    "ansatz": {"data": example.ANSATZ_OPENQASM},
+                    "penalty": 0.0,
+                },
+            },
+            "params": [0.25],
+        },
+        "name": "ionq-core hamiltonian energy example",
+        "shots": 200,
+    }
+
+
+def test_evaluate_energy_submits_payload_and_polls_job(auth_client):
+    calls = []
+
+    class CreatedJob:
+        id = "job-123"
+
+    class CompletedOutput:
+        def to_dict(self):
+            return {"energy": -0.75}
+
+    class CompletedJob:
+        output = CompletedOutput()
+
+    def fake_create_job(*, client, body):
+        calls.append(("create", client, body.to_dict()))
+        return CreatedJob()
+
+    def fake_wait_for_job(client, job_id, *, poll_interval, timeout):
+        calls.append(("wait", client, job_id, poll_interval, timeout))
+        return CompletedJob()
+
+    energy = example.evaluate_energy(
+        auth_client,
+        [0.5],
+        create_job_sync=fake_create_job,
+        wait_for_job_fn=fake_wait_for_job,
+        poll_interval=0.25,
+        timeout=12.0,
+    )
+
+    assert energy == -0.75
+    assert calls[0][0] == "create"
+    assert calls[0][1] is auth_client
+    assert calls[0][2]["input"]["params"] == [0.5]
+    assert calls[1] == ("wait", auth_client, "job-123", 0.25, 12.0)
+
+
+def test_coordinate_search_reports_and_lowers_energy():
+    messages = []
+
+    def bowl(params):
+        return (params[0] - 0.25) ** 2
+
+    result = example.coordinate_search(
+        bowl,
+        [1.25],
+        step_size=0.5,
+        min_step=0.125,
+        max_iterations=4,
+        log=messages.append,
+    )
+
+    assert result.energy == pytest.approx(0.0)
+    assert result.parameters == pytest.approx([0.25])
+    assert result.history[-1] == (2, [0.25], 0.0)
+    assert any(message.startswith("iteration 2:") for message in messages)