Quantum Data Representation via Circuit Partitioning and Reintegration

TL;DR

This paper introduces shardQ, a novel quantum data encoding method that optimizes circuit partitioning and reintegration to reduce errors and improve quantum computation efficiency on hardware with connectivity limitations.

Contribution

The study presents shardQ, combining SparseCut, MPS compilation, and global knitting to enhance quantum data encoding and error mitigation, with theoretical analysis and practical validation.

Findings

Achieved 15% error reduction on IBM Heron QPU

Demonstrated optimal trade-off between computation time and error rate

Enhanced quantum image encoding readiness

Abstract

Quantum data encoding (QDE) enables faster com-putations than classical algorithms through superposition and en-tanglement. Circuit cutting and knitting are effective techniques for ameliorating current noisy quantum processing unit (QPUs) errors via a divide-and-conquer approach that splits quantum circuits into subcircuits and recombines them using classical postprocessing. Unfortunately, the existing QDE frameworks fail to consider quantum hardware limitations, such as the topology of the chip. Designing a computation model that supports the algorithm level of quantum computation and optimizes non-all-to-all connected quantum circuit simulations remains underde-veloped. In this study, we introduce shardQ, a method that leverages the SparseCut algorithm with matrix product state (MPS) compilation and a global knitting technique to mitigate the quantum error rates. 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 Heron-type QPUs with 15% error reduction. This study also presents the results of quantum image encoding readiness. The proposed model advances the current quantum computation towards the fault-tolerant regime as QDE is the input of grand unified quantum algorithms.