A parallel algorithm based on quantum annealing and double-elite spiral search for mixed-integer optimal control problems in engineering

Liu, Zhe; Li, Shurong; Ge, Yulei

doi:10.1016/j.asoc.2022.109018

Cited by 6 publications

(1 citation statement)

References 52 publications

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“…In aid of this, efforts have gone into reducing the number of binary variables required to solve these optimization problems. Existing approaches include attempts to reformulate the classical problem reduce the number of binary variables required, [36][37][38][39][40][41] divide-and-conquer approaches that break down the problem or quantum circuit into smaller parts, [42][43][44][45][46][47][48][49][50][51][52][53][54][55] and qubit encoding schemes, [56][57][58][59] among others. [60][61][62][63][64][65][66] This work explores the use of the encoding scheme in [59], to reduce the number of qubits required to solve classical binary optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Qubit Efficient Quantum Algorithms for the Vehicle Routing Problem on Noisy Intermediate‐Scale Quantum Processors

Leonidas,

Dukakis,

Tan

et al. 2024

Adv Quantum Tech

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The vehicle routing problem with time windows (VRPTW) is a common optimization problem faced within the logistics industry. In this work, the use of a previously‐introduced qubit encoding scheme is explored to reduce the number of qubits, to evaluate the effectiveness of Noisy Intermediate‐Scale Quantum (NISQ) devices when applied to industry relevant optimization problems. A quantum variational approach is applied to a testbed of multiple VRPTW instances ranging from 11 to 3964 routes. These intances are formulated as quadratic unconstrained binary optimization (QUBO) problems based on realistic shipping scenarios. The results are compared with standard binary‐to‐qubit mappings after executing on simulators as well as various quantum hardware platforms, including IBMQ, AWS (Rigetti), and IonQ. These results are benchmarked against the classical solver, Gurobi. The approach can find approximate solutions to the VRPTW comparable to those obtained from quantum algorithms using the full encoding, despite the reduction in qubits required. These results suggest that using the encoding scheme to fit larger problem sizes into fewer qubits is a promising step in using NISQ devices to find approximate solutions for industry‐based optimization problems, although additional resources are still required to eke out the performance from larger problem sizes.

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