Example methods and mechanisms are described herein for implementing and adiabatically operating a topological quantum computing (TQC) phase gate that complements the existing Clifford operations, and thereby allows universal quantum computation with Majorana systems. Further embodiments include a testing system for the phase gate that is feasible with Majorana zero modes and demonstrates violations of the CHSH-Bell inequality. Further, the design used for the testing of the inequality leads directly to a practical platforms for performing universal TQC with Majorana wires in which explicit braiding need never occur. Thus, certain embodiments of the disclosed technology involve three synergistically connected aspects of anyonic TQC the context of the currently active area of using MZMs for topological quantum computation): a practical phase gate for universal topological quantum computation using MZMs, a precise protocol (using CHSH inequality) for testing that the desired gate operation has been achieved, and bypassing the necessity of MZM braiding (and so avoiding, e.g., problems of nonadiabaticity in the braids).
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for operating an adjustable phase gate in a quantum circuit, the adjustable phase gate comprising a stationary pair of Ising anyons, comprising: causing a mobile Ising anyon to pass through the adjustable phase gate, thereby creating a targeted phase change in the stationary pair of Ising anyons; and controlling the mobile Ising anyon as the mobile Ising anyon passes through the adjustable phase gate so that the mobile Ising anyon has a complex amplitude during passage, wherein the controlling is performed such that the targeted phase change experienced by the stationary pair of Ising anyons is between 0 and π or 0 and −π. 2. The method of claim 1, wherein the controlling comprises performing one or more of: (a) adjusting a gate voltage of one or more gates capacitively coupled to one or more superconducting islands that form the adjustable phase gate, (b) adjusting a capacitance of one or more of the superconducting islands; or (c) adjusting a strength of at least one Josephson junction relative to at least one other Josephson junction, the Josephson junctions connecting two or more of the superconducting islands to one another. 3. The method of claim 1, further comprising: in a first operational stage, altering a magnetic flux through the adjustable phase gate in a first direction, the first direction comprising either increasing the magnetic flux or decreasing the magnetic flux; and in a second operational stage, altering the magnetic flux through the adjustable phase gate in a second direction that is opposite of the first direction. 4. The method of claim 3, further comprising: during either or both operational stages, adjusting a strength of a first Josephson junction at a first end of a superconducting region in the adjustable phase gate; and during either or both operational stages, adjusting a strength of a second Josephson junction at a second end of the superconducting region in the adjustable phase gate, wherein the strengths of the first and second Josephson junctions are selected to create a relative difference that produces the targeted phase change in the Ising pair. 5. The method of claim 1, wherein the adjustable phase gate comprises a plurality of superconducting regions arranged to form a superconducting loop, wherein adjacent ones of the superconducting regions are connected to one another via respective Josephson junctions, and one of the superconducting regions comprises a Majorana wire located on the one of the superconducting regions. 6. The method of claim wherein the adjustable phase gate is implemented in a transmission line resonator comprising three Majorana wires arranged to form a qubit between a bus and a phase ground of the transmission line resonator. 7. The method of claim 1, further comprising measuring one or more Pauli operators of the qubit by selectively controlling: (a) Josephson couplings between a first superconducting region on which a first Majorana wire is located and a bus and phase ground; and (b) Josephson couplings between a second superconducting region on which a second Majorana wire is located and the bus and the phase ground, and wherein a superconducting loop is formed by the second superconducting region, the phase ground, and a third superconducting region containing no Majorana wire. 8. A quantum circuit phase gate, comprising: a plurality of superconducting components arranged in a ring to form a superconducting loop, wherein adjacent superconducting components are connected to each other via Josephson junctions; a Majorana wire located on a respective one of the superconducting components; and a magnetic field generator configured to apply actable magnetic field to the superconducting loop formed by the ring of superconductive components. 9. The quantum circuit phase gate of claim 8, wherein the magnetic field generator and the capacitance of one or more of the superconducting components are controllable to draw a Josephson vortex into the superconducting loop. 10. The quantum circuit phase gate of claim 8, wherein the superconducting components comprise first and second superconducting islands connected to a bulk superconductor. 11. The quantum circuit phase gate of claim 10, wherein the first superconducting island is connected to the bulk superconductor via a first controllable Josephson junction, the second superconducting island is connected to the bulk superconductor via a second controllable Josephson junction,and the e first superconducting island is connected to the second superconducting island via a third Josephson junction. 12. The quantum circuit phase gate of claim in only the first and second Josephson junctions are controllable. 13. A microwave resonator system configured to implement a qubit register between a bus and a phase ground, the qubit register comprising the phase gate of claim 8. 14. The microwave resonator of claim 13, wherein the Majorana wire is a first Majorana wire, and wherein the plurality of superconducting components arranged in a ring comprises: a first superconducting component coupled to the phase ground via a first controllable Josephson junction and coupled to the bus via a second controllable Josephson junction, the first Majorana wire being located on the first superconducting component; and a second superconducting component coupled to the phase ground via a third controllable Josephson junction and coupled to the first superconducting component via a fixed Josephson junction, the second superconducting component being disconnected from the bus. 15. The microwave resonator of claim 14, further comprising: a third superconducting component coupled to the phase ground via a fifth controllable Josephson junction and to the bus via a sixth controllable Josephson junction; a second Majorana created on the third superconducting component; a third Majorana wire located on a superconducting component connected to the bus, wherein the first, second, and third Majorana wires are positioned to create the qubit register with no braiding mechanism. 16. A Clauser-Horne-Shimony-Holt (CHSH) inequality or Bell inequality measurement system comprising the phase gate of claim 8. 17. A method of operating a quantum circuit phase gate, comprising: applying a time-varying magnetic field to a set of regions in the quantum circuit phase gate, at least some of the regions being connected to one another via respective Josephson junctions; and controlling a first of the Josephson junctions and a second of the Josephson junctions to create a Josephson vortex in the quantum circuit phase gate as the time-varying magnetic field is applied. 18. The method of claim 17, wherein the regions are superconducting regions, and wherein the regions form a superconducting loop. 19. The method of claim 17, wherein the Josephson vortex produces a phase change to a quint stored in a qubit register formed with the quantum circuit phase gate. 20. The method of claim 19, further comprising selectively varying the phase change between 0 and π or 0 and −π.