page_title: Superconducting quantum computing
section_title: Qubit archetypes
hierarchical_section_title: Superconducting quantum computing / Qubit archetypes
caption_attribution_description: a Cooper-pair box (CPB). The system is almost the same as the single-electron box.there is an island to store charges, a bulk electrode to provide these charges, and a gate electrode to shift the electrostatic potential of the island with respect to the bulk electrode and to tune the number of charges thereby. The crucial difference is that now both the island and source electrodes are superconducting, and the tunnel junction that connects them is in fact a Josephson junction. There are two energies that characterize the system. The first energy is the Josephson energy of the junction.it is a periodic function of the superconducting phase difference across the junction,−EJcosϕ. It is convenient to set the phase of the lead to zero, so that the phase difference is just a phase that characterizes the superconducting state of the island. The second energy is the same as for the non-superconducting setup: the charging energy associated with discrete charge Ne in the island. Why is the system called a Cooperpairbox? Each superconductor is a coherent reservoir of Cooper pairs rather than electrons, provided the energies involved are smaller than the superconducting energy gap. In this section, we will assume that there is always an even number of extra elementary charges in the island, and that charges are always transferred in Cooper pairs. a Cooper-pair box (CPB). The system is almost the same as the single-electron box.there is an island to store charges, a bulk electrode to provide these charges, and a gate electrode to shift the electrostatic potential of the island with respect to the bulk electrode and to tune the number of charges thereby. The crucial difference is that now both the island and source electrodes are superconducting, and the tunnel junction that connects them is in fact a Josephson junction. There are two energies that characterize the system. The first energy is the Josephson energy of the junction.it is a periodic function of the superconducting phase difference across the junction,−EJcosϕ. It is convenient to set the phase of the lead to zero, so that the phase difference is just a phase that characterizes the superconducting state of the island. The second energy is the same as for the non-superconducting setup: the charging energy associated with discrete charge Ne in the island. Why is the system called a Cooperpairbox? Each superconductor is a coherent reservoir of Cooper pairs rather than electrons, provided the energies involved are smaller than the superconducting energy gap. In this section, we will assume that there is always an even number of extra elementary charges in the island, and that charges are always transferred in Cooper pairs.
context_page_description: Superconducting quantum computing is an implementation of a quantum computer in superconducting electronic circuits. Research in superconducting quantum computing is conducted by Google, IBM, IMEC, BBN Technologies, Rigetti, and Intel. as of May 2016, up to nine fully controllable qubits are demonstrated in a 1D array, up to sixteen in a 2D architecture.
  More than two thousand superconducting qubits are in a commercial product by D-Wave Systems, however these qubits implement quantum annealing instead of a universal model of quantum computation.
context_section_description: The three superconducting qubit archetypes are the phase, charge and flux qubits, though many hybridizations exist (Fluxonium, Transmon, Xmon, Quantronium). For any qubit implementation, the logical quantum states  are to be mapped to the different states of the physical system, typically to the discrete (quantized) energy levels or to their quantum superpositions. In the charge qubit, different energy levels correspond to an integer number of Cooper pairs on a superconducting island. In the flux qubit, the energy levels correspond to different integer numbers of magnetic flux quanta trapped in a superconducting ring. In the phase qubit, the energy levels correspond to different quantum charge oscillation amplitudes across a Josephson junction, where the charge and the phase are analogous to momentum and position correspondingly of a quantum harmonic oscillator. Note that the phase here is the complex argument of the superconducting wavefunction, also known as the superconducting order parameter, not the phase between the different states of the qubit.
  In the table below, the three archetypes are reviewed. In the first row, the qubit electrical circuit diagram is presented. In the second, the quantum Hamiltonian derived from the circuit is shown. Generally, the Hamiltonian can be divided to a "kinetic" and "potential" parts, in analogy to a particle in a potential well. The particle mass corresponds to some inverse function of the circuit capacitance, while the shape of the potential is governed by the regular inductors and Josephson junctions. One of the first challenges in qubit design is to shape the potential well and to choose the particle mass in a way that the energy separation between specific two of the energy levels will differ from all other inter-level energy separations in the system. These two levels will be used as the logical states of the qubit. The schematic wave solutions in the third row of the table depict the complex amplitude of the phase variable. In other words, if a phase of the qubit is measured while the qubit is in a specific state, there is a non-zero probability to measure a specific value only where the depicted wave function oscillates. All three rows are essentially three different presentations of the same physical system.
caption: Charge qubit circuit
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