Quantum　computer　is　one　of　the　future　development　directions　of　computer　science.　It　is　a　kind　of　physical　device　that　follows　the　laws　of　quantum　mechanics　and　can　efficiently　store　and　process　quantum　information.　The　quantum　mechanical　system　is　described　by　Dirac　and　von　Neumann　by　using　Hilbert　space　theory,　which　is　a　vector　space　given　by　the　inner　product.　With　the　rapid　development　of　quantum　computing,　the　inner　product　of　quantum　states　and　its　modulus　have　received　extensive　attention　in　various　fields　such　as　quantum　machine　learning,　quantum　cryptography,　and　quantum　signal　processing.　Therefore,　quantum　inner　product　and　its　modulus　were　reviewed.　Unlike　the　method　of　the　classical　algorithm,　the　unitary　operator　must　be　used　to　operate　the　quantum　state　and　measurement　to　obtain　the　quantum　inner　product.　The　quantum　inner　product　is　a　complex　number,　and　both　the　complex　number　and　its　modulus　play　a　critical　role　in　quantum　computing.　The　main　content　of　this　paper　was　divided　into　two　parts:　the　quantum　inner　product　modulus　and　the　quantum　inner　product.　The　quantum　state　|0〉⨂n　is　generally　evolved　from　the　initial　state　by　the　unitary　operator.　Therefore,　the　calculation　methods　of　the　inner　product　modulus　and　inner　product　of　the　quantum　state　are　divided　into　direct　methods　and　indirect　methods　according　to　whether　the　unitary　operator　is　used　in　the　calculation　process.　Then,　the　applications　of　the　quantum　inner　product　and　its　modulus　were　summarized.　Finally,　the　shortcomings　of　the　current　research　and　the　future　research　directions　were　put　forward.　©　2023　Beijing　University　of　Technology.　All　rights　reserved.