Fig. 1: Schematic representation of quantum state transfer.

a Single-excitation QST is achieved by finding a suitable Hamiltonian \(\hat{H}\) which transfers initial state \(\left\vert \psi \right\rangle\) encoded in qubit Q_A to qubit Q_B. Here we assume ℏ = 1. b Large-spin representation of a QST in a 2D network. Without cross-couplings or defects, a QST from Q_A to its opposite-symmetric qubit Q_B can be regarded as the independent precession of two fictitious spins, each mapping a direction of the qubit network; here N₁ = N₂ = 6. NN couplings along the x(y) directions are denoted by \({J}_{m,n}^{x}\)(\({J}_{m,n}^{y}\)), whereas gives the amplitude of the intraplaquette next-nearest neighbor couplings. Gray bond with a cross marker depicts the defect, a malfunctioning coupler in our device. c Pulse sequences for realizing single-excitation QST. Square pulses are applied on all other qubits except for Q_A to bring them to the resonant frequency ω_I, and on all the couplers non-neighboring to Q_A to engineer them to the desired couplings. To suppress the effects of small pulse distortions caused by step responses, we wait for 2 μs (prepad) before exciting Q_A and bringing it and its neighboring couplers to target frequencies. After a transfer time t_QST, all the qubits, and couplers are tuned to read work points for qubit state measurements. d Trajectory \(\{\langle {\hat{S}}_{i,x}(t)\rangle,\langle {\hat{S}}_{i,y}(t)\rangle,\langle {\hat{S}}_{i,z}(t)\rangle \}\) in the enlarged Bloch sphere of the two mapped spins, i = 1, 2, when the NN couplings are parametrically selected as \({J}_{n,n+1}^{x\to 1,y\to 2}=J\sqrt{n(6-n)}\), without cross-couplings (\({J}_{m,{m}^{{\prime} }}^{\times }=0\)) or defect. e \({J}_{m,{m}^{{\prime} }}^{\times }\ne 0\) and defect disturb the perfect precessions, breaking the standard protocol³¹, and the desired QST fails. Optimizing couplings \({J}_{n,n+1}^{1,2}\) compensates for the effects of imperfections, allowing the “wiggled” evolution to achieve QST within desired time scales. f Cartoon contrasting the general picture for the evolution in Fock space of an initial state (green dot) under generic or QST-optimized Hamiltonians. General dynamics tend to be ergodic and quickly diffuse the initial information in Fock space, while the QST dynamics manifest nonergodic behavior, re-converging to the final target state (red dot) at later times.