mechanics such that a quantum Hamiltonian is derived describing the total energy of the system. Technology Manufacturing Superconducting quantum computing devices are typically designed in the radio-frequency spectrum, cooled in dilution refrigerators below 15 mK (millikelvins) and addressed with conventional electronic instruments, e.g. frequency synthesizers and spectrum analyzers. Typical dimensions fall on the range of micrometers, with sub-micrometer resolution, allowing for the convenient design of a Hamiltonian system with well-established integrated circuit technology. Manufacturing superconducting qubits follows a process involving lithography, depositing of metal, etching, and controlled oxidation as described in. Manufacturers continue to improve the lifetime of superconducting qubits and have made significant improvements since the early 2000s as illustrated in the chart to the right. Josephson junctions One distinguishable attribute of superconducting quantum circuits is the use of Josephson junctions. Josephson junctions are an electrical element which does not existent in normal conductors. Recall that a junction is a weak connection between two leads of wire (in this case a superconductive wire) on either side of a thin layer of insulator material only a few atoms thick, usually implemented using shadow evaporation technique. The resulting Josephson junction device exhibits the Josephson Effect whereby the junction produces a supercurrent. An image of a single Josephson junction is shown to the right. The condensate wave function on the two sides of the junction are weakly correlated, meaning that they are allowed to have different superconducting phases. This distinction of nonlinearity contrasts continuous superconducting wire for which the wave function across the junction must be continuous. Current flow through the junction occurs by quantum tunneling, seeming to instantaneously "tunnel" from one side of the junction to the other. This tunneling phenomenon is unique to quantum systems. Thus, quantum tunneling is used to create nonlinear inductance, essential for qubit design as it allows a design of anharmonic oscillators for which energy levels are discretized (or quantized) with nonuniform spacing between energy levels, denoted . In contrast, the quantum harmonic oscillator cannot be used as a qubit as there is no way to address only two of its states. Qubit archetypes The three primary superconducting qubit archetypes are the phase, charge and flux qubit. Many hybridizations of these archetypes exist including the Fluxonium, transmon, Xmon, and Quantronium. For any qubit implementation the logical quantum states are mapped to different states of the physical system (typically to discrete energy levels or their quantum superpositions).