Net-Zero Power UAVs: Facilitating Quantum HRLLC in Multi-Hop UAV Repeaters

I. INTRODUCTION

• Coordinated quantum UAV repeaters are motivated as a way to maintain connectivity when degraded line-of-sight conditions make single-hop links vulnerable.The introduction describes quantum links as sensitive to atmospheric turbulence, noise, and decoherence.Source: §I · p. 1
• Earlier classical UAV methods omit quantum-specific effects, while theoretical quantum-capacity work does not address practical UAV constraints such as mobility and energy harvesting.The omitted effects include decoherence, entanglement degradation, quantum noise, and gate imperfections.Source: §I · p. 1
• The joint optimization of qubit allocation, UAV positioning, and transmit power across aerial repeater channels under energy-harvesting constraints remains unexplored.The introduction also notes that computational complexity for this joint problem has not been characterized.Source: §I · p. 1
• The paper proposes a symmetric dual-UAV repeater framework and QRO-GA to jointly optimize qubit allocation, 3D positioning, and transmit powers for net-zero operation and bounded latency.The architecture shortens transmission hops to mitigate distance-related decoherence.Source: §I · pp. 1–2

II. SYSTEM MODEL AND PROBLEM FORMULATION

• Two UAV repeaters connect a command station to a remediation robot through three sequential quantum channels in a post-explosion chemical-plant setting.Classical command data are encoded in photonic qubits; plant structures, debris, and smoke prevent direct communication.Source: §II · p. 2
• The UAVs share an altitude z and are positioned symmetrically, making the first and third channel distances equal while the inter-UAV distance varies with x.This geometry permits dynamic positioning around local obstacles.Source: §II · p. 2
• The model assumes sufficient altitude for dominant line-of-sight and uses free-space path loss as a tractable baseline, deferring stochastic fading models to future work.The stated altitude assumption is intended to clear ground-level macro-structures despite dense smoke.Source: §II · p. 2

A. Quantum Error Model

• The paper assumes M denotes the total available qubits and represents their distribution with the allocation vector m = [m1, m2, m3].Source: A. Quantum Error Model · p. 2
• The channel model incorporates quantum noise into effective SNR and scales measurement variance by gate efficiency and entanglement preservation.These factors represent imperfect measurements and decoherence-related degradation.Source: A. Quantum Error Model · p. 2
• Channel capacity under decoherence models reduced classical data throughput, and the per-channel error probability is then used to form total decoding error.The model also specifies a physical-realizability condition for the error probability.Source: A. Quantum Error Model · pp. 2–3
• Solar and wind power are combined into total harvested power, with both modeled as nonlinear functions of altitude.The wind model uses an altitude-dependent wind-speed profile, while the solar model includes atmospheric attenuation and cloud effects.Source: B. Energy Harvesting Model · p. 3

C. Latency Model

• To meet HRLLC requirements, the end-to-end (E2E) delay for each multi-hop repeater link i ∈ {1, 2, 3} should satisfy the stated condition.Source: C. Latency Model · p. 3
• Transmission delay for m_i qubits is τ_i = m_i/B_sym, with HARQ round-trip propagation and processing delays added to obtain total delay.Source: C. Latency Model · p. 3
• The maximum transmission duration is τ_max = T_th − (T_HARQ + T_proc), so the latency budget bounds each hop's blocklength.Source: C. Latency Model · p. 3

D. Optimization Problem

• The objective is to minimize total decoding error by jointly optimizing UAV coordinates (x, z), qubit distribution m, and transmit power P.Source: D. Optimization Problem · p. 3
• QRO-GA initializes a bounded population, evaluates fitness with constraint penalties, preserves elites, and creates offspring through tournament selection, crossover, and mutation.Source: D. Optimization Problem · p. 3
• Each generation retains elites and fills the population with the best selected offspring, stopping at early convergence or returning the lowest-fitness chromosome.Source: D. Optimization Problem · p. 3
• Constraints C1–C2 bound latency-based qubit allocation, C3–C5 set geometric and stability limits, C6 enforces system-wide net-zero energy, and C7 bounds individual transmit powers.Source: D. Optimization Problem · p. 3

III. QUANTUM-RESOURCE OPTIMIZED GENETIC ALGORITHM (QRO-GA)

• QRO-GA encodes seven decision variables in a chromosome and minimizes decoding-error fitness, bypassing local optima without gradient reliance.Source: §III · p. 3

Simulation setup and complexity

• The simulation uses D=1000 m, Dsafe=50 m, and Xmax=475 m, permits harvested-energy surplus storage, and has runtime complexity O(Gmax·Npop·Teval).The inequality models an onboard battery buffer; fitness evaluation dominates the stated complexity.Source: §IV · pp. 3–4

Benchmark convergence

• Against four fixed baselines—geometry, altitude, power, and resource allocation—QRO-GA vastly outperforms them; fixed resource allocation fails instantly, while geometry or power restrictions stall suboptimally, and QRO-GA achieves best convergence well below ε = 10−9 HRLLC target.Source: §IV · p. 4

Qubit allocation

• With M=80, 100, and 120, convergence takes about 30, 10, and 5 iterations, respectively, while larger allocations lower final εtot.The figure compares convergence behavior across total qubit allocations.Source: §IV · p. 4, Figure 3 · p. 4

Latency tradeoff

• U-shaped εtot curves show that an optimal latency distribution is required within τmax=80 µs to remain in the HRLLC feasible region.The limit subtracts 20 µs of HARQ and processing overhead from the 100 µs factory-automation target.Source: §IV · pp. 4–5, Figure 4 · p. 4

2-D positioning

• Optimizing horizontal distance x and altitude z identifies favorable coordinates for minimizing εtot and link degradation.Figure 5 presents total decoding error against the two spatial-positioning dimensions.Source: Figure 5 · p. 4, §IV · p. 5

Energy balance

• Consumed power equals harvested power, satisfying C6 and net-zero operation; consumption includes three link transmit powers and both UAV hover loads, while harvest combines solar and wind.Figure 6 compares total consumed and harvested power.Source: Figure 6 · p. 4, §IV · p. 5

Overall result

• QRO-GA significantly outperformed fixed benchmark methods while jointly optimizing qubits, 2-D UAV positions, and transmit powers under strict harvesting constraints.The optimization minimizes total decoding error.Source: §V · p. 5

Qubit allocation

• As few as 5 iterations suffice for convergence at higher total qubit allocations, which also dramatically reduce εtot.The conclusion states that increasing M improves convergence speed and lowers total decoding error.Source: §V · p. 5

Latency and positioning

• An optimal latency distribution within a strict 80 µs transmission window is required to maintain HRLLC reliability, and optimized 2-D positioning minimizes total decoding error.Source: §V · p. 5

Energy balance

• QRO-GA identifies operating points balancing consumed and harvested power, achieving a net-zero system under the nonlinear energy constraints.Source: §V · p. 5

• The total decoding-error objective εtot is non-convex over its domain.Source: APPENDIX · p. 5
• For h1(x,z)=β0/(x^2+z^2), the Hessian has eigenvalues of opposite signs and is therefore indefinite.Source: APPENDIX · p. 5
• The channel gain's saddle-point geometry makes its non-convexity propagate to the composite objective εtot.Source: APPENDIX · p. 5