Communicating Josephson qubits

Abstract

We propose a scheme to implement a quantum information transfer protocol with a superconducting circuit and Josephson charge qubits. The information exchange is mediated by an L-C resonator used as a data bus. The main decoherence sources are analyzed in detail. PACS numbers: 74.50.+r,03.67.Hk,73.23.Hk One of the main purposes of quantum information processing is the faithful transmission of quantum states between distant parties, eventually exploiting entanglement among subsystems. Examples include quantum teleportation 1 and dense coding 2 , both of them demonstrated using entangled photon pairs 3 , with the ultimate aim of performing quantum cryptography 4 . Until now, however, much of the work has been done within the realm of quantum optics 5 and very little efforts have been devoted to describe and implement these phenomena with solid state devices. On the other hand, nano-electronic devices have been proposed as candidates for quantum computer implementation 6,7,8,9 since they are easily embedded in electronic circuits and scaled up to contain a large number of qubits. In particular, superconducting Josephson junction circuits, whose fabrication is now performed with well established lithographyc methods, combine the intrinsic stability of the superconducting phase with the possibility of controlling the circuit dynamics through manipulations of the applied voltages or magnetic fluxes 10 . Direct experimental evidence that a single-Cooper-pair box can be used as a controllable coherent two level system has been provided by Nakamura et al 11 . Either the charge on the island or the phase differences at junction can be used to store and manipulate quantum information 12 , the two regimes being characterized by dominating charging and Josephson energies, respectively. Here, we concentrate on the charge regime and propose a set-up that allows quantum information transfer and entanglement generation between two Josephson qubits. The circuit is designed so that interaction between the two subsystems is mediated by an L-C resonator, see Fig. 1, playing the role of a data bus. The spirit of the proposal is very similar to the Cirac-Zoller scheme for trapped ion qubit 13 . As will be shown below, this set-up is flexible enough to allow for quantum information transfer from one qubit to another and for the generation of Bell states. Furthermore, the circuit can be generalized to include more qubits and we give the necessary prescriptions to implement a universal set of quantum gates.The coupling of a single charge qubit to a large Josephson junction (which may implement the resonator) has been recently exploited to perform on chip quantum state measurements 15 , and to prepare a mesoscopic Schrödinger cat state 16 . We consider here a similar coupling, but replace the single junction with a SQUID to achieve a tuning of the Josephson energy 7 , which allows to operate in both the dispersive and the resonant coupling regimes, as required by the protocols described below.We first analyze the model for a single qubi...

Dispersive manipulation of paired superconducting qubits

“…Let δ = B z − ω be the detuning. If we let the PCB and the (initially un-excited) LC resonator interact right in resonance, i.e., |δ − 2γ| ≪ g ≪ ω or |δ + 2γ| ≪ g ≪ ω [23], state transfer occurs between the PCB and the LC resonator [13,14]. This is not allowed in our scheme, since it will drive the PCB out of the DFS.…”

“…Starting from |0 = | ↓ a ↑ b , letting the PCB evolve under the effective Hamiltonian (2) for a time t = π(δ+2γ) g 2 or t 2 , we can swap the states of a and b or generate a maximally entangled state between them. The LC resonator is initially in the vacuum state and will not be excited due to the dispersive interaction with the PCB; therefore unlike in previous schemes [13,14]we are not subject to decoherence caused by its finite quality. Also, notice that our dispersive scheme is fundamentally different from the previous method of using the virtual excitation of a large LC circuit capacitively coupled to all the qubits [8], in which the LCfrequency is much larger than the CB-energies and the coupling strength is tuned by changing the E J 's of the qubits.…”

“…Schemes allowing to compute with invariable couplings were also studied [11,12]. Others have recently discussed to use an LC circuit to actively mediate the interaction between superconducting qubits [13,14].The requirement to reduce decoherence and the desire for the easiest manipulation apply to all QIP implementations. Unfortunately, it is not always easy to accomplish both -actually the goals are often contradictory -since reducing decoherence may require extra complication in the manipulation.…”

“…Schemes allowing to compute with invariable couplings were also studied [11,12]. Others have recently discussed to use an LC circuit to actively mediate the interaction between superconducting qubits [13,14].…”

“…This is not allowed in our scheme, since it will drive the PCB out of the DFS. Besides, once the LC resonator is excited, we will have additional decoherence due to the finite quality of the LC resonator [13,14]. Therefore, we only work in the dispersive region, g ≪ |δ ± 2γ| ≪ ω.…”