As　a　newly　developed　simple　and　effective　optimization　technology,　the　fruit　fly　optimization　algorithm　(FOA)　has　been　successfully　applied　in　many　fields.　To　accelerate　the　algorithm　convergence　and　avoid　the　local　optimum,　the　enhanced　FOA　based　on　quantum　theory　called　QFOA　is　proposed　in　this　paper.　When　establishing　the　quantum　Delta　potential　well　around　the　location　of　fruit　fly　swarm,　QFOA　introduces　the　quantum　behavior-based　searching　mechanism　into　the　original　osphresis-based　search　procedure　of　FOA.　In　the　process　that　fruit　flies　find　and　move　toward　the　food　source,　fruit　flies　follow　the　wave　function　property　of　the　Delta　potential　well　rather　than　the　Newtonian　mechanics.　Taking　advantage　of　the　probability　and　uncertainty　of　quantum　theory,　the　proposed　QFOA　can　effectively　overcome　the　weakness　in　premature　convergence　and　easy　trapping　into　local　optimum.　Since　there　are　two　popular　models　of　the　basic　FOA,　this　paper　also　develops　two　corresponding　QFOAs.　Experimental　results　on　various　benchmark　functions　show　that　both　the　two　QFOA　models　has　overall　better　performance　compared　with　the　basic　FOA　as　well　as　other　FOA　variants　and　other　well-known　optimization　algorithms.　In　addition,　the　proposed　QFOAs　are　also　applied　to　unmanned　aerial　vehicle　(UAV)　path　planning　problem　in　the　three-dimensional　environment,　and　comparative　results　about　the　obtained　optimal　flight　path　and　population　convergence　process　show　the　effectiveness　of　QFOAs.　(C)　2020　The　Authors.　Published　by　Atlantis　Press　B.V.