Solid-state quantum communication with Josephson arrays

Josephson junction arrays can be used as quantum channels to transfer quantum information between distant sites. In this paper we discuss simple protocols to realize state transfer with high fidelity. The channels do not require complicated gating but use the natural dynamics of a properly designed array. We investigate the influence of static disorder both in the Josephson energies and in the coupling to the background gate charges, as well as the effect of dynamical noise. We also analyze the readout process, and its back action on the state transfer.

Figure 1

Dashed box: one-dimensional Josephson array proposed for the transmission of quantum states. The crossed rectangles denote the Josephson junctions between the islands. The state prepared on the left-most island is transfered to the right-most island by the time evolution generated by the Hamiltonian. Left: the Cooper-pair box (charge qubit) used to prepare the state. Right: the SET transistor used as measurement device.

Figure 2

(Color online) Maximum value of the fidelity as a function of the length of the chain for two different values of $C∕C_0⪡1$ and ${\left(2e\right)}^2∕\left(E_J{C}_0\right)=10$. Inset: The time at which the maximum is reached.

Figure 3

(Color online) Maximum value of the fidelity as a function of the length of the chain for three different values of $C∕C_0\gtrsim 1$ and ${\left(2e\right)}^2∕\left(E_J{C}_0\right)=10$. Inset: The time at which the maximum is reached.

Figure 4

(Color online) Fidelity as a function of time for an array of length $L=7$, ${\left(2e\right)}^2∕\left(E_J{C}_0\right)=10$ and $C=0$, i.e., a junction capacitance much smaller than the ground capacitance. Disorder parameters: relative variance $\Delta E_J∕E_J=0.1$ for bond disorder; absolute variance $\Delta Q_x∕2e=0.025$ for site disorder. Dotted line (right axis): variance of the fidelity for the case without disorder.

Figure 5

(Color online) Fidelity vs time in the presence of gate voltage fluctuations (full line). The dashed line is the noiseless case. $L=7$, $e^2∕\left(E_J{C}_0\right)=10$, $C∕C_0=0.1$, $\gamma =0.01$.

Figure 6

(Color online) Full line: time dependence of the current (in units of $e∕T$) through the SET. Dashed line: fidelity of the isolated chain. $\Gamma =0.05$; all other parameters as in Fig. 5.