QUANTUM COMPUTATION AND QUANTUM INFORMATION GROVERS ALGORITHM Igor

QUANTUM COMPUTATION AND QUANTUM INFORMATION GROVER'S ALGORITHM Igor Ilijašević 1 / 26

Igor Ilijašević 2 / 26

COMPLEX NUMBERS BASICS Igor Ilijašević 3 / 26

BASICS • Dirac (bra–ket) notation �φ|ψ� • Introduced in 1939 by Paul Dirac • Interpreted as the probability amplitude for the state ψ to collapse into the state φ Igor Ilijašević 4 / 26

BASICS • Igor Ilijašević 5 / 26

BASICS • Igor Ilijašević 6 / 26

BASICS • Igor Ilijašević 7 / 26

BASICS • Igor Ilijašević 8 / 26

BASICS • Igor Ilijašević 9 / 26

BASICS • Igor Ilijašević 10 / 26

MORE BASICS • Igor Ilijašević 11 / 26

QUANTUM GATES AND CIRCUIT SYMBOLS Igor Ilijašević 12 / 26

QUANTUM GATES AND CIRCUIT SYMBOLS Igor Ilijašević 13 / 26

QUANTUM GATES AND CIRCUIT SYMBOLS Igor Ilijašević 14 / 26

QUANTUM GATES • Igor Ilijašević 15 / 26

QUANTUM GATES Igor Ilijašević 16 / 26

QUANTUM GATES • Igor Ilijašević 17 / 26

QUANTUM PARALLELISM Igor Ilijašević 18 / 26

WALSH–HADAMARD TRANSFORM • Igor Ilijašević 19 / 26

GROVER'S ALGORITHM • Igor Ilijašević 20 / 26

GROVER'S ALGORITHM • Igor Ilijašević 21 / 26

GROVER'S ALGORITHM • Igor Ilijašević 22 / 26

GROVER'S ALGORITHM Igor Ilijašević 23 / 26

GOOGLE QUANTUM COMPUTING PLAYGROUND EXAMPLES Igor Ilijašević 24 / 26

GOOGLE QUANTUM COMPUTING PLAYGROUND GROVER'S ALGORITHM IMPLEMENTATION Igor Ilijašević 25 / 26

REFERENCES • “Quantum Computation and Quantum Information, 10 th Anniversary Edition”, Michael A. Nielsen & Isaac L. Chuang • Google Quantum Computing Playground, http: //qcplayground. withgoogle. com/ • http: //twistedoakstudios. com/blog/Post 2644_grovers-quantum-searchalgorithm • http: //en. wikipedia. org/wiki/Grover's_algorithm • http: //www. quantiki. org/wiki/Main_Page • https: //www. youtube. com/watch? v=T 2 DXrs 0 Op. HU • https: //www. youtube. com/watch? v=Xmq_FJd 1 o. UQ Igor Ilijašević 26 / 26