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applications/chemistry/quantum_walk_fmo/quantum_walk_fmo.ipynb

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"cells": [
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{
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"cell_type": "markdown",
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"id": "7eacc601",
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"id": "0",
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"metadata": {},
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"source": [
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"# Continuous-Time Quantum Walk in Photosynthetic Energy Transfer"
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "64efa93c",
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"id": "1",
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"metadata": {},
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"outputs": [],
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"source": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "8ff1c0a6",
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"id": "2",
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"metadata": {},
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"outputs": [],
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"source": [
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"import time\n",
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"from functools import reduce\n",
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"from operator import mul\n",
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"import numpy as np\n",
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"\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"from scipy.linalg import expm\n",
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"\n",
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"from classiq import *"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3",
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"metadata": {},
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"source": [
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"## Continuous-Time Quantum Walk on a graph\n",
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},
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{
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"cell_type": "markdown",
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"id": "4",
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"metadata": {},
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"source": [
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"## Frenkel exciton Hamiltonian"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5",
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"metadata": {},
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"source": [
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"$$\n",
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "6",
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The aforementioned Hamiltonian can also be written as follows:\n",
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "3a01e104",
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"id": "8",
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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": 4,
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"id": "9",
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"metadata": {},
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"outputs": [],
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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": "10",
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"metadata": {},
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"source": [
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"Since it is difficult to directly execute the time evolution of the constructed Hamiltonian, we implement it using the following first-order Suzuki-Trotter decomposition:\n",
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "11",
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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": 6,
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"id": "12",
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"metadata": {},
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"outputs": [
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{
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let's compare the calculation results with those obtained using `scipy`."
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "4a84856b",
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"id": "14",
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"metadata": {},
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"outputs": [
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{
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## References\n",
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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"nbformat_minor": 9
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}
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{
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"title": "Photosynthetic Energy Transfer",
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"subtitle": "Continuous-Time Quantum Walk in Photosynthetic Energy Transfer",
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"description": "Continuous-Time Quantum Walk in Photosynthetic Energy Transfer",
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"friendly_name": "Photosynthetic Energy Transfer",
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"problem_domain_tags": [
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"chemistry"
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],
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"qmod_type": [
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"algorithms"
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],
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"level": [
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"demos"
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]
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"title": "Photosynthetic Energy Transfer",
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"subtitle": "Continuous-Time Quantum Walk in Photosynthetic Energy Transfer",
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"description": "Continuous-Time Quantum Walk in Photosynthetic Energy Transfer",
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"friendly_name": "Photosynthetic Energy Transfer",
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"problem_domain_tags": ["chemistry"],
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"qmod_type": ["algorithms"],
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"level": ["demos"]
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}

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