the more than 10300 continuously variable parameters defining the quantum state of such a system? My answer is simple. No, never." Candidates for physical realizations For physically implementing a quantum computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits): Superconducting quantum computing (qubit implemented by the state of nonlinear resonant superconducting circuits containing Josephson junctions) Trapped ion quantum computer (qubit implemented by the internal state of trapped ions) Neutral atoms in optical lattices (qubit implemented by internal states of neutral atoms trapped in an optical lattice) Quantum dot computer, spin-based (e.g. the Loss-DiVincenzo quantum computer) (qubit given by the spin states of trapped electrons) Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot) Quantum computing using engineered quantum wells, which could in principle enable the construction of a quantum computer that operates at room temperature Coupled quantum wire (qubit implemented by a pair of quantum wires coupled by a quantum point contact) Nuclear magnetic resonance quantum computer (NMRQC) implemented with the nuclear magnetic resonance of molecules in solution, where qubits are provided by nuclear spins within the dissolved molecule and probed with radio waves Solid-state NMR Kane quantum computer (qubit realized by the nuclear spin state of phosphorus donors in silicon) Vibrational quantum computer (qubits realized by vibrational superpositions in cold molecules) Electrons-on-helium quantum computer (qubit is the electron spin) Cavity quantum electrodynamics (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities) Molecular magnet (qubit given by spin states) Fullerene-based ESR quantum computer (qubit based on the electronic spin of atoms or molecules encased in fullerenes) Nonlinear optical quantum computer (qubits realized by processing states of different modes of light through both linear and nonlinear elements) Linear optical quantum computer (LOQC) (qubits realized by processing states of different modes of light through linear elements e.g. mirrors, beam splitters and phase shifters) Diamond-based quantum computer (qubit realized by the electronic or nuclear spin of nitrogen-vacancy centers in diamond) Bose-Einstein condensate-based quantum computer Transistor-based quantum computer (string quantum computers with entrainment of positive holes using an electrostatic trap) Rare-earth-metal-ion-doped inorganic crystal based quantum computer (qubit realized by the internal electronic state of dopants in optical fibers) Metallic-like carbon nanospheres-based quantum computer The large number of candidates demonstrates that quantum computing, despite rapid progress, is still in its infancy. Theory Computability Any computational problem