Control-limited perfect state transfer, quantum stochastic resonance, and many-body entangling gate in imperfect qubit registers

We propose a protocol for perfect quantum state transfer that is resilient to a broad class of realistic experimental imperfections, including noise sources that could be modeled either as independent Markovian baths or as certain forms of spatially correlated environments. We highlight interesting connections between the fidelity of state transfer and quantum stochastic resonance effects. The scheme is flexible enough to act as an effective entangling gate for the generation of genuine multipartite entanglement in a control-limited setting. Possible experimental implementations using superconducting qubits are also briefly discussed.

Figure 1

(Color online) (a) Oriented graph describing the way the operators entering Eqs. (3) are related. The operator in each circle (a node) gives rise to its nearest neighbors under commutation with ${\hat{\mathcal{H}}}_C$ in Eq. (2), for $N=3$. The oriented edges connect such nodes. The corresponding coefficients are also shown and an outgoing (ingoing) edge with respect to a node implies a $+$ $(-)$ sign. (b) Information flux from ${\widehat{Y}}_1$ to ${\widehat{X}}_N$ against the dimensionless interaction time $Jt$, for $N=3$ and $J_i=\pm J\sqrt{4i\left(N-i\right)}$, $B_i=J\sqrt{\left(2i-1\right)\left(2N-2i+1\right)}$ in Eq. (2). Qubits 2 and 3 are prepared in ${|00⟩}_{23}$. (c) Information flux from ${\widehat{X}}_1$ to ${\widehat{Y}}_N$, for the same conditions as in panel (b).

Figure 2

Equivalent quantum circuit for a spin-chain that evolves according to $e^{-i\hat{\mathcal{H}}\pi /4J}$. The inset shows the explicit composition of the local operators before the interqubit interaction structure. We show the symbols for $T$, $H$, and controlled-phase operations. For clarity of presentation, we have omitted to show a set of swap gates (performing mirror inversion) at the end of the circuit.

Figure 3

(Color online) (a) State fidelity against dimensionless time $Jt$ with no disorder and $N=7$. (b) Same with $\delta =0.05$, corresponding to a 5% maximum deviation of the disordered parameters from the ideal values.

Figure 4

(Color online) (a) Bloch sphere of the logical input qubit for various choices of $\alpha$. (b) Reconstructed Bloch sphere showing the state of the $N$th qubit for a disordered chain of $N=7$ and $\delta /J=5\%$ at $Jt=\pi /4$.

Figure 5

(Color online) (a) Fidelity ${\mathcal{F}}_{1N}^{\text{av}}$ for an input state ${|-⟩}_1$ against $Jt$ with $\delta /J=5\%$, $\Gamma /J=0.5$, $\gamma /J=0.2$, $\overline{n}=0.01$, and $N=7$. The average fidelity is calculated over a set of 200 disordered patterns. (b) Bloch sphere of the output qubit evaluated with QPT for the same parameters assumed in panel (a).

Figure 6

(Color online) Fidelity ${\mathcal{F}}_{1N}^{\text{av}}$ versus $\gamma /J$ and $\Gamma /J$ for $Jt=\pi /4$, $\delta /J=5\%$, $\overline{n}=0.01$, and $N=6$.

Figure 7

(Color online) Fidelity ${\mathcal{F}}_{1N}^{\text{av}}$ with $N=6$ at $Jt=\pi /4$, $\delta /J=5\%$, $\gamma /J=0.2$, $\overline{n}=0.01$ against $\Gamma /J$. The transmission fidelity is maximal for an optimal value of the environmental noise and is the result of the average over many noisy and disordered runs. The fact that the efficiency of the protocol depends nonmonotonically on the noise strength can be viewed as a form of stochastic resonance.

Figure 8

(Color online) Fidelity ${\mathcal{F}}_{1N}^{\text{av}}$ for a chain interacting with collective baths addressing two qubits simultaneously with $Jt=\pi /4$, $\delta /J=5\%$, and $N=6$ against $\gamma /J$ and in absence of dissipation.

Figure 9

(Color online) (a) State fidelity for GHZ-state generation against dimensionless time $Jt$ in the ideal case and $N=7$. (b) Same with disorder $\delta /J=5\%$, $\gamma /J=0.5$, $\Gamma /J=0.2$, and $\overline{n}=0.01$.