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UNIQ: Communication-Efficient Distributed Quantum Computing via Unified Nonlinear Integer Programming

Hui Zhong, Jiachen Shen, Lei Fan, Xinyue Zhang, Hao Wang, Miao Pan, Zhu Han

TL;DR

The paper tackles the high latency of remote operations in distributed quantum computing by proposing UNIQ, a unified optimization framework that jointly handles qubit allocation, entanglement management, and network scheduling via a nonlinear integer program. It introduces time-slot based modeling and EPR pre-establishment to enable parallel entanglement generation, supported by a Greedy–JIT two-stage planning approach for reproducible warm starts. Through extensive simulations across diverse circuits and QPU topologies, UNIQ consistently reduces circuit runtime and remote-gate communication costs, outperforming both algorithmic baselines and the CloudQC framework. The work presents a practical, scalable pathway to more efficient DQC deployments with unified optimization and proactive entanglement management.

Abstract

Distributed quantum computing (DQC) is widely regarded as a promising approach to overcome quantum hardware limitations. A major challenge in DQC lies in reducing the communication cost introduced by remote CNOT gates, which are significantly slower and more resource-consuming than local operations. Existing DQC approaches treat the three essential components (qubit allocation, entanglement management, and network scheduling) as independent stages, optimizing each in isolation. However, we observe that these components are inherently interdependent, and therefore adopting a unified optimization strategy can be more efficient to achieve the global optimal solutions. Consequently, we propose UNIQ, a novel DQC optimization framework that integrates all three components into a non-linear integer programming (NIP) model. UNIQ aims to reduce the circuit runtime by maximizing parallel Einstein-Podolsky-Rosen (EPR) pair generation through the use of idle communication qubits, while simultaneously minimizing the communication cost of remote gates. To solve this NP-hard formulated problem, we adopt two key strategies: a greedy algorithm for efficiently mapping logical qubits to different QPUs, and a JIT (Just-In-Time) approach that builds EPR pairs in parallel within each time slot. Extensive simulation results demonstrate that our approach is widely applicable to diverse quantum circuits and QPU topologies, while substantially reducing communication cost and runtime over existing methods.

UNIQ: Communication-Efficient Distributed Quantum Computing via Unified Nonlinear Integer Programming

TL;DR

The paper tackles the high latency of remote operations in distributed quantum computing by proposing UNIQ, a unified optimization framework that jointly handles qubit allocation, entanglement management, and network scheduling via a nonlinear integer program. It introduces time-slot based modeling and EPR pre-establishment to enable parallel entanglement generation, supported by a Greedy–JIT two-stage planning approach for reproducible warm starts. Through extensive simulations across diverse circuits and QPU topologies, UNIQ consistently reduces circuit runtime and remote-gate communication costs, outperforming both algorithmic baselines and the CloudQC framework. The work presents a practical, scalable pathway to more efficient DQC deployments with unified optimization and proactive entanglement management.

Abstract

Distributed quantum computing (DQC) is widely regarded as a promising approach to overcome quantum hardware limitations. A major challenge in DQC lies in reducing the communication cost introduced by remote CNOT gates, which are significantly slower and more resource-consuming than local operations. Existing DQC approaches treat the three essential components (qubit allocation, entanglement management, and network scheduling) as independent stages, optimizing each in isolation. However, we observe that these components are inherently interdependent, and therefore adopting a unified optimization strategy can be more efficient to achieve the global optimal solutions. Consequently, we propose UNIQ, a novel DQC optimization framework that integrates all three components into a non-linear integer programming (NIP) model. UNIQ aims to reduce the circuit runtime by maximizing parallel Einstein-Podolsky-Rosen (EPR) pair generation through the use of idle communication qubits, while simultaneously minimizing the communication cost of remote gates. To solve this NP-hard formulated problem, we adopt two key strategies: a greedy algorithm for efficiently mapping logical qubits to different QPUs, and a JIT (Just-In-Time) approach that builds EPR pairs in parallel within each time slot. Extensive simulation results demonstrate that our approach is widely applicable to diverse quantum circuits and QPU topologies, while substantially reducing communication cost and runtime over existing methods.

Paper Structure

This paper contains 26 sections, 2 theorems, 12 equations, 11 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Qubits and Quantum Gates
  4. Distributed Quantum Computing
  5. UNIQ DQC Model
  6. Problem Formulation
  7. Mapping Validity
  8. QPU Capacity
  9. Gate Scheduling
  10. Same-QPU Indicator
  11. EPR Generation Requirement
  12. EPR Before Execution Ordering
  13. Precedence
  14. Undirected Mapping Indicator
  15. Concurrent EPR Generation and Inventory
  16. ...and 11 more sections

Key Result

Theorem 1

For every finite instance $(Q,\mathcal{G},\mathcal{P},\mathcal{U}, \mathrm{Cap},E,C,H)$, the Greedy–JIT constructor terminates after at most $O\!\bigl( n\log n + np + m+e + mH + p^{2}H \bigr) \;=\; O\!\bigl(m^{2}\bigr)$ primitive operations when $n,e,H=\Theta(m)$ and $p=o(m)$.

Figures (11)

  • Figure 1: Solving a large-scale problem via DQC. A quantum circuit is partitioned into two subcircuits, each assigned to a different QPU for parallel execution.
  • Figure 2: DQC architecture with two QPUs.
  • Figure 3: Cat-Comm implementation of one remote CNOT gate. $q_0$ and $q_1$ are computing qubits; $q_{c0}$ and $q_{c1}$ are communication qubits. $q_0$ and $q_{c0}$ belong to QPU $u_1$; $q_1$ and $q_{c1}$ belong to QPU $u_2$.
  • Figure 4: Example circuit illustrating constraints a-e, g-i.
  • Figure 5: (a) Two EPR pairs for $g_1$ and $g_5$ are generated in parallel and completed together in the same time slot. (b) Example circuit illustrating constraint f.
  • ...and 6 more figures

Theorems & Definitions (4)

  • Theorem 1: Convergence
  • proof
  • Theorem 2: Feasibility
  • proof