Depth-Optimal Addressing of 2D Qubit Array with 1D Controls Based on Exact Binary Matrix Factorization

Reducing control complexity is essential for achieving large-scale quantum computing, particularly on platforms operating in cryogenic environments. Wiring each qubit to a room-temperature control poses a challenge, as this approach would surpass the thermal budget in the foreseeable future. An essential tradeoff becomes evident: reducing control knobs compromises the ability to independently address each qubit. Recent progress in neutral atom-based platforms suggests that rectangular addressing may strike a balance between control granularity and flexibility for
$2\mathrm{D}$
qubit arrays. This scheme allows addressing qubits on the intersections of a set of rows and columns each time. While quadratically reducing controls, it may necessitate more depth. We formulate the depth-optimal rectangular addressing problem as exact binary matrix factorization, an NP-hard problem also appearing in communication complexity and combinatorial optimization. We introduce a satisfiability modulo theories-based solver for this problem, and a heuristic, row packing, performing close to the optimal solver on various benchmarks. Furthermore, we discuss rectangular addressing in the context of fault-tolerant quantum computing, leveraging a natural two-level structure.