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Distributed Quantum Computation with Minimum Circuit Execution Time over Quantum Networks

Ranjani G Sundaram, Himanshu Gupta, C. R. Ramakrishnan

TL;DR

The paper tackles distributed quantum computation over quantum networks by minimizing circuit execution time under memory, entanglement-generation, and decoherence constraints. It introduces a two-step framework: (1) allocate circuit qubits to network memories using a max-QAP-based approximation, augmenting the circuit graph with dummy nodes to fit a max-QAP formulation, and (2) devise efficient EP-generation schedules using dynamic programming for total consumption orders and greedy methods for general orders, incorporating telegates and cat-entanglements. Key contributions include provable NP-hardness of the core problem, a 4-approximation qubit-allocation method, optimal DP and scalable greedy EP-generation strategies, and a near-optimal CE-based approach via a densest-subgraph formulation. The approach is validated with NetSquid simulations, showing up to 95% improvements over prior work and highlighting the practical impact for scalable quantum-network-assisted computations. The framework lays the groundwork for dynamic qubit allocation and more sophisticated EP-generation policies in future distributed quantum computing systems.

Abstract

Present quantum computers are constrained by limited qubit capacity and restricted physical connectivity, leading to challenges in large-scale quantum computations. Distributing quantum computations across a network of quantum computers is a promising way to circumvent these challenges and facilitate large quantum computations. However, distributed quantum computations require entanglements (to execute remote gates) which can incur significant generation latency and, thus, lead to decoherence of qubits. In this work, we consider the problem of distributing quantum circuits across a quantum network to minimize the execution time. The problem entails mapping the circuit qubits to network memories, including within each computer since limited connectivity within computers can affect the circuit execution time. We provide two-step solutions for the above problem: In the first step, we allocate qubits to memories to minimize the estimated execution time; for this step, we design an efficient algorithm based on an approximation algorithm for the max-quadratic-assignment problem. In the second step, we determine an efficient execution scheme, including generating required entanglements with minimum latency under the network resource and decoherence constraints; for this step, we develop two algorithms with appropriate performance guarantees under certain settings or assumptions. We consider multiple protocols for executing remote gates, viz., telegates and cat-entanglements. With extensive simulations over NetSquid, a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform a scheme based on prior work by up to 95%.

Distributed Quantum Computation with Minimum Circuit Execution Time over Quantum Networks

TL;DR

The paper tackles distributed quantum computation over quantum networks by minimizing circuit execution time under memory, entanglement-generation, and decoherence constraints. It introduces a two-step framework: (1) allocate circuit qubits to network memories using a max-QAP-based approximation, augmenting the circuit graph with dummy nodes to fit a max-QAP formulation, and (2) devise efficient EP-generation schedules using dynamic programming for total consumption orders and greedy methods for general orders, incorporating telegates and cat-entanglements. Key contributions include provable NP-hardness of the core problem, a 4-approximation qubit-allocation method, optimal DP and scalable greedy EP-generation strategies, and a near-optimal CE-based approach via a densest-subgraph formulation. The approach is validated with NetSquid simulations, showing up to 95% improvements over prior work and highlighting the practical impact for scalable quantum-network-assisted computations. The framework lays the groundwork for dynamic qubit allocation and more sophisticated EP-generation policies in future distributed quantum computing systems.

Abstract

Present quantum computers are constrained by limited qubit capacity and restricted physical connectivity, leading to challenges in large-scale quantum computations. Distributing quantum computations across a network of quantum computers is a promising way to circumvent these challenges and facilitate large quantum computations. However, distributed quantum computations require entanglements (to execute remote gates) which can incur significant generation latency and, thus, lead to decoherence of qubits. In this work, we consider the problem of distributing quantum circuits across a quantum network to minimize the execution time. The problem entails mapping the circuit qubits to network memories, including within each computer since limited connectivity within computers can affect the circuit execution time. We provide two-step solutions for the above problem: In the first step, we allocate qubits to memories to minimize the estimated execution time; for this step, we design an efficient algorithm based on an approximation algorithm for the max-quadratic-assignment problem. In the second step, we determine an efficient execution scheme, including generating required entanglements with minimum latency under the network resource and decoherence constraints; for this step, we develop two algorithms with appropriate performance guarantees under certain settings or assumptions. We consider multiple protocols for executing remote gates, viz., telegates and cat-entanglements. With extensive simulations over NetSquid, a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform a scheme based on prior work by up to 95%.
Paper Structure (17 sections, 5 theorems, 2 equations, 8 figures)

This paper contains 17 sections, 5 theorems, 2 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Distribution of Quantum Circuits over QNs
  4. Generating EPs over Remote Nodes
  5. Decoherence and Fidelity
  6. Problem Formulation and Related Work
  7. Related Work
  8. High-Level Approach
  9. Step 1: Determining Qubit Allocation Function
  10. Step 2: Executing Remote Gates by Generating EPs
  11. Dynamic Programming (DP) for Generating EPs
  12. Greedy Approach for Generating EPs
  13. Cat-Entanglements to Execute Remote Gates
  14. Selecting CEs (and EPs) to Execute Remote Gates
  15. Other Generalizations
  16. ...and 2 more sections

Key Result

Theorem 1

The 4-approximation max- QAP algorithm from Esther returns a $6/p$-approximate solution for the max- QAP problem over $G"_C$ and $G_N$; here, $p$ is the entanglement-swapping's success probability.

Figures (8)

  • Figure 1: Quantum communication. (a) Teleportation, (b) Telegate, (c) Cat-Entanglement. Dashed boxes are the network nodes; the initial (final) state of the qubits is at the top (bottom).
  • Figure 2: Swapping tree to generate remote EPs.
  • Figure 3: DQC-QR Problem Example 1. (a) Quantum circuit, with the remote gates (based on the qubit allocation in (b)) colored and labeled with the EPs required. (b) Qubit allocation over the quantum network. (c) Execution scheme, i.e., the batches and order in which the required EPs are generated; the colored paths in (c) represent the entanglement routes along which the corresponding EPs are generated.
  • Figure 4: Overall plan and organization of the schemes developed.
  • Figure 5: Consumption order of EPs required in Example 1. A directed edge from $e_i$ to $e_j$ indicates $e_i$ must be consumed before $e_j$.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Lemma 1
  • Theorem 2
  • Lemma 2
  • Theorem 3