WP 4. Multiple SQUBIT gates and circuit architecture

WP 4 is the systems level where it all comes together. Although it may take several decades to achieve the goals, it is nevertheless necessary from the start to establish a framework on the systems level, incorporating increasingly sophisticated hardware and software components and tools, as they appear. WP4 is an engine for the experimental and theoretical development within SQUBIT-2.

At this time, all three types of single qubits - charge, charge-phase and flux qubits - are operational, with the CEA-Saclay charge-phase qubit in the frontline (0.5 microsecond coherence time under optimal conditions). In the coming three years, the strong effort in SQUBIT-2 will be directed towards multiple qubit gates.

With the CEA-Saclay charge-phase qubits, coupling is performed by means of a link-capacitor between the charge islands of each device. In the Hamiltonian for the joint system this introduces a sigma_z-sigma_z-type coupling in the basis of the charge states. The coupling strength depends on the value of the coupling capacitor relative to the junction capacitances. From simple estimates the time needed for a two-qubit gate action can be of the same order as the time needed for single-qubit operations (e.g. in strongly coupled flux qubits; in weakly capacitively coupled charge-phase qubits the two-qubit operation times will be longer). In the first single-qubit measurements, a discrepency is present between theory and experiment that first must be understood and/or eliminated before the theory can be extended with confidence to multiple qubits. Practical problems may arise when two coupled qubits are optimised. Each requires careful tuning of two parameters to reach the operation point where the qubit is insensitive to charge as well as flux noise. Two qubits require four-parameter optimisation to get the qubits in the operating regime, apart from the optimisation of the coupling effects. We expect that two-qubit coupling should certainly be possible, but more practical experience is needed to see to how many qubits the concept can be extended.

With the flux-type qubit, all depends on the question if the flux noise can be sufficiently suppressed to obtain reliable single-qubit operation away from the degeneracy point. If so, coupling of multiple qubits should be relatively easy. Coupling of qubits can be performed with inductive coupling loops, and the coupling strength can be made high. If the qubits are of the gradiometer type, coupling is equally easy.

For charge-phase as well as flux-type qubits, separate measurements on each qubit are possible. A detector (electrometer, large junction or SQUID) is simply connected to each qubit. In particular, if successful single-shot measurement is developed, successive timed measurements on each of two coupled qubits is extremely valuable to demonstrate conclusively the presence of entanglement. We will strongly pursue such measurements in the project. The accuracy of two-qubit operation will be established in detail.

Extension of the experiments to more than two qubits will be implemented. It seems reasonable to expect that four qubits can be addressed within the next project period. The accuracy of that type of operation is hard to predict. At this time it is known how to make permanent coupling between qubits; however, schemes for variable coupling can also be developed (see WP1, WP2). Resonant coupling, with one qubit tuned to (or detuned from) the same level splitting is one method. Reducing the Josephson coupling by means of squid-like interference is another. We will investigate variable coupling, not expecting that the coupling can be reduced to zero.

Multiple qubit structures will be fabricated and investigated with high numbers of qubits, but with limited functionality. One should think of linear arrays, closed loops or two-dimensional regular arrays with high symmetry. Spectroscopic measurements can be performed to study the energy levels, special degrees of freedom detected. The possibility to transport quantum information dynamically through an array over certain distances will be investigated. Theory should play a particularly important role here.

The decoherence in systems of multiple qubits will be studied. Theory is not yet available here; it will be developed and experimentally verified. On the basis of the knowledge gained, a beginning will be made with the conceptual design of a large scalable quantum computer. Finally we would like to mention the "ultimate" challenge in a 5-10 year perspective, defining what could be regardes as a "Road Map for Quantum Computing". The SQUBIT-2 project will have a major long-term objective a vision to investigate how to implement a 5+5 qubit system. The obvious motivation will be to operate at two-logic-qubit gate within an error correction scheme, coding one logic qubit in 5 physical ones. Such a scheme requires repeatedly coding (entangling 5 qubits), measuring 4 qubits and extracting the error syndrom, and performing the associated unitary transformations to restore the state, including error corrections.

A successful scheme means keeping two logical qubits alive "forever" and performing two-logic- qubit gate operations "forever". If this is possible scaling up the system may be possible, and a "Roadmap for Quantum Computing" might be meaningful: At present, such a roadmap is merely a plan for organising fundamental research.

A nice intermediate result, an ultimate challenge for SQUBIT-2, would be to demonstrate a "Teleportation Protocol", by coding an unknown qubit in 3 qubits and then repeatedly decode and recode it, to see how far one can get. This is really the first step towards realistic attempts at coding and decoding to achieve error correction (3 instead of 5 qubits).