## Controllable coupling of charge qubits

This work describes a new solution for controllable physical qubit-qubit coupling of charge and charge-phase qubits based on Josephson junctions (JJ). The network has the following properties: (a) nearest-neighbour qubit-qubit coupling controlled by external bias current, (b) qubits parked at the degeneracy points, also during qubit-qubit interaction, (c) separate knobs for controlling individual qubits and qubit-qubit coupling, (d) scalability. An important feature is that the network is easily fabricated, and is in line with current mainstream experiments.

There are many proposed schemes for two (multi)-qubit gates where an effective qubit coupling is controlled by tunings of qubits or bus resonators. However, there are also suggestions how to control physical qubit interaction, most of which require local magnetic field control. Recently, Yamamoto et al. successfully implemented a CNOT gate using fixed capacitive coupling between two charge qubits, controlling the effective qubit-qubit interaction by tuning single-qubit level splittings into resonance - however, this method might not be well suited for more advanced gates on charge qubits because of strong decoherence when qubits are operated away from the degeneracy points.

We therefore design and evaluate a scalable charge qubit chain network with controllable current-current coupling of neighbouring qubit loops via local dc-current gates. The network under consideration consists of a chain of charge qubits - Single Cooper Pair Transistors (SCT) - with loop-shaped electrodes coupled together by current biased coupling JJs at the loop intersections. The loop design creates an (inductive) interface to the qubit by means of circulating currents, which has been used as a tool for qubit readout by Vion et al. We employ these current states in the qubit loops to create controllable coupling of neighbouring qubits. The results are derived in the charge qubit limit EC >> EJ. However, the analysis and the coupling mechanism also apply to the case of EC approximately equal to EJ, describing the charge-phase qubit.

Left without any external current biasing of the coupling and readout JJs, the network acts as a quantum memory of independent qubits (neglecting a weak residual interaction). When a bias current is sent through the coupling JJ, the current-current interaction between the neighbouring qubits is switched on and increases with increasing bias current. This provides a realistic solution for easy local control of the physical coupling of charge qubits via current biasing of coupling JJs or, alternatively, pairs of readout junctions. The design is in line with experimental mainstream development of charge qubit circuits and can easily be fabricated and tested experimentally. Most importantly, it allows readout via currently tested methods that promise single-shot projective measurement and even non-destructive measurements, via e.g. RF-reflection readout of a JJ threshold detector or an SET. The tuneable coupling of the qubit chain allows easy implementation of CNOT and CNOT-SWAP operations. Independent two-qubit operations can be performed in parallel when the network consists of five qubits or more, and generalization to single-shot N-qubit gates seems possible. This may offer interesting new opportunities for operating qubit clusters in parallel and swapping and teleporting qubits along the chain, for experimental implementations of elementary quantum information processing.

There are many proposed schemes for two (multi)-qubit gates where an effective qubit coupling is controlled by tunings of qubits or bus resonators. However, there are also suggestions how to control physical qubit interaction, most of which require local magnetic field control. Recently, Yamamoto et al. successfully implemented a CNOT gate using fixed capacitive coupling between two charge qubits, controlling the effective qubit-qubit interaction by tuning single-qubit level splittings into resonance - however, this method might not be well suited for more advanced gates on charge qubits because of strong decoherence when qubits are operated away from the degeneracy points.

We therefore design and evaluate a scalable charge qubit chain network with controllable current-current coupling of neighbouring qubit loops via local dc-current gates. The network under consideration consists of a chain of charge qubits - Single Cooper Pair Transistors (SCT) - with loop-shaped electrodes coupled together by current biased coupling JJs at the loop intersections. The loop design creates an (inductive) interface to the qubit by means of circulating currents, which has been used as a tool for qubit readout by Vion et al. We employ these current states in the qubit loops to create controllable coupling of neighbouring qubits. The results are derived in the charge qubit limit EC >> EJ. However, the analysis and the coupling mechanism also apply to the case of EC approximately equal to EJ, describing the charge-phase qubit.

Left without any external current biasing of the coupling and readout JJs, the network acts as a quantum memory of independent qubits (neglecting a weak residual interaction). When a bias current is sent through the coupling JJ, the current-current interaction between the neighbouring qubits is switched on and increases with increasing bias current. This provides a realistic solution for easy local control of the physical coupling of charge qubits via current biasing of coupling JJs or, alternatively, pairs of readout junctions. The design is in line with experimental mainstream development of charge qubit circuits and can easily be fabricated and tested experimentally. Most importantly, it allows readout via currently tested methods that promise single-shot projective measurement and even non-destructive measurements, via e.g. RF-reflection readout of a JJ threshold detector or an SET. The tuneable coupling of the qubit chain allows easy implementation of CNOT and CNOT-SWAP operations. Independent two-qubit operations can be performed in parallel when the network consists of five qubits or more, and generalization to single-shot N-qubit gates seems possible. This may offer interesting new opportunities for operating qubit clusters in parallel and swapping and teleporting qubits along the chain, for experimental implementations of elementary quantum information processing.