Brief Primer on the Fundaments of Quantum Computing Richard L Amoroso amoroso@noeticadvancedstudies.us Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 PART 1 From Concept to Conundrum 1.1 Preamble – Bits, Qubits and Complex Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Panoply of QC Architectures and Substrates – Limited Overview . . . . . . . . . . . .9 1.2.1 Quantum Turing Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 1.2.2 Quantum Circuit Computing Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2.3 Measurement Based Quantum Computing . . . . . . . . . . . . . . . . . . . . . . . . .11 1.2.4 Adiabatic Quantum Computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 1.2.5 The Kane Nuclear Spin QC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2.6 QRAM Models of Quantum Computation . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.7 Electrons-On-Helium Quantum Computers . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.8 Fullerene-Based ESR Quantum Computer . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2.9 Superconductor-Based Quantum Computers . . . . . . . . . . . . . . . . . . . . . . 16 1.2.9.1 SQUID-BASED SUPERCONDUCTOR QC . . . . . . . . . . . . . . . . . . . . . 16 1.2.9.2 TRAPPED ION-BASED SUPERCONDUCTOR QC . . . . . . . . . . . . . . 17 1.2.10 Diamond Based Quantum Computers . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2.11 Quantum Dot Quantum Computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.12 Transistor-Based Quantum Computer . . . . . . . . . . . . . . . . . . . . . . . . . . .20 1.2.13 Molecular Magnet Quantum Computer . . . . . . . . . . . . . . . . . . . . . . . . . . .21 1.2.14 Bose–Einstein Condensate-Based Quantum Computer . . . . . . . . . . . . . . 22 1.2.15 Rare-Earth-Metal-Ion-Doped Inorganic Crystal QC . . . . . . . . . . . . . . . . . 22 1.2.16 Linear Optical Quantum Computer (LOQC) . . . . . . . . . . . . . . . . . . . . . . .23 1.2.17 Optical Lattice Based Quantum Computing (OLQC) . . . . . . . . . . . . . . . . 24 1.2.18 Cavity Quantum Electrodynamics Quantum Computing. . . . . . . . . . . . . . 25 1.2.19 Nuclear Magnetic Resonance (NMR) Quantum Computing. . . . . . . . . . . 26