Network Operations Scheduling for Distributed Quantum Computing

TL;DR

Two approaches to solving the make span minimization problem are compared, an approach based on the resource constrained project scheduling (RCPSP) framework, and another based on a greedy heuristic algorithm, to illustrate the effectiveness of the RCPSP framework, while also underlining the relevance and usefulness of greedy heuristics.

Abstract

Realizing distributed architectures for quantum computing is crucial to scaling up computational power. A key component of such architectures is a scheduler that coordinates operations over a short-range quantum network required to enable the necessary non-local entangling gates between quantum processing units (QPUs). It is desirable to determine schedules of minimum make span, which in the case of networks with constrained resources hinges on their efficient usage. Here we compare and contrast two approaches to solving the make span minimization problem, an approach based on the resource constrained project scheduling (RCPSP) framework, and another based on a greedy heuristic algorithm. The workflow considered is as follows. Firstly, the computational circuit is partitioned and assigned to different QPUs such that the number of nonlocal entangling gates acting across partitions is minimized while the qubit load is nearly uniform on the individual QPUs, which can be accomplished using, e.g., the METIS solver. Secondly, the nonlocal entangling gate requirements with respect to the partitions are identified, and mapped to network operation sequences that deliver the necessary entanglement between the QPUs. Finally, the network operations are scheduled such that the make span is minimized. As illustrative examples, we analyze the implementation of a small instance of the Quantum Fourier Transform algorithm over instances of a simple hub and spoke (star) network architecture comprised of a quantum switch as the hub and QPUs as spokes, each with a finite qubit resource budget. In one instance, our results show the RCPSP approach outperforming the greedy heuristic. In another instance, we find the two performing equally well. Our results thus illustrate the effectiveness of the RCPSP framework, while also underlining the relevance and usefulness of greedy heuristics.

Figures (9)

• Figure 1: Workflow for optimizing network operations scheduling in DQC. The input to the process is a compiled quantum circuit that is to be executed over a networked quantum computer, represented in the form of a Gantt chart. The circuit is first partitioned using the METIS solver to minimize the number of nonlocal entangling gates. Secondly, the nonlocal gates are extracted out and mapped to sequences of network operations to generate the necessary entanglement between QPUs. Finally, scheduling approaches based on a Greedy algorithm and on the RCPSP framework are analyzed to find the optimal schedule with the minimum make span.
• Figure 2: Quantum circuit diagram for a 4-qubit Quantum Fourier Transform (QFT). The circuit begins with Hadamard gates, followed by controlled phase rotations with decreasing angles, and concludes with optional SWAP gates to reverse the qubit order. This circuit transforms the input quantum state from the computational basis to the Fourier basis, a key operation in various quantum algorithms.
• Figure 3: Directed Acyclic Graph (DAG) representation of a 4-qubit Quantum Fourier Transform (QFT) circuit. The nodes represent quantum gates applied during the QFT process, including Hadamard (h) gates, Controlled Phase (cp) gates with decreasing angles, and Swap gates to reverse the order of qubits.
• Figure 4: Gantt chart representation of a 4-qubit Quantum Fourier Transform (QFT) circuit, illustrating the scheduled execution of Hadamard (H), controlled-phase (CP) which is in the format CP (Control Qubit, Target Qubit), and SWAP (S) gates. The chart ensures no overlap on the same qubit and synchronizes gate durations to optimize the overall execution time.
• Figure 5: METIS algorithm implemented to distribute 4-qubit QFT circuit in 2 QPUs. The algorithm divides it such that the edges with maximum weight are in one QPU, so qubits (0 & 3) are in one QPU and qubits (1 & 2) are in the other QPU in order to minimize non-local controlled gates.