Charge qubit


In quantum computing, a charge qubit is a qubit whose basis states are charge states. In superconducting quantum computing, a charge qubit is formed by a tiny superconducting island coupled by a Josephson junction to a superconducting reservoir. The state of the qubit is determined by the number of Cooper pairs which have tunneled across the junction. In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. The quantum superposition of charge states can be achieved by tuning the gate voltage U that controls the chemical potential of the island. The charge qubit is typically read-out by electrostatically coupling the island to an extremely sensitive electrometer such as the radio-frequency single-electron transistor.
Typical T2 coherence times for a charge qubit are on the order of 1–2 μs. Recent work has shown T2 times approaching 100 μs using a type of charge qubit known as a transmon inside a three-dimensional superconducting cavity. Understanding the limits of T2 is an active area of research in the field of superconducting quantum computing.

Fabrication

Cooper-Pair Boxes are fabricated using techniques similar to those used for microelectronics. The devices are usually made on silicon or sapphire wafers using electron beam lithography and metallic thin film evaporation processes. To create Josephson junctions, a technique known as shadow evaporation is normally used; this involves evaporating the source metal alternately at two angles through the lithography defined mask in the electron beam resist. This results in two overlapping layers of the superconducting metal, in between which a thin layer of insulator is deposited.

Hamiltonian

If the Josephson Junction has a junction capacitance, and the gate capacitor, then the charging energy of one Cooper-pair is:
If denotes the number of excess Cooper-pairs in the island, then the Hamiltonian is:
where is a control parameter known as effective offset charge, and the Josephson energy of the tunneling junction.
At low temperature and low gate voltage, one can limit the analysis to only the lowest and states, and therefore obtain a two-level quantum system.
Note that some recent papers adopt a different notation, and define the charging energy as that of one electron:
and then the corresponding Hamiltonian is:

Benefits

To-date, the realizations of qubits that have had the most success are ion traps and NMR, with Shor's algorithm even being implemented using NMR. However, it is hard to see these two methods being scaled to the hundreds, thousands, or millions of qubits necessary to create a quantum computer. Solid-state representations of qubits are much more easily scalable, but they themselves have their own problem: decoherence. Superconductors, however, have the advantage of being more easily scaled, and they are more coherent than normal solid-state systems.

Experimental Progress

Superconducting charge qubits have been progressing quickly. They were first suggested in 1997 by Shnirman, and by 2001 coherent oscillations were observed.