Reducing control complexity is essential for achieving large-scale quantum computing. Inspired by the success of the neutral atom array architectures, we have proposed a conceptual general architecture where a 2D array of qubits are controlled by the product of 1D controls. Such an architecture will be especially beneficial for quantum computing platforms that require extensive cooling, as in the case of superconducting qubit technology, where wiring each qubit to a room-temperature control would surpass the thermal budget for the foreseeable future.

While quadratically reducing controls, this architecture may necessitate higher circuit depths to implement quantum programs because it only allows addressing qubits on the intersections of a set of rows and columns at each time. We formulate the problem of depth-optimal addressing of 2D qubit arrays with 1D-product controls as finding an exact binary matrix factorization (EBMF). We then introduce a satisfiability modulo theories-based optimal solver for EBMF, and a highly efficient heuristic, named row packing, whose performance is very close to the optimal solver on various benchmarks. Furthermore, we discuss the addressing problem in the context of fault-tolerant quantum computing, leveraging a natural logical-physical two-level structure. This work, by graduate students Daniel Bochen Tan and Shuohao Ping led by Prof. Jason Cong from the Computer Science Department, will be presented in the Design and Test in Europe (DATE'2024) during March 25 - 27, 2024. Click on the link below to access the arxiv article.