Quantum Algorithm for Shortest Path Search in Directed Acyclic Graph

Khadiev, Kamil; Safina, Liliya

doi:10.3103/s0278641919010023

Cited by 2 publications

(1 citation statement)

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“…Notice that SSSP can be defined on either directed, undirected or mixed graphs, and we choose to study the undirected version for consistency with the study of EDP. Efficient classical algorithms for SSSP [3,8] are textbook-standard materials (see also [20] for a quantum algorithm for directed acyclic graphs).…”

Section: The Single Source Shortest Path Problemmentioning

confidence: 99%

QED driven QAOA for network-flow optimization

Zhang

Potter

2021

Quantum

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We present a general framework for modifying quantum approximate optimization algorithms (QAOA) to solve constrained network flow problems. By exploiting an analogy between flow-constraints and Gauss' law for electromagnetism, we design lattice quantum electrodynamics (QED)- inspired mixing Hamiltonians that preserve flow constraints throughout the QAOA process. This results in an exponential reduction in the size of the configuration space that needs to be explored, which we show through numerical simulations, yields higher quality approximate solutions compared to the original QAOA routine. We outline a specific implementation for edge-disjoint path (EDP) problems related to traffic congestion minimization, numerically analyze the effect of initial state choice, and explore trade-offs between circuit complexity and qubit resources via a particle-vortex duality mapping. Comparing the effect of initial states reveals that starting with an ergodic (unbiased) superposition of solutions yields better performance than beginning with the mixer ground-state, suggesting a departure from the ``short-cut to adiabaticity" mechanism often used to motivate QAOA.

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Section: The Single Source Shortest Path Problemmentioning

confidence: 99%

QED driven QAOA for network-flow optimization

Zhang

Potter

2021

Quantum

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Solving the Network Shortest Path Problem on a Quantum Annealer

Krauss

McCollum

2020

IEEE Trans. Quantum Eng.

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This article addresses the formulation for implementing a single source, single-destination shortest path algorithm on a quantum annealing computer. Three distinct approaches are presented. In all the three cases, the shortest path problem is formulated as a quadratic unconstrained binary optimization problem amenable to quantum annealing. The first implementation builds on existing quantum annealing solutions to the traveling salesman problem, and requires the anticipated maximum number of vertices on the solution path |P| to be provided as an input. For a graph with |V | vertices, |E| edges, and no self-loops, it encodes the problem instance using |V ||P| qubits. The second implementation adapts the linear programming formulation of the shortest path problem, and encodes the problem instance using |E| qubits for directed graphs or 2|E| qubits for undirected graphs. The third implementation, designed exclusively for undirected graphs, encodes the problem in |E| + |V | qubits. Scaling factors for penalty terms, complexity of coupling matrix construction, and numerical estimates of the annealing time required to find the shortest path are made explicit in the article. INDEX TERMSQuantum annealing, quantum computing, shortest path problem, simulated annealing. Engineering uantum Transactions on IEEE Krauss and McCollum: SOLVING THE NETWORK SHORTEST PATH PROBLEM ON A QUANTUM ANNEALER FIGURE 1. Example undirected graph with specified edge costs.

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Quantum Algorithm for Shortest Path Search in Directed Acyclic Graph

Cited by 2 publications

References 5 publications

QED driven QAOA for network-flow optimization

QED driven QAOA for network-flow optimization

Solving the Network Shortest Path Problem on a Quantum Annealer

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