Emulating quantum state transfer through a spin-1 chain on a one-dimensional lattice of superconducting qutrits

Spin-1 systems, in comparison to spin-$\frac{1}{2}$ systems, offer a better security for encoding and transferring quantum information, primarily due to their larger Hilbert spaces. Superconducting artificial atoms possess multiple energy levels, thereby being capable of emulating higher-spin systems. Here I consider a one-dimensional lattice of nearest-neighbor-coupled superconducting transmon systems, and devise a scheme to transfer an arbitrary qutrit state (a state encoded in a three-level quantum system) across the chain. I assume adjustable couplings between adjacent transmons, derive an analytic constraint for the control pulse, and show how to satisfy the constraint to achieve a high-fidelity state transfer under current experimental conditions. My protocol thus enables enhanced quantum communication and information processing with promising superconducting qutrits.

Figure 1

(a) Optimal trapezoidal control pulse for $g\left(t\right)$ while two qutrits are in resonance. (b) Probability of population in the $|01\rangle$ and $|02\rangle$ states under the trapezoidal pulse, assuming that the $|10\rangle$ and $|20\rangle$ states are occupied initially.

Figure 2

Trapezoidal pulses for $g_k\left(t\right)$ for a state transfer across a chain of four nearest-neighbor-coupled superconducting qutrits. To emulate a QST across a chain of $N$ qutrits, we need to concatenate $(N-1)$ such pulses.

Figure 3

Accumulation of intrinsic and decoherence-induced errors with the number of steps. The red diamonds and blue squares are numerically computed data points, and the solid black and green (gray) curves are the linear and quartic fit for the decoherence-induced and intrinsic errors, respectively.