Quantum router based on ac control of qubit chains

We study the routing of quantum information in qubit chains. This task is achieved by suitably chosen time-dependent local fields acting on the qubits. Employing the physics of coherent destruction of tunneling, we demonstrate that a driving-induced renormalization of the coupling between neighboring qubits provides the key for controlling the transduction of quantum information between permanently coupled qubits. We employ this idea for building a quantum router. Moreover, we discuss the experimental implementation with Penning traps and study the robustness of our protocol under realistic experimental conditions, such as fabrication uncertainties and decoherence.

Figure 1

(Color online) Hub configuration. One qubit of an entangled pair is connected to a line with perfect transfer. Then the entanglement propagates and is later steered to one of the possible outputs, i.e., distributed to the desired transmission line. This enables quantum communication inside the quantum computer by both direct state transfer and teleportation once the entanglement of distant parties has been established.

Figure 2

(Color online) T-shaped configuration. Alice sends the state of one of her qubits without dispersion along the horizontal chain. When the state arrives at the node, an ac field with a ratchetlike profile transfers the signal to Bob or to Charlie.

Figure 3

(Color online) (a) Spatial variation in the local qubit energy splittings along the vertical chain. It is chosen such that the absolute value of differences between two neighboring sites alternates between ${\Lambda }_1$ and ${\Lambda }_2$. (b) Ac field with alternating driving amplitude. The amplitudes [see Eq. (10)] are such that tunneling between qubits with either energy difference ${\Lambda }_1$ or ${\Lambda }_2$ is suppressed.

Figure 4

(Color online) (a) Time evolution of the concurrence between Alice’s qubit and qubit $n$ of the vertical chain with length $N=13$ for the parameters $\omega =10J$, $b=J$, ${\Lambda }_1=3J$, ${\Lambda }_2=1.5J$. Alice’ qubit is initially entangled with the qubit at $n_{\text{node}}=7$. The onset of the driving field [Eq. (10)] is such that initially transfer to Charlie is suppressed. (b) Same as panel (a) but for an arrival time $t=T_1$ at the node, such that the entanglement propagates to Charlie.

Figure 5

(Color online) Same as Fig. 4 for the arrival time $t=T_1/2$ at the node, such that the traveling qubit is split.

Figure 6

(Color online) Study of dynamical reflection of entanglement at the entrance of the router (joint between horizontal and vertical lines in Fig. 2). The amount of entanglement is given by the concurrence, see Eq. (14). Here the horizontal chain is formed by the first two qubits and the rest is router, with the same parameters as in Fig. 4; a slight reflection is seen, but the transmitted entanglement lies above 0.98.

Figure 7

(Color online) Length dependence of the final concurrence for chains of various frequencies. The differences of the energy splittings are ${\Lambda }_1=100J$ and ${\Lambda }_2=59.02J$, corresponding to the ratio ${\Lambda }_2/{\Lambda }_1=0.5902$ which provides the optimum transfer velocity.

Figure 8

(Color online) Fidelity distribution for the initial state ${|\psi ⟩}_A=\left(|0⟩+|1⟩\right)/\sqrt{2}$ in a chain with length $N=40$ and the driving frequencies (a) $\omega =30$ and (b) $\omega =40$. The qubits splittings are ${\Lambda }_1=100J$ and ${\Lambda }_2=59.02J$, while the parameter uncertainties read ${ϵ}_J={ϵ}_b={10}^{-7}$ and ${ϵ}_T={10}^{-3}$. The data have been obtained from 500 realizations. The resulting standard deviations of the concurrence are 0.01 and 0.1, respectively.

Figure 9

(Color online) Concurrence decay as a function of the chain length for two different decoherence rates $\gamma$ (symbols) and $\omega =30$. The solid lines mark the estimate [Eq. (23)]. All other parameters are as in Fig. 8.

Figure 10

(Color online) Fidelity spread for a chain of length $N=40$ with the initial state ${|\psi ⟩}_A=\left(|0⟩+|1⟩\right)/\sqrt{2}$. The driving frequency is $\omega =30$ and dissipation strengths (a) $\gamma ={10}^{-3}J$ and (b) $\gamma ={10}^{-4}J$. The histogram is obtained from 500 realizations yielding a standard deviation of 0.01 in both of them. All other parameters are as in Figs. 8, 9.