Quantum Tensor Representation via Circuit Partitioning and Reintegration

Abstract: Quantum computing enables faster computations than clas-sical algorithms through superposition and entanglement. Circuit cutting and knitting are effective techniques for ame-liorating current noisy quantum processing unit (QPUs) er-rors via a divide-and-conquer approach that splits quantum circuits into subcircuits and recombines them using classical post-processing. The development of circuit partitioning and recomposing has focused on tailoring the simulation frame-work by replacing generic non-local gates with probabilistic local gates and measuring the classical communication com-plexity. Designing a protocol that supports algorithms and non-all-to-all qubit-connected physical hardware remains underdeveloped owing to the convoluted properties of cut-ting compact controlled unitary gates and hardware topology. In this study, we introduce shardQ, a method that leverages the SparseCut algorithm with matrix product state (MPS) compilation and a global knitting technique. This method elucidates the optimal trade-off between the computational time and error rate for quantum encoding with a theoretical proof, evidenced by an ablation analysis using an IBM Mar-rakesh superconducting-type QPU. This study also presents the results regarding application readiness.