Distributed Quantum Computation with Minimum Circuit Execution Time over Quantum Networks (2405.07499v1)

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%.

• The paper introduces efficient heuristic and dynamic programming algorithms to optimize qubit allocation and remote gate execution on quantum networks.
• It demonstrates up to a 95% performance improvement through simulations on benchmark circuits such as QFT, QPE, and GHZ.
• The work addresses decoherence and entanglement constraints, paving the way for more efficient distributed quantum computing applications.

Distributed Quantum Computation with Minimum Circuit Execution Time over Quantum Networks

The paper "Distributed Quantum Computation with Minimum Circuit Execution Time over Quantum Networks" addresses the significant challenge of distributing quantum computations across a network of quantum computers (QCs) to minimize execution time under constraints such as generation latency, decoherence, and network resources. This issue arises due to existing quantum computers' limited qubit capacity and restricted physical connectivity.

Problem Formulation and Objectives

The core problem under consideration is the efficient allocation and execution of quantum circuits over a quantum network, which involves mapping circuit qubits to network qubit memories in a manner that minimizes the execution time. The execution time includes latency incurred in generating the necessary entanglements (EPs) to execute remote gates under decoherence constraints. The authors present the problem as a two-step optimization problem:

1. Qubit Allocation: Assigning qubits to memories to minimize the estimated execution time.
2. Execution Scheme: Determining an efficient execution scheme that includes generating required entanglements with minimal latency considering network resource and decoherence constraints.

Algorithms and Contributions

The authors provide two main algorithms for these steps:

1. Qubit Allocation Algorithm

For the initial allocation of qubits, the authors propose an efficient heuristic-based algorithm, drawing parallels to the max-quadratic-assignment problem. This involves:

• Defining the circuit graph and network-coupling graph.
• Utilizing a heuristic derived from a 4-factor approximation algorithm for the max-quadratic assignment problem to determine a near-optimal qubit allocation.

2. Execution Scheme Algorithms

For executing the remote gates, the paper offers two significant algorithms based on dynamic programming (DP) and greedy approaches:

• Dynamic Programming (DP):
  • Suitable for cases with total consumption order.
  • Provides a provably optimal approach under these conditions.
• Greedy Heuristic:
  • Designed for scenarios where there is no consumption order.
  • Offers appropriate performance guarantees under reasonable assumptions.

Additionally, the authors explore the use of cat-entanglements (CEs) alongside telegates for executing remote gates. The CE approach allows multiple binary gates to leverage a single entanglement, thereby potentially reducing the total number of required EPs. They formulate the problem of selecting a near-optimal set of CEs as a generalized densest subgraph problem, providing solutions for minimum-cost entanglement generation.

Evaluation and Results

Extensive simulations on the NetSquid quantum network simulator demonstrate the efficacy of the proposed techniques. Key findings include:

• Performance Improvement: The developed techniques outperform previous approaches by up to 95%.
• Influence of Parameters: Varying parameters such as the number of qubits, gate ratios, and network nodes affirmed the robustness and superior performance of the algorithms.
• Benchmark Circuits: Evaluations on benchmark circuits like QFT, QPE, and GHZ further validate the practical applicability and efficiency of the algorithms.

Implications and Future Work

The results underscore the practical and theoretical potential of the proposed methods for optimizing distributed quantum computations, making significant strides in addressing the qubit capacity and connectivity limitations of current quantum computing hardware. The practical implications include more efficient execution of large quantum computations and potentially accelerating quantum algorithm deployment over distributed quantum architectures.

Future work could involve:

• Exploring more sophisticated dynamic qubit allocation strategies.
• Incorporating additional network constraints and fidelities into the optimization processes.
• Extending the algorithms to cater to a broader range of quantum gates beyond CZ and CNOT gates.

Conclusion

The paper presents a comprehensive approach to optimizing distributed quantum computation with an emphasis on minimizing execution times under stringent constraints. Through innovative heuristic and algorithmic solutions, the authors provide a significant contribution to the field, highlighting pathways for further advancements and real-world application of distributed quantum computing infrastructure.