Circuit Folding: Modular and Qubit-Level Workload Management in Quantum-Classical Systems

TL;DR

CiFold tackles circuit cutting scalability in quantum-classical systems by identifying qubit-level recurring patterns and folding them into a meta-graph that guides modular partitioning. It blends graph-based layered pattern discovery with qubit-level unfolding to minimize Quantum Resource Overhead (QRO) while preserving fidelity. Empirical results show up to 799.2% QRO reduction and fast cut-point identification across diverse circuits compared to state-of-the-art methods, demonstrating practical viability on NISQ hardware. Overall, CiFold provides a scalable middleware approach for executing large quantum circuits by exploiting modularity and recurring structures.

Abstract

Quantum computing is an emerging technology that offers exponential speedups for certain problems. At the core of quantum-centric supercomputing is advanced middleware that manages the interaction between quantum hardware and classical computing infrastructure. Circuit knitting is a technique that leverages classical computation to offload some of the computational burden from quantum circuits, enabling them to exceed the capacity of current Noisy Intermediate-Scale Quantum (NISQ) devices. This is done by partitioning large circuits into smaller subcircuits, though at the cost of classical reconstruction and increased sampling overhead. Despite significant advancements in reducing the theoretical costs of circuit knitting, efficiently deploying these techniques across a broad range of quantum algorithms remains a challenge. In this work, we propose CiFold, a novel graph-based system that, at the individual qubit's level, identifies and leverages repeated structures within quantum circuits. By folding these repeated modules in parallel, CiFold constructs a meta-graph that guides the partitioning process, optimizing the cutting strategy through the integration of advanced circuit knitting techniques. Our system has been extensively evaluated across various quantum algorithms, achieving up to 799.2\% reduction in quantum resource usage, demonstrating its scalability and substantial performance improvements over state-of-the-art approaches.

Figures (11)

• Figure 1: Three types of cuts: in black box cut, parallel cuts are blocked by unknown, irrelevant operations
• Figure 2: Two cut types: gate cut and wire cut.
• Figure 3: Four sample circuits with repeated patterns: (a) Bernstein Vazirani (BV); (b) Quantum Fourier Transform (QFT); (c) Hardware efficient ansatz (HWEA) and (d) Grover's Search Algorithm (Grovers).
• Figure 4: CiFold System Overview
• Figure 5: Illustration of Circuit Folding:(a) The input quantum circuit is first converted into a circuit-level graph, shown in a, and a qubit-level graph, shown in b. (b) In the first folding layer, the Maximum Entangled Partition identified in b is highlighted using the same color and folded in parallel. (c) During the folding process, a common gate sequence between $q_2$ and $q_3$ is detected using the LCCS algorithm (Algorithm \ref{['alg:LCCS']}), resulting in a folded structure with a folding weight($w$)of 2, as illustrated in c. (d) The folded structure involving [$q_2, q_3$] leads to self-folding of $q_4$, which is indicated by a green edge pointing towards itself. (e) The final meta-graph exhibits a reduction in nodes (from 19 to 14) and edges (from 18 to 10). The folded nodes in the meta-graph can still be mapped back to the original circuit graph, with each fold indicated by the corresponding $w$.