Tensor networks represent a many-body quantum state, or a large high-dimensional array more generally, as a network of smaller tensors connected along shared indices — with the pattern of connections encoding how much entanglement the state carries between different parts of the system. Common families, such as matrix product states, tree tensor networks, and two- and three-dimensional lattice networks, trade full generality for an efficient classical representation of states whose entanglement grows slowly enough (so-called “area-law” states), letting problems that are formally exponential in system size be handled with far less than exponential memory and compute.
Because a state’s cost to represent depends on how much entanglement the network has to encode rather than directly on the number of qubits or particles, tensor networks serve two roles at once: a practical classical simulation tool for many-body physics and quantum-computing benchmarks, and a lens for understanding which physical systems are “easy” or “hard” to simulate classically — independent of whether the hardware being compared against is itself quantum or classical.
Related papers
- Tindall, Mello, Fishman, Stoudenmire, and Sels, “Dynamics of disordered quantum systems with two- and three-dimensional tensor networks”, Science 392, 868 (2026) — uses two- and three-dimensional lattice tensor networks, combined with belief propagation, to classically simulate disordered spin-glass dynamics at a scale previously reported only on a quantum annealer. Covered in 2026-w32.