FragQC: An Efficient Quantum Error Reduction Technique using Quantum Circuit Fragmentation

TL;DR

This paper presents FragQC, a software tool that cuts a quantum circuit into sub-circuits when its error probability exceeds a certain threshold and achieves an increase of fidelity by 14.83% compared to direct execution without cutting the circuit, and 8.45% over the state-of-the-art ILP-based method for the benchmark circuits.

Abstract

Quantum computers must meet extremely stringent qualitative and quantitative requirements on their qubits in order to solve real-life problems. Quantum circuit fragmentation techniques divide a large quantum circuit into a number of sub-circuits that can be executed on the smaller noisy quantum hardware available. However, the process of quantum circuit fragmentation involves finding an ideal cut that has exponential time complexity, and also classical post-processing required to reconstruct the output. In this paper, we represent a quantum circuit using a weighted graph and propose a novel classical graph partitioning algorithm for selecting an efficient fragmentation that reduces the entanglement between the sub-circuits along with balancing the estimated error in each sub-circuit. We also demonstrate a comparative study over different classical and quantum approaches of graph partitioning for finding such a cut. We present {\it FragQC}, a software tool that cuts a quantum circuit into sub-circuits when its error probability exceeds a certain threshold. With this proposed approach, we achieve an increase of fidelity by 14.83\% compared to direct execution without cutting the circuit, and 8.45\% over the state-of-the-art ILP-based method, for the benchmark circuits.

Figures (9)

• Figure 1: Example of quantum circuit fragmentation: (a) a quantum circuit $C$ with 5 qubits and 4 two-qubit gates; (b) the corresponding graph $G$ of $C$; (c) the two quantum sub-circuits after a fragmentation.
• Figure 2: Error Map of 7-qubit $ibm\_nairobi$ device.
• Figure 3: Flowchart of the proposed tool FragQC.
• Figure 4: Block diagram of our error efficient cut searcher.
• Figure 5: An example circuit and its corresponding doubly-weighted graph.