Flux qubit
[1] During fabrication, the Josephson junction parameters are engineered so that a persistent current will flow continuously when an external magnetic flux is applied.
Only an integer number of flux quanta are allowed to penetrate the superconducting ring, resulting in clockwise or counter-clockwise mesoscopic supercurrents (typically 300 nA[2]) in the loop to compensate (screen or enhance) a non-integer external flux bias.
The two lowest energy eigenstates differ only by the relative quantum phase between the composing current-direction states.
This separation, known as the "qubit non linearity" criteria, allows operations with the two lowest eigenstates only, effectively creating a two level system.
Properly selected pulse duration and strength can put the qubit into a quantum superposition of the two basis states while subsequent pulses can manipulate the probability weighting that the qubit will be measured in either of the two basis states, thus performing a computational operation.
The devices are usually made on silicon or sapphire wafers using electron beam lithography and metallic thin film evaporation processes.
The resonator can be fabricated by e-beam lithography and CF4 reactive ion etching of thin films of niobium or a similar metal.
Josephson junctions are the only electronic element that are non-linear as well as non-dissipative at low temperatures [citation needed].
These are requirements for quantum integrated circuits, making the Josephson junction essential in the construction of flux qubits.
Essentially, Josephson junctions consist of two pieces of superconducting thin film that are separated by a layer of insulator.
Thus, Josephson junctions are an integral element of flux qubits and superconducting circuits in general.
In the Pauli Matrices formalism, a σzσz term appears in the Hamiltonian, essential for the controlled NOT gate implementation.
[7] The direct coupling might be further enhanced by kinetic inductance, if the qubit loops are made to share an edge, so that the currents will flow through the same superconducting line.
The control magnetic flux applied to the coupler loop switches the coupling on and off, as implemented, for example, in the D-Wave Systems machines.
The second method of coupling uses an intermediate microwave cavity resonator, commonly implemented in a coplanar waveguide geometry.
By tuning the energy separation of the qubits to match that of the resonator, the phases of the loop currents are synchronized, and a σxσx coupling is implemented.
Tuning the qubits in and out of resonance (for example, by modifying their bias magnetic flux) controls the duration of the gate operation.
Like all quantum bits, flux qubits require a suitably sensitive probe coupled to it in order to measure its state after a computation has been carried out.
The read-out probe is typically the technology aspect that separates the research of different University groups working on flux qubits.
Dr. Il'ichev's group at IPHT Jena in Germany[8] are using impedance measurement techniques based on the flux qubit influencing the resonant properties of a high quality tank circuit, which, like the Delft group is also inductively coupled to the qubit.
In this scheme the qubit's magnetic susceptibility, which is defined by its state, changes the phase angle between the current and voltage when a small A.C. signal is passed into the tank circuit.
Prof. Petrashov's group at Royal Holloway[9] are using an Andreev interferometer probe to read out flux qubits.
A length of normal metal is connected at either end to either side of the qubit using superconducting leads, the phase across the qubit, which is defined by its state, is translated into the normal metal, the resistance of which is then read-out using low noise resistance measurements.
