Online Job Scheduler for Fault-tolerant Quantum Multiprogramming

TL;DR

This work addresses the challenge of online job scheduling for fault-tolerant quantum multiprogramming using lattice-surgery-based surface codes. It introduces a practical preprocessing step that converts complex polycubes into cuboids, enabling online 3D bin-packing-like scheduling, and compares two online schedulers (ILP-based and corner greedy) augmented with a defragmentation mechanism. Empirical results show that the corner greedy scheduler with defragmentation achieves substantial throughput gains (2.3–2.4× on average, up to 4.53× in some classes) while maintaining real-time responsiveness, whereas the ILP approach struggles with scalability. The study also discusses resource sharing, non-deterministic execution, and extensions toward distributed quantum computing and multi-job compiling, outlining directions for more robust, scalable FTQC multiprogramming stacks.

Abstract

Fault-tolerant quantum computers are expected to be offered as cloud services due to their significant resource and infrastructure requirements. Quantum multiprogramming, which runs multiple quantum jobs in parallel, is a promising approach to maximize the utilization of such systems. A key challenge in this setting is the need for an online scheduler capable of handling jobs submitted dynamically while other programs are already running. In this study, we formulate the online job scheduling problem for fault-tolerant quantum computing systems based on lattice surgery and propose an efficient scheduler to address it. To meet the responsiveness required in an online environment, our scheduler approximates lattice surgery programs, originally represented as polycubes, by using simpler cuboid representations. This approximation enables efficient scheduling while improving overall throughput. In addition, we incorporate a defragmentation mechanism into the scheduling process, demonstrating that it can further enhance QPU utilization.

Figures (11)

• Figure 1: (a) A $[\![ d^2, 1, d ]\!]$ rotated surface code patch with $d=3$. The white circles represent the physical qubits for encoding the codeword. Red/blue regions are X/Z stabilizers of the code. (b) Merging and splitting lattice surgery operations for realizing a two-qubit Pauli $ZZ$ measurement between $Q0$ and $Q1$ logical data qubits. Orange patches are logical data qubits and the white patch is a logical auxiliary qubit. $X/Z$ subscripts is showing the $X/Z$-boundary of the patch. (c) A floorplan of surface code patches. Green patches are frame qubits, which are used as auxiliary qubits for the lattice surgery paths. (d) Multiple lattice surgery operations were compiled on the floorplan of (c). Each color represents a gate. (e) Representation of a quantum circuit with lattice surgery operations as a 3D polycube.
• Figure 2: An example of schedule for $\mathcal{P}_1, \dots, \mathcal{P}_4$
• Figure 3: The workflow of the scheduling for FTQC Multiprogramming
• Figure 4: Preprocessing of a polycube. For simplicity, the illustration is shown in two dimensions. (a) A polycube. (b) A cuboid which is a bounding box of (a). (c) $k$-cuboids. Original polycube divided into $k$ segments perpendicular to the time axis, each approximated by a bounding box.
• Figure 5: An example of potential placement candidates for the corner-greedy scheduler. Each colored box is a scheduled job, and red dots are the candidates.