The　filtering　of　quantum　signals　that　encode　a　message　in　qubits　has　become　increasingly　attractive　in　the　past　few　years.　Some　problems　associated　with　boundary　will　occur　due　to　the　finiteness　of　the　quantum　signal　length.　However,　there　have　been　few　results　in　solving　the　quantum　boundary　problem　until　now.　In　this　paper,　we　investigate　four　different　methods　for　boundary　extension　of　quantum　signals　(BEQS).　An　auxiliary　qubit　is　entangled　with　the　position　of　the　original　signal　to　extend　the　signal　at　first.　Next,　four　extension　methods　are　implemented　by　using　quantum　operators　such　as　swap,　Adder,　and　cycle　shift.　Then,　two　quantum　signal　filters　and　their　quantum　circuits　are　proposed　based　on　BEQS.　The　complexity　analysis　shows　that　the　proposed　scheme　has　computational　complexity　that　is　a　second-order　polynomial　in　the　number　of　qubits　that　encode　the　signal.　Finally,　we　use　the　root　mean　square　error　to　describe　the　visual　quality　of　a　filtered　signal.　Several　experiments　demonstrate　that　the　extension　method　of　being　symmetric　extension　has　a　good　performance　in　noise　suppression.　The　significance　of　this　paper　is　to　present　boundary　extension　methods　for　quantum　signal.