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Merge pull request #123 from ColibrITD-SAS/feat-pauli-decomposition
Feat pauli decomposition
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‎docs/tools.rst

+11-1
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@@ -128,4 +128,14 @@ Theoretical simulations
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from mpqp.tools.theoretical_simulation import *
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.. automodule:: mpqp.tools.theoretical_simulation
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.. automodule:: mpqp.tools.theoretical_simulation
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Observable decomposition
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------------------------
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.. code-block:: python
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:class: import
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from mpqp.tools.obs_decomposition import *
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.. automodule:: mpqp.tools.obs_decomposition

‎examples/notebooks/3_Expectation_value_of_observables.ipynb

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@@ -115,26 +115,32 @@
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 22,
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"id": "b1cb8ad4",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Result: ATOSDevice, MYQLM_PYLINALG\n",
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" Expectation value: -3.5935083233096687\n",
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"BatchResult: 2 results\n",
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"Result: circuit 1, ATOSDevice, MYQLM_PYLINALG\n",
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" Expectation value: -0.12200000000000011\n",
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" Error/Variance: 0.09998468351171062\n",
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"Result: circuit 1, IBMDevice, AER_SIMULATOR\n",
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" Expectation value: 1.9081958235744878e-17\n",
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" Error/Variance: 0.0\n",
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"-3.5935083233096687\n"
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"expectation_value: -0.12200000000000011\n",
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"expectation_value: 1.9081958235744878e-17\n"
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]
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}
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],
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"source": [
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"from mpqp.execution import run, ATOSDevice, IBMDevice\n",
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"result = run(circuit, ATOSDevice.MYQLM_PYLINALG)\n",
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"print(result)\n",
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"print(result.expectation_value)"
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"results = run(circuit, [ATOSDevice.MYQLM_PYLINALG, IBMDevice.AER_SIMULATOR])\n",
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"print(results)\n",
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"for result in results:\n",
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" print(f\"expectation_value:\", result.expectation_value)"
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]
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},
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{
@@ -159,12 +165,12 @@
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"output_type": "stream",
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"text": [
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"BatchResult: 2 results\n",
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"Result: ATOSDevice, MYQLM_PYLINALG\n",
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" Expectation value: -3.6279999999999997\n",
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" Error/Variance: 0.10472127540648739\n",
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"Result: IBMDevice, AER_SIMULATOR\n",
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" Expectation value: -3.2729999999999992\n",
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" Error/Variance: 22.060085000000004\n"
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"Result: circuit 1, ATOSDevice, MYQLM_PYLINALG\n",
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" Expectation value: -3.722\n",
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" Error/Variance: 0.10571682351161849\n",
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"Result: circuit 1, IBMDevice, AER_SIMULATOR\n",
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" Expectation value: -3.5935083233096723\n",
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" Error/Variance: 0.0\n"
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]
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}
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],
@@ -231,12 +237,6 @@
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"everything in term of expression based on the fundamental atoms. Let's see how."
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]
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},
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{
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"cell_type": "markdown",
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"id": "9ab10e2e",
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"metadata": {},
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"source": []
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},
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{
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"cell_type": "markdown",
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"id": "7d07ec4b",
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"ps_1=1*I@Z + -3*X@Y\n"
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"ps_1=1*I@Z - 3*X@Y\n"
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]
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}
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],
@@ -266,6 +266,65 @@
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"print(f\"{ps_1=}\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "937f1a84",
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"metadata": {},
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"source": [
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"#### Using Symbolic Variables in a PauliString\n",
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"\n",
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"We can also define `PauliString` objects with symbolic coefficients using `sympy`:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "032ff198",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(θ)*I@X + (k)*Z@Y\n"
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]
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}
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],
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"source": [
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"from sympy import symbols\n",
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"\n",
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"theta, k = symbols(\"θ k\")\n",
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"ps_symbol = theta * I @ X + k * Z @ Y\n",
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"print(ps_symbol)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d153fda4",
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"metadata": {},
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"source": [
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"We can substitute numerical values for the symbolic coefficients:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"id": "5dd3c74b",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"3.1416*I@X - 1*Z@Y\n"
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]
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}
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],
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"source": [
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"ps_symbol = ps_symbol.subs({theta: np.pi, k: -1})\n",
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"print(ps_symbol)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7824baf5",
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": 13,
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"id": "06784ef3",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"ps_2 = 1*I@Z + 2.555555555*Y@I + 1*X@Z + -1*X@Z\n",
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" = 2.555555555*Y@I + 1*I@Z\n",
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" ~= 1*I@Z + 2.6*Y@I + 1*X@Z + -1*X@Z\n",
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"ps_2 = 1*I@Z + 2.555555555*Y@I + 1*X@Z - 1*X@Z\n",
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" = 1*I@Z + 2.555555555*Y@I\n",
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" ~= 1*I@Z + 2.6*Y@I + 1*X@Z - 1*X@Z\n",
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" ~= 1*I@Z + 2.5556*Y@I\n"
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]
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}
@@ -318,7 +377,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 14,
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"id": "b9cadb08",
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"metadata": {},
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"outputs": [
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"output_type": "stream",
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"text": [
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"Addition:\n",
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"(1*I@Z + -3*X@Y) + (1*I@Z + 2.6*Y@I) = 2*I@Z + -3*X@Y + 2.6*Y@I\n",
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"(1*I@Z - 3*X@Y) + (1*I@Z + 2.6*Y@I) = 2*I@Z - 3*X@Y + 2.6*Y@I\n",
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"\n",
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"Subtraction:\n",
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"(1*I@Z + -3*X@Y) - (1*I@Z + 2.6*Y@I) = -3*X@Y + -2.6*Y@I\n",
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"(1*I@Z - 3*X@Y) - (1*I@Z + 2.6*Y@I) = -3*X@Y - 2.6*Y@I\n",
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"\n",
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"Scalar product:\n",
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"2 * (1*I@Z + -3*X@Y) = 2*I@Z + -6*X@Y\n",
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"2 * (1*I@Z - 3*X@Y) = 2*I@Z - 6*X@Y\n",
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"\n",
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"Scalar division:\n",
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"(1*I@Z + 2.6*Y@I) / 3 ~= 0.3333*I@Z + 0.8667*Y@I\n",
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"\n",
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"Tensor product:\n",
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"(1*I@Z + -3*X@Y) @ Z = 1*I@Z@Z + -3*X@Y@Z\n",
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"(1*I@Z + -3*X@Y) @ (1*I@Z + 2.6*Y@I) = 1*I@Z@I@Z + -3*I@Z@X@Y + 2.6*Y@I@I@Z + -7.8*Y@I@X@Y\n"
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"(1*I@Z - 3*X@Y) @ Z = 1*I@Z@Z - 3*X@Y@Z\n",
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"(1*I@Z - 3*X@Y) @ (1*I@Z + 2.6*Y@I) = 1*I@Z@I@Z + 2.6*I@Z@Y@I - 3*X@Y@I@Z - 7.8*X@Y@Y@I\n"
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]
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}
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],
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"execution_count": 15,
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"id": "5b0537a1",
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"metadata": {},
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"outputs": [],
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": 23,
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"id": "1732e099",
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"metadata": {},
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"outputs": [
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"text": [
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"`obs` created with matrix:\n",
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"matrix:\n",
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"[[ 4.+0.j 2.+0.j 3.+0.j 8.+0.j]\n",
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" [ 2.+0.j -3.+0.j 1.+0.j 0.+0.j]\n",
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" [ 3.+0.j 1.+0.j -1.+0.j 5.+0.j]\n",
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" [ 8.+0.j 0.+0.j 5.+0.j 2.+0.j]]\n",
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"[[4, 2 , 3 , 8],\n",
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" [2, -3, 1 , 0],\n",
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" [3, 1 , -1, 5],\n",
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" [8, 0 , 5 , 2]]\n",
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"Pauli string:\n",
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"0.5*I@I + 3.5*I@X + 1*I@Z + 1.5*X@I + 4.5*X@X + 1.5*X@Z + -3.5*Y@Y + -1.5*Z@X + 2.5*Z@Z\n",
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"0.5*I@I + 3.5*I@X + 1*I@Z + 1.5*X@I + 4.5*X@X + 1.5*X@Z - 3.5*Y@Y - 1.5*Z@X + 2.5*Z@Z\n",
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"\n",
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"\n",
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"`obs1` created with Pauli string:\n",
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"Pauli string:\n",
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"1*I@Z + -3*X@Y\n",
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"1*I@Z - 3*X@Y\n",
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"matrix:\n",
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"[[ 1.+0.j 0.+0.j 0.+0.j 0.-3.j]\n",
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" [ 0.+0.j -1.+0.j 0.+3.j 0.+0.j]\n",
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" [ 0.+0.j 0.-3.j 1.+0.j 0.+0.j]\n",
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" [ 0.+3.j 0.+0.j 0.+0.j -1.+0.j]]\n"
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"[[1 , 0 , 0 , -3j],\n",
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" [0 , -1 , 3j, 0 ],\n",
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" [0 , -3j, 1 , 0 ],\n",
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" [3j, 0 , 0 , -1 ]]\n"
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]
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}
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],
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"source": [
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"from mpqp.tools import pprint\n",
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"\n",
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"\n",
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"print(\"`obs` created with matrix:\")\n",
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"print(\"matrix:\")\n",
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"print(obs.matrix)\n",
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"pprint(obs.matrix)\n",
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"print(\"Pauli string:\")\n",
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"print(obs.pauli_string)\n",
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"\n",
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"print(\"Pauli string:\")\n",
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"print(obs1.pauli_string)\n",
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"print(\"matrix:\")\n",
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"print(obs1.matrix)"
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"pprint(obs1.matrix)"
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]
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},
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{
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"execution_count": 17,
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"id": "892f0b6e",
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"metadata": {},
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"outputs": [],
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"execution_count": 18,
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"id": "745aa999",
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"metadata": {},
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"outputs": [
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"output_type": "stream",
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"text": [
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"BatchResult: 3 results\n",
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"Result: ATOSDevice, MYQLM_CLINALG\n",
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" Expectation value: 0.08200000000000007\n",
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" Error/Variance: 0.10000294289963965\n",
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"Result: ATOSDevice, MYQLM_PYLINALG\n",
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" Expectation value: 0.12600000000000006\n",
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" Error/Variance: 0.10000590573151757\n",
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"Result: IBMDevice, AER_SIMULATOR\n",
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" Expectation value: 0.14800000000000002\n",
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" Error/Variance: 9.987479999999998\n"
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"Result: circuit 1, ATOSDevice, MYQLM_PYLINALG\n",
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" Expectation value: -0.031999999999999945\n",
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" Error/Variance: 0.100047316133245\n",
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"Result: circuit 1, IBMDevice, AER_SIMULATOR\n",
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" Expectation value: 1.9081958235744878e-17\n",
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" Error/Variance: 0.0\n",
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"Result: circuit 1, ATOSDevice, MYQLM_CLINALG\n",
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" Expectation value: -0.29800000000000015\n",
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" Error/Variance: 0.0996658079447173\n"
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]
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}
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],
@@ -510,7 +572,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.12"
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"version": "3.9.5"
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}
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},
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"nbformat": 4,

‎mpqp/core/instruction/measurement/expectation_value.py

+1-1
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@@ -61,7 +61,7 @@ class Observable:
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[ 0.+0.j, 0.+4.j, 3.+0.j, 0.+0.j],
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[ 0.-4.j, 0.+0.j, 0.+0.j, -3.+0.j]],
6363
dtype=complex64))
64-
>>> Observable(3 * I @ Z + 4 * X @ Y).pauli_string.sort_monomials()
64+
>>> Observable(3 * I @ Z + 4 * X @ Y).pauli_string.sorted_monomials()
6565
3*I@Z + 4*X@Y
6666
6767
"""

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