Resonant adiabatic passage with three qubits

We investigate the nonadiabatic implementation of an adiabatic quantum teleportation protocol, finding that perfect fidelity can be achieved through resonance. We clarify the physical mechanisms of teleportation, for three qubits, by mapping their dynamics onto two parallel and mutually coherent adiabatic passage channels. By transforming into the adiabatic frame, we explain the resonance by analogy with the magnetic resonance of a spin-1/2 particle. Our results establish a fast and robust method for transferring quantum states and suggest an alternative route toward high-precision quantum gates.

Figure 1

Couplings and the information distribution (by color and arrow) among three qubits shown at the initial, intermediate, and final stages of adiabatic quantum teleportation.

Figure 2

Adiabatic passage protocols for (a) $\Lambda$-type levels, (b) the up component (red $|0\rangle$) of a three-qubit system, and (c) the corresponding spin configurations. Shown from right to left are the initial, intermediate, and final stages of evolution. In (a) and (b) solid circles represent populations of levels. In (a) $S$ and $P$ stand for the Stokes and pump pulses.

Figure 3

Infidelity $1-F$ plotted as a function of $JT/\pi \hslash$ for (a) $\mathit{XX}$ and (b) Heisenberg couplings, using harmonic and linear interpolation functions (solid red and dotted blue lines, respectively). The black dashed line represents $1-F\propto 1/{(JT/\hslash )}^2$ for comparison. (c) Infidelity of a conventional swap operation or Rabi oscillation (if $2J$ is replaced by ${\mu }_B{B}_x$) given by $1-F={\cos }^2(2JT/\hslash )$. Windows of tolerable timing errors to get $1-F\le {10}^{-2}$ are indicated by blue shaded regions for (c) conventional swap gates vs (d) AQT with $\mathit{XX}$ coupling and harmonic interpolation shown in (a). (d) The robustness improves monotonically in the adiabatic limit and always surpasses the robustness in (c).

Figure 4

Schematic representation of the time evolution in the adiabatic frame, given by Eq. (13). The instantaneous eigenvector is represented by a thick blue arrow and the exact evolved state by a thick red arrow.

Figure 5

Infidelity $1-F$ plotted as a function of $JT/\pi \hslash$ for (a) $\mathit{XX}$ and (b) Heisenberg couplings when a uniform magnetic field $B_0$ is applied. At ${\mu }_B{B}_0/J=0.5$ the infidelity and the modified infidelity are represented by dashed blue lines and blue dots, respectively. The modified infidelity (blue dots) when $B_0\ne 0$ is identical to the infidelity $1-F$ (red solid lines) when $B_0=0$. The input state is an equal superposed state $|{\psi }_1\rangle =\frac{1}{\sqrt{2}}\left(\right|0\rangle +|1\rangle )$.

Figure 6

Modified infidelity $1-F^{\prime }$ plotted as a function of $JT/\pi \hslash$ for (a) $\mathit{XX}$ and (b) Heisenberg couplings when random magnetic fields $\delta B_i$ are applied. The input state is an equal superposed state $|{\psi }_1\rangle =\frac{1}{\sqrt{2}}\left(\right|0\rangle +|1\rangle )$.