A quantum computer is a computation device that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), quantum computation uses quantum properties to represent data and perform operations on these data.

A classical computer has a memory made up of bits, where each bit represents either a one or a zero. A quantum computer maintains a sequence of qubits. A single qubit can represent a one, a zero, or any quantum superposition of these two qubit states; moreover, a pair of qubits can be in any quantum superposition of 4 states, and three qubits in any superposition of 8. A quantum computer operates by setting the qubits in a controlled initial state that represents the problem at hand and by manipulating those qubits with a fixed sequence of quantum logic gates. The sequence of gates to be applied is called a quantum algorithm.

There are a number of quantum computing models, distinguished by the basic elements in which the computation is decomposed. The four main models of practical importance are:

  • Quantum gate array (computation decomposed into sequence of few-qubit quantum gates)
  • One-way quantum computer (computation decomposed into sequence of one-qubit measurements applied to a highly entangled initial state or cluster state)
  • Adiabatic quantum computer or computer based on Quantum annealing (computation decomposed into a slow continuous transformation of an initial Hamiltonian into a final Hamiltonian, whose ground states contains the solution)[25]
  • Topological quantum computer (computation decomposed into the braiding of anyons in a 2D lattice)
  • The Quantum Turing machine is theoretically important but direct implementation of this model is not pursued. All four models of computation have been shown to be equivalent to each other in the sense that each can simulate the other with no more than polynomial overhead.
  • For physically implementing a quantum computer, many different candidates are being pursued, among them (distinguished by the physical system used to realize the qubits):
  • Superconductor-based quantum computers (including SQUID-based quantum computers) (qubit implemented by the state of small superconducting circuits (Josephson junctions))
  • Trapped ion quantum computer (qubit implemented by the internal state of trapped ions)
  • Optical lattices (qubit implemented by internal states of neutral atoms trapped in an optical lattice)
  • electrically defined or self-assembled quantum dots (e.g. the Loss-DiVincenzo quantum computer or) (qubit given by the spin states of an electron trapped in the quantum dot)
  • Quantum dot charge based semiconductor quantum computer (qubit is the position of an electron inside a double quantum dot)
  • Nuclear magnetic resonance on molecules in solution (liquid-state NMR) (qubit provided by nuclear spins within the dissolved molecule)
  • Solid-state NMR Kane quantum computers (qubit realized by the nuclear spin state of phosphorus donors in silicon)
  • Electrons-on-helium quantum computers (qubit is the electron spin)
  • Cavity quantum electrodynamics (CQED) (qubit provided by the internal state of atoms trapped in and coupled to high-finesse cavities)
  • Molecular magnet
  • Fullerene-based ESR quantum computer (qubit based on the electronic spin of atoms or molecules encased in fullerene structures)
  • Optics-based quantum computer (Quantum optics) (qubits realized by appropriate states of different modes of the electromagnetic field, e.g.)
  • 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 computers (qubit realized by the internal electronic state of dopants in optical fibers)

The large number of candidates demonstrates that the topic, in spite of rapid progress, is still in its infancy. But at the same time, there is also a vast amount of flexibility.