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arXiv:2602.14327

Scalable Clifford-Based Classical Initialization for the Quantum Approximate Optimization Algorithm

Dhanvi Bharadwaj, Yuewen Hou, Guang-Yi Li, Gokul Subramanian Ravi

quant-phSubmitted Feb 15, 2026• Announced Feb 17, 2026• 0 citations• Revised Aug 23, 2026 (v2)
v1 · Feb 15, 2026v2 · Aug 23, 2026
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Abstract

Variational Quantum Algorithms (VQAs), such as the Quantum Approximate Optimization Algorithm (QAOA), offer a promising route to tackling combinatorial optimization problems on near and intermediate-term quantum devices. However, their performance critically depends on the choice of initial parameters, and the limited expressiveness of the QAOA ansatz makes identifying effective initializations both difficult and unscalable. To address this, we propose a framework, Scalable Parameter Initialization for QAOA (SPIQ), that employs a relaxed QAOA ansatz to enable classical search over a set of Clifford-preparable quantum states that yield high-quality solutions. These states serve as superior QAOA initializations, driving rapid convergence while significantly reducing the quantum circuit evaluations needed to reach high-quality solutions and consequently lowering quantum-device cost. We present a scalable, application-agnostic initialization framework that achieves an absolute accuracy improvement of up to 80% over state-of-the-art initialization and reduces initial-state diversity by up to 10,000x across QUBO, PUBO, and PCBO problems spanning tens to hundreds of qubits. We further benchmark its performance on a wide range of problem formulations and instances derived from real-world datasets, demonstrating consistent and scalable improvements. Furthermore, we introduce two complementary strategies for selecting high-quality Clifford points identified by our search procedure and using them to seed multi-start optimization, thereby enhancing exploration and improving solution quality.

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Variational Quantum Algorithms (VQAs), such as the Quantum Approximate Optimization Algorithm (QAOA), offer a promising route to tackling combinatorial optimization problems on near and intermediate-term quantum devices. However, their performance critically depends on the choice of initial parameters, and the limited expressiveness of the QAOA ansatz makes identifying effective initializations both difficult and unscalable. To address this, we propose a framework, Scalable Parameter Initialization for QAOA (SPIQ), that employs a relaxed QAOA ansatz to enable classical search over a set of Clifford-preparable quantum states that yield high-quality solutions. These states serve as superior QAOA initializations, driving rapid convergence while significantly reducing the quantum circuit evaluations needed to reach high-quality solutions and consequently lowering quantum-device cost. We present a scalable, application-agnostic initialization framework that achieves an absolute accuracy improvement of up to 80% over state-of-the-art initialization and reduces initial-state diversity by up to 10,000x across QUBO, PUBO, and PCBO problems spanning tens to hundreds of qubits. We further benchmark its performance on a wide range of problem formulations and instances derived from real-world datasets, demonstrating consistent and scalable improvements. Furthermore, we introduce two complementary strategies for selecting high-quality Clifford points identified by our search procedure and using them to seed multi-start optimization, thereby enhancing exploration and improving solution quality.
Variational Quantum Algorithms are promising candidates for near-term quantum advantage, but face significant scalability challenges due to barren plateaus. In this work, we address the trainability of the Variational Quantum Eigensolver for combinatorial portfolio optimization by evaluating three warm-start initialization strategies: Clifford, near-Clifford and a mixed approach. We compare these against a cold-start baseline initialized with the initial parameters close to zero across system sizes from [Formula: see text] to [Formula: see text]. Our results show that while the uninformed cold start fails to converge for larger systems, all warm-start strategies achieve a [Formula: see text] success rate and high initial-state fidelities. Crucially, we observe no clear difference in convergence behavior among the warm-start methods. Consequently, for this class of QUBO-based portfolio optimization problems, we identify the purely Clifford-based approach as the most efficient strategy; it consistently places the optimizer in a region from which the variational optimization converges successfully while remaining polynomially simulable on classical hardware during the quantum phase of the algorithm, indicating that the additional computational cost of non-Clifford resources offers negligible benefits for initialization in this specific context.
Variational Quantum Algorithms (VQAs) potentially offer a pathway to practical quantum advantage, but their optimization is heavily hindered by barren plateaus and numerous local minima. While classically simulable Clifford circuits can warm-start VQAs to accelerate convergence, existing heuristic-based initialization methods struggle to scale within vast combinatorial search spaces. To overcome this bottleneck, we propose CRiSP (a Clifford Reinforcement Learning agent for State Preparation), a framework that formulates discrete prefix selection as a sequential decision-making problem. CRiSP utilizes Neural-Guided Monte Carlo Tree Search, driven by a Transformer-based policy trained via self-play, to insert learned Clifford gates before fixed parameterized rotations. This enables the construction of high-quality initial states entirely through polynomial-time classical stabilizer simulation without altering the underlying circuit architecture. By integrating a curriculum learning strategy that progressively expands the search horizon, the agent efficiently scales to deep circuits. Evaluated on QAOA benchmarks of up to 222222 qubits and 1,3701{,}3701,370 parameters, CRiSP outperforms state-of-the-art Clifford initialization methods by a mean of 3.17×3.17\times3.17× (max 45.02×45.02\times45.02×) in average energy accuracy and 2.44×2.44\times2.44× (max 16.01×16.01\times16.01×) in best-achieved energy accuracy. Assessments on VQE tasks further demonstrate the framework's robustness and generalizability.
This work tackles the problem of finding a good ansatz initialization for Variational Quantum Algorithms (VQAs), by proposing CAFQA, a Clifford Ansatz For Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation. The resulting initial states always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and enable high-accuracy VQA estimations. CAFQA is well-suited to classical computation because: a) Clifford-only quantum circuits can be exactly simulated classically in polynomial time, and b) the discrete Clifford space is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation (up to 18 qubits), CAFQA's Clifford Ansatz achieves a mean accuracy of nearly 99% and recovers as much as 99.99% of the molecular correlation energy that is lost in Hartree-Fock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, on different metrics. The scalability of the approach allows for preliminary ground state energy estimation of the challenging chromium dimer (Cr2_22​) molecule. With CAFQA's high-accuracy initialization, the convergence of VQAs is shown to accelerate by 2.5x, even for small molecules. Furthermore, preliminary exploration of allowing a limited number of non-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% of the correlation energy can be recovered at bond lengths for which Clifford-only CAFQA accuracy is relatively limited, while remaining classically simulable.
Join Order Optimization (JOO) is one of the most computationally expensive tasks in relational query optimization due to the exponential growth of possible join plans with increasing query size. Recent work has explored quantum and quantum-inspired approaches for solving JOO by reformulating the problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem suitable for optimization using quantum hardware. However, many existing approaches have limited scalability on current gate-based quantum devices. In addition, little work has investigated the role of initialization strategies in improving the performance of gate-based quantum optimization for database workloads. In this work, we investigate gate-based quantum join order optimization using the Quantum Approximate Optimization Algorithm (QAOA) initialized with Scalable Parameter Initialization for QAOA (SPIQ). SPIQ is used to efficiently identify high-quality initial points in the quantum solution landscape for QAOA executed on a gate-based quantum computer. We evaluate the interaction between QUBO encoding, SPIQ initialization, and gate-based optimization on small-scale join ordering problems involving 3 and 4 relations. Our results show that structured initialization improves optimization stability and increases convergence toward high-quality join plans compared to uninformed initialization approaches. Across these small-scale, simulation-based instances, SPIQ increases the sampling frequency of the optimal join order by up to approximately 5×\times× and yields final-state energies significantly lower than a randomly initialized QAOA. Overall, this work enhances existing gate-based quantum optimization while providing an initial proof of concept for applying SPIQ initialization to database query optimization workloads.
The Quantum Approximate Optimisation Algorithm (QAOA) has emerged as a leading candidate for near-term quantum advantage in combinatorial optimisation, but most evaluations remain confined to synthetic benchmarks such as random MaxCut instances. Translating QAOA to real-world problem instances -- with irregular graph structures, heterogeneous constraint types, and practical scale requirements -- introduces additional challenges including QUBO formulation overhead, hardware embedding costs, and the performance gap between QAOA on structured real instances vs. random benchmarks. This paper presents the Real-World QAOA (RW-QAOA) framework, a systematic methodology for applying QAOA to four real-world application domains: supply chain network optimisation, financial portfolio rebalancing, telecommunications frequency assignment, and traffic signal timing optimisation. RW-QAOA introduces three methodological contributions: a domain-adaptive QUBO formulator (DAQF) encoding real-world constraints as penalised QUBO terms with penalty coefficient auto-tuning; a warm-start initialisation strategy (WSIS) using classical heuristic solutions to seed QAOA parameter search; and a layered noise adaptation protocol (LNAP) adjusting circuit depth based on real-time device calibration data. RW-QAOA is evaluated on real problem instances from industry partners across all four domains on IBM Quantum Eagle (127-qubit). RW-QAOA achieves solution quality within 4.2% of classical exact solvers across all four domains, outperforming classical greedy heuristics by 12.4% (SD = 3.8%) on average. WSIS reduces QAOA parameter convergence iterations by 48.4%. LNAP improves approximation ratio by 8.4pp vs. fixed-depth QAOA under device noise variation.
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles introduction to QAOA and its properties, focusing on its application to Quadratic and Polynomial Unconstrained Binary Optimization (QUBO and PUBO) problems. The tutorial begins by outlining variational quantum circuits and QUBO problems, focusing on their key properties and the encoding of problem constraints through quadratic penalty terms. Next, it explores the QAOA in detail, covering its Hamiltonian formulation, gate decomposition, and example applications, along with their implementation and performance results. This is followed by an analysis of the algorithm's energy landscape, where proofs are provided for its symmetry and periodicity, and where a resulting parameter space reduction is proposed. Finally, the tutorial extends these concepts to PUBO problems by generalizing the results to higher-order Hamiltonians and discussing the associated symmetries and circuit construction.