Quantum Genetic Algorithm on Multilevel Quantum Systems

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width="24.2734pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-6.668)"><path d="M162 0V316H101V0H162Z" id="g119-34"></path></g><g transform="matrix(.013,0,0,-0.013,0,-3.066)"><path d="M162 0V316H101V0H162Z" id="g119-34"></path></g><g transform="matrix(.013,0,0,-0.013,0,.535)"><path d="M162 0V316H101V0H162Z" id="g119-34"></path></g><g transform="matrix(.013,0,0,-0.013,0,4.136)"><path d="M162 0V316H101V0H162Z" id="g119-34"></path></g><g transform="matrix(.013,0,0,-0.013,3.432,0)"><path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z" id="g113-114"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.75,3.132)"><path d="M870 650H622L613 619C694 615 708 606 708 559C708 531 702 477 686 396L636 136H633L281 650H127L120 619C180 616 198 611 212 592C227 572 232 558 220 503L166 254C148 169 139 131 126 89C112 43 85 35 33 32L24 0H280L286 32C208 37 189 44 189 93C189 124 198 179 212 250L267 526H271L622 -8H655L732 396C747 477 762 532 770 556C785 600 798 616 862 619L870 650Z" id="g50-79"></path></g><g transform="matrix(.013,0,0,-0.013,18.03,2.33939e-05)"><path d="M360 267V273L125 799H62L297 270L62 -259H125L360 267Z" id="g119-14"></path></g></svg></span></td></tr><tr><td class="align_left" colspan="9"><hr/></td></tr><tr><td class="align_center" colspan="9">Measurement</td></tr><tr><td class="align_left" colspan="9"><hr/></td></tr><tr><td class="align_center"><span style="width: 6.6762ptpx;"><svg height="12.0262pt" id="M125" style="vertical-align:-2.68566pt" version="1.1" viewbox="-0.0498162 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xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M451 -27L435 -6L281 -101V690H223V-101L69 -6L53 -27C139 -97 215 -165 252 -202C289 -165 365 -97 451 -27Z" id="g117-161"></path></g></svg></span></td><td class="align_center"><span style="width: 6.6762ptpx;"><svg height="12.0262pt" id="M130" style="vertical-align:-2.68566pt" version="1.1" viewbox="-0.0498162 -9.34054 6.6762 12.0262" width="6.6762pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M451 -27L435 -6L281 -101V690H223V-101L69 -6L53 -27C139 -97 215 -165 252 -202C289 -165 365 -97 451 -27Z" id="g117-161"></path></g></svg></span></td><td class="align_center"><span style="width: 6.6762ptpx;"><svg height="12.0262pt" id="M131" style="vertical-align:-2.68566pt" version="1.1" viewbox="-0.0498162 -9.34054 6.6762 12.0262" width="6.6762pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M451 -27L435 -6L281 -101V690H223V-101L69 -6L53 -27C139 -97 215 -165 252 -202C289 -165 365 -97 451 -27Z" id="g117-161"></path></g></svg></span></td><td class="align_center"><span style="width: 6.6762ptpx;"><svg height="12.0262pt" id="M132" style="vertical-align:-2.68566pt" version="1.1" viewbox="-0.0498162 -9.34054 6.6762 12.0262" width="6.6762pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M451 -27L435 -6L281 -101V690H223V-101L69 -6L53 -27C139 -97 215 -165 252 -202C289 -165 365 -97 451 -27Z" id="g117-161"></path></g></svg></span></td><td class="align_center"><span style="width: 6.6762ptpx;"><svg height="12.0262pt" id="M133" style="vertical-align:-2.68566pt" version="1.1" viewbox="-0.0498162 -9.34054 6.6762 12.0262" width="6.6762pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M451 -27L435 -6L281 -101V690H223V-101L69 -6L53 -27C139 -97 215 -165 252 -202C289 -165 365 -97 451 -27Z" id="g117-161"></path></g></svg></span></td></tr><tr><td class="align_left" colspan="9"><hr/></td></tr><tr><td class="align_center" colspan="9"> </td></tr><tr><td class="align_left" colspan="9"><hr/></td></tr><tr><td class="align_center">0</td><td class="align_center">7</td><td class="align_center">3</td><td class="align_center">…</td><td class="align_center">1</td><td class="align_center">…</td><td class="align_center">…</td><td class="align_center">…</td><td class="align_center">0</td></tr><tr class="table-tr"><td colspan="9"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Quantum Genetic Algorithm on Multilevel Quantum Systems 