sampler vqe

Sampling VQE.ipynb

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+   "id": "b1f28f06",
+   "metadata": {},
+   "source": [
+    "# The sampler version of VQE\n",
+    "\n",
+    "The VQE is originally formulated for minimizing the expectation value of some Hamiltonian $H$. The best solution is the parameter set that yields the smallest energy. \n",
+    "\n",
+    "In a classical optimization setting, where $H$ is a diagonal matrix, the goals, results and methods are slightly different than in the general case:\n",
+    "* the best result is the best _measurement/bitstring_, not the best energy\n",
+    "* we can use aggregation functions on the single measurements (like CVaR) which is only possible for diagonal Hamiltonians \n",
+    "* the Hamiltonian can be given as function on bitstrings\n",
+    "\n",
+    "Therefore we suggest to add a `SamplerVQE` (`SamplingVQE`?) that's specific to this use case and can be leveraged in QAOA and Qiskit Optimization."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "83e818b2",
+   "metadata": {},
+   "source": [
+    "### Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "52a93f3d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class SamplerVQE:\n",
+    "    def __init__(\n",
+    "        self,\n",
+    "        ansatz: QuantumCircuit,\n",
+    "        optimizer: Union[Optimizer, Minimizer],\n",
+    "        sampler: Sampler,\n",
+    "        gradient: EstimatorGradient,  # bit weird that's it's not a sampler gradient\n",
+    "        aggregation: Union[float, AGGREATOR],  # CVaR alpha if a float, but any aggregation possible\n",
+    "    ) -> None:\n",
+    "        ...\n",
+    "    \n",
+    "    def compute_minimum_eigenvalue(\n",
+    "        self,\n",
+    "        operator: OperatorBase,  # could also support a function f: bitstr -> float\n",
+    "        aux_operators: ListOrDict[operator]\n",
+    "    ) -> SamplerVQEResult:\n",
+    "        ..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0e602c65",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "@dataclass\n",
+    "def SamplerVQEResult:\n",
+    "    # same as VQE\n",
+    "    eigenvalue: float\n",
+    "    cost_function_evals: int\n",
+    "    optimal_point: np.ndarray\n",
+    "    optimal_parameters: Dict[Parameter, float]\n",
+    "    optimizer_time: float\n",
+    "    \n",
+    "    # different\n",
+    "    best_measurement: str\n",
+    "    final_samples: QuasiDistribution  # could also be called \"eigenstate\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f0a0c332",
+   "metadata": {},
+   "source": [
+    "### QAOA\n",
+    "\n",
+    "**Note** If QAOA inherits from `SamplerVQE` the new version can only handle diagonal Hamiltonians, not like right now any Hamiltonian!\n",
+    "\n",
+    "#### Option 1\n",
+    "\n",
+    "QAOA inherits from `SamplerVQE` and can from now on only handle diagonal Hamiltonians."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "81ed65d5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class QAOA(SamplerVQE)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d8197208",
+   "metadata": {},
+   "source": [
+    "#### Option 2\n",
+    "\n",
+    "QAOA still inherits from `VQE` and we add a new `SamplerQAOA` inheriting from `SamplerVQE`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4b160fb9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "class QAOA(VQE)\n",
+    "class SamplerQAOA(SamplerVQE)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98f9c873",
+   "metadata": {},
+   "source": [
+    "### SamplerMinimumEigensolver\n",
+    "\n",
+    "Should we add a `SamplingMinimumEigensolver` as common base class of `SamplerVQE`, `(Sampler)QAOA` and add a `SamplerNumPyMES`?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a6cd9697",
+   "metadata": {},
+   "source": [
+    "#### Pro SamplerMES\n",
+    "\n",
+    "* The `SamplerVQE` cannot be used as drop-in replacement for other MES as it only supports diagonal Hamiltonians.\n",
+    "* Results types also differ\n",
+    "* We can have a classical, exact reference algo: `SamplerNumPyMES`"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bddeeb77",
+   "metadata": {},
+   "source": [
+    "#### Contra SamplerMES\n",
+    "\n",
+    "The alternative solution would be that `SamplerVQE` & co. derive from `MinimumEigensolver` but raise an error if the Hamiltonian is not diagonal.\n",
+    "\n",
+    "* The `MinimumEigenOptimizer` could continue to just accept any MES (otherwise we have to start supporting MES and SamplerMES)\n"
+   ]
+  }
+ ],
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