Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of each lattice site in a highly coherent quantum system. Here, we experimentally study quantum transport in one-dimensional and two-dimensional tight-binding lattices, emulated by a fully controllable 3 × 3 array of superconducting qubits. We probe the propagation of entanglement throughout the lattice and extract the degree of localization in the Anderson and Wannier-Stark regimes in the presence of site-tunable disorder strengths and gradients. Our results are in quantitative agreement with numerical simulations and match theoretical predictions based on the tight-binding model. The demonstrated level of experimental control and accuracy in extracting the system observables of interest will enable the exploration of larger, interacting lattices where numerical simulations become intractable.

凝聚态系统中的粒子传输和定位现象可以使用紧束缚晶格哈密顿量来建模。这种模型的理想实验仿真利用高度相干量子系统中每个晶格位点的同时、高保真控制和读出。在这里，我们通过实验研究了一维和二维紧束缚晶格中的量子传输，由完全可控的 3 × 3 超导量子位阵列模拟。我们探索了纠缠在整个晶格中的传播，并在存在位点可调的无序强度和梯度的情况下提取了 Anderson 和 Wannier-Stark 方案中的定位程度。我们的结果与数值模拟在定量上一致，并且与基于紧束缚模型的理论预测相匹配。