PREreviews of Quantum-Enhanced LLM Cascade Routing: A QAOA Approach to Cost-Optimal Model Selection in Multi-Agent Systems | PREreview

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Quantum-Enhanced LLM Cascade Routing: A QAOA Approach to Cost-Optimal Model Selection in Multi-Agent Systems

by Amit Patole

Posted: April 9, 2026
Server: Preprints.org
DOI: 10.20944/preprints202604.0413.v2

Abstract

The rapid proliferation of large language model (LLM) powered multi-agent systems creates a non-trivial combinatorial optimization problem: routing heterogeneous tasks to the most cost-effective model tier while maintaining quality guarantees. Current production systems rely on static lookup tables, which over-provision expensive models and waste computational budget. We formalize the LLM Cascade Routing Problem (LCRP) as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solve it using the Quantum Approximate Optimization Algorithm (QAOA). We benchmark QAOA against greedy heuristics and simulated annealing using both Google Cirq simulation and real IBM Quantum hardware (156-qubit Heron processors). Experiments across three IBM backends (ibm_fez, ibm_kingston, ibm_marrakesh) on problem instances from 6 to 18 qubits reveal three key findings: (i) shallow QAOA circuits (p=1, depth 52) achieve 15.4% valid assignment rate on real hardware versus 0.8% for deeper circuits (p=2, depth 101), demonstrating that NISQ noise favors shallow ansatze; (ii) hardware constraint satisfaction degrades steeply with problem size, dropping from 37-43% at 6 qubits to 0.2-0.3% at 18 qubits; and (iii) results are reproducible across all three backends with consistent valid rates within plus or minus 1.5%. To our knowledge, this is the first quantum computing formulation of the LLM model routing problem. We provide an open-source implementation and discuss the projected quantum advantage horizon.

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3 PREreviews

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PREreview by Tamanna Nandlal Choithani

Authored by Tamanna Nandlal Choithani

Summary

This paper takes on an interesting and timely problem: as multi-agent LLM systems scale up, the question of how to route tasks across model tiers in a cost-aware way becomes genuinely hard. The authors reframe this as a combinatorial optimization problem, specifically a QUBO and then…

Read the PREreview by Tamanna Nandlal Choithani
PREreview by Tamanna Nandlal Choithani

Authored by Tamanna Nandlal Choithani

Summary

This paper takes on an interesting and timely problem: as multi-agent LLM systems scale up, the question of how to route tasks across model tiers in a cost-aware way becomes genuinely hard. The authors reframe this as a combinatorial optimization problem, specifically a QUBO and then…

Read the PREreview by Tamanna Nandlal Choithani
PREreview by Mattia Gaggi

Authored by Mattia Gaggi

Summary

This paper appears to present the first QUBO-based formulation of the LLM Cascade Routing Problem, translating the model-selection process in multi-agent systems into an optimization framework that can be executed on quantum hardware. By benchmarking the method on IBM’s Heron processors,…

Read the PREreview by Mattia Gaggi