Quantum-Based Feature Selection for Multiclassification Problem in Complex Systems with Edge Computing

<div>One of the ideal experiment circuits of similarity calculation in QReliefF algorithm running on Rigetti platform. q[0] − q [<a href="/journals/complexity/2020/8216874/#B7">7</a>] represents the randomly selected quantum state <span class="nowrap"><svg height="14.6294pt" id="M107" style="vertical-align:-5.34107pt" version="1.1" viewbox="-0.0498162 -9.28833 24.8328 14.6294" width="24.8328pt" 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="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.765,0)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.134,3.132)"><path d="M463 633C453 636 427 644 417 648C388 660 349 667 316 667C183 667 100 592 100 483C100 398 176 335 223 305L259 282C321 242 358 203 358 149C358 66 301 22 234 22C110 22 70 131 57 208L24 205L28 48C51 23 128 -17 215 -17C342 -17 446 60 446 174C446 262 394 310 317 361L284 383C229 420 183 455 183 515C183 569 222 628 298 628C384 628 418 563 428 481L461 487C459 527 458 593 463 633Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,20.438,5.233)"><path d="M455 312C455 472 400 635 248 635C95 635 39 458 39 312C39 144 93 -12 248 -12C400 -12 455 166 455 312ZM361 314C361 173 337 30 249 30C163 30 131 174 131 313C131 451 155 594 248 594C334 594 361 454 361 314Z"></path></g></svg>,</span> q [<a href="/journals/complexity/2020/8216874/#B9">9</a>] − q [<a href="/journals/complexity/2020/8216874/#B16">16</a>] represents <span class="nowrap"><svg height="14.5707pt" id="M108" style="vertical-align:-5.28237pt" version="1.1" viewbox="-0.0498162 -9.28833 24.8328 14.5707" width="24.8328pt" 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="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.765,0)"><path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.134,3.132)"><path d="M463 633C453 636 427 644 417 648C388 660 349 667 316 667C183 667 100 592 100 483C100 398 176 335 223 305L259 282C321 242 358 203 358 149C358 66 301 22 234 22C110 22 70 131 57 208L24 205L28 48C51 23 128 -17 215 -17C342 -17 446 60 446 174C446 262 394 310 317 361L284 383C229 420 183 455 183 515C183 569 222 628 298 628C384 628 418 563 428 481L461 487C459 527 458 593 463 633Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,20.438,5.233)"><path d="M394 0V37C301 42 295 50 295 122V635C236 613 178 596 109 583V553L165 551C205 549 209 544 209 495V122C209 50 203 42 111 37V0H394Z"></path></g></svg>,</span> and q [<a href="/journals/complexity/2020/8216874/#B17">17</a>] is the resultant qubit. X is the Not operation, and <i>Ry</i> is R<sub><i>y</i></sub> operation which can be expressed as a matrix in equation (<a href="https://static-preview.hindawi.com/articles/complexity/volume-2020/8216874/figures/#EEq9">9</a>).</div>

Complexity

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Figure 9

Figure 9: Quantum-Based Feature Selection for Multiclassification Problem in Complex Systems with Edge Computing 