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arXiv:2609.13669

Batched pattern search for QAOA parameter optimization on cloud-accessed quantum hardware

Muhammad Faryad

quant-phSubmitted Sep 12, 2026• Announced Sep 15, 2026• 0 citations
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Abstract

On a cloud-accessed quantum processor the classical optimizer of a variational algorithm communicates with the device through submitted jobs, and each job carries a queueing and turnaround overhead that does not depend on how many circuits it contains. We study a simple consequence of this for the quantum approximate optimization algorithm (QAOA). An optimizer whose next set of trial parameters is known before any result returns can evaluate the whole set in one job, whereas a sequential optimizer such as COBYLA spends one job per function evaluation. We compare a batched pattern search with COBYLA on IBM's \ibmfez\ processor for cardinality-constrained portfolio selection with six to twelve assets, giving both optimizers the same number of jobs and the same number of shots. At every size the batched search reaches, after its first job, a parameter quality that the serial optimizer takes several jobs to match, and the two methods converge to comparable final values; repeating the eight-asset comparison from four starting points gives the same ordering each time. The instances are small enough to be solved exactly, which lets us check that the device's output distribution is correlated with the true ranking of portfolios and is clearly separated from a control circuit of the same depth with the cost layer removed. A short scan over circuit depth at classically optimal parameters shows that on this device the measured solution quality peaks at two or three QAOA layers. The protocol is described in enough detail to be reproduced, and the notebooks and raw counts are released.

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On a cloud-accessed quantum processor the classical optimizer of a variational algorithm communicates with the device through submitted jobs, and each job carries a queueing and turnaround overhead that does not depend on how many circuits it contains. We study a simple consequence of this for the quantum approximate optimization algorithm (QAOA). An optimizer whose next set of trial parameters is known before any result returns can evaluate the whole set in one job, whereas a sequential optimizer such as COBYLA spends one job per function evaluation. We compare a batched pattern search with COBYLA on IBM's \ibmfez\ processor for cardinality-constrained portfolio selection with six to twelve assets, giving both optimizers the same number of jobs and the same number of shots. At every size the batched search reaches, after its first job, a parameter quality that the serial optimizer takes several jobs to match, and the two methods converge to comparable final values; repeating the eight-asset comparison from four starting points gives the same ordering each time. The instances are small enough to be solved exactly, which lets us check that the device's output distribution is correlated with the true ranking of portfolios and is clearly separated from a control circuit of the same depth with the cost layer removed. A short scan over circuit depth at classically optimal parameters shows that on this device the measured solution quality peaks at two or three QAOA layers. The protocol is described in enough detail to be reproduced, and the notebooks and raw counts are released.
We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless of the number of qubits, Hamiltonian complexity, or circuit depth. By separating schedule function optimization from circuit digitization, FPC-QAOA enables accurate schedule approximations with minimal parameters while supporting arbitrarily deep digitized adiabatic evolutions, constrained only by NISQ hardware capabilities. This separation allows depth to scale without expanding the classical search space, mitigating overparameterization and optimization challenges typical of deep QAOA circuits, such as barren plateaus-like behaviors. We benchmark FPC-QAOA on random MaxCut instances and the Tail Assignment Problem, achieving performance comparable to or better than standard QAOA with nearly constant classical effort and significantly fewer quantum circuit evaluations. Experiments on the IBM Kingston superconducting processor with up to 50 qubits confirm robustness and hardware efficiency under realistic noise. These results position FPC-QAOA as a practical and scalable paradigm for variational quantum optimization on near-term quantum devices.
Abstract We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless of the number of qubits, Hamiltonian complexity, or circuit depth. By separating schedule function optimization from circuit digitization, FPC-QAOA enables accurate schedule approximations with minimal parameters while supporting arbitrarily deep digitized adiabatic evolutions, constrained only by NISQ hardware capabilities. This separation allows depth to scale without expanding the classical search space, mitigating overparameterization and optimization challenges typical of deep QAOA circuits, such as barren plateaus-like behauvious. We benchmark FPC-QAOA on random MaxCut instances and the Tail Assignment Problem, achieving performance comparable to or better than standard QAOA with nearly constant classical effort and significantly fewer quantum circuit evaluations. Experiments on the IBM Kingston superconducting processor with up to 50 qubits confirm robustness and hardware efficiency under realistic noise. These results position FPC-QAOA as a practical and scalable paradigm for variational quantum optimization on near-term quantum devices.
Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum heuristic with empirical evidence of speedup over classical state-of-the-art for some problems. QAOA uses a parameterized circuit with ppp layers, where higher ppp yields better solutions, but requires optimizing 2p2p2p independent parameters, which is challenging at large ppp. We present an iterative interpolation method that exploits the smoothness of optimal parameter schedules by expressing them in a basis of orthogonal functions, generalizing the work of Zhou et al. By optimizing a small number of basis coefficients and iteratively increasing both circuit depth and coefficient count until convergence, our method constructs high-quality schedules for large ppp. We provide theoretical justification using Jackson's theorem and Lipschitz continuity to bound the required number of basis coefficients for a given accuracy. Our approach achieves better performance with fewer optimization steps than existing methods across three benchmark problems: the Sherrington-Kirkpatrick (SK) model, portfolio optimization, and Low Autocorrelation Binary Sequences (LABS). For the largest LABS instance, we achieve near-optimal merit factors with schedules exceeding 1000 layers, an order of magnitude beyond previous methods. Additionally, we observe that a mild growth in QAOA depth suffices to solve the SK model exactly, a result of independent theoretical interest.
The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial variational parameters. Hence, parameter selection for QAOA becomes an active area of research, as bad initialization might deteriorate the quality of the results, especially at great circuit depths. We first discuss the patterns of optimal parameters in QAOA in two directions: the angle index and the circuit depth. Then, we discuss the symmetries and periodicity of the expectation that is used to determine the bounds of the search space. Based on the patterns in optimal parameters and the bounds restriction, we propose a strategy that predicts the new initial parameters by taking the difference between the previous optimal parameters. Unlike most other strategies, the strategy we propose does not require multiple trials to ensure success. It only requires one prediction when progressing to the next depth. We compare this strategy with our previously proposed strategy and the layerwise strategy for solving the Max-cut problem in terms of the approximation ratio and the optimization cost. We also address the non-optimality in previous parameters, which is seldom discussed in other works despite its importance in explaining the behavior of variational quantum algorithms.
Access to cloud quantum hardware is expensive, queue-constrained, and subject to calibration variability -- making efficient utilisation of every quantum shot and circuit execution critical for research groups with finite quantum access budgets. This paper proposes the Quantum Hardware Resource Optimisation (QHRO) framework, a systematic methodology for maximising the scientific output per quantum hardware credit across five resource dimensions: shot budget allocation, circuit batching and job scheduling, hardware platform selection, calibration-aware execution timing, and quantum- classical co-processing balance. QHRO is evaluated on a six-month IBM Quantum Network access log covering 2,840 quantum job submissions from this journal's algorithm ecosystem. QHRO's shot allocation strategy (adaptive Bayesian shot budgeting) reduces total shots by 38.4% at equal result quality. Circuit batching reduces queue wait time by 48.4% through intelligent job packing. Calibration-aware scheduling reduces effective error rate by 18.4% by submitting jobs during low-noise calibration windows. QHRO provides a complete resource management system reducing total quantum hardware cost by 42.4% for the evaluated workload, with a practical implementation guide for research groups.
Training parameterized quantum circuits requires balancing optimization progress with limited evaluation budgets and the statistical uncertainty of near-term quantum hardware. We present a modular benchmarking framework that separates quantum search-direction estimation from classical parameter-update rules, allowing their interactions and sensitivities to be examined independently. We evaluate a suite of gradient-based, stochastic, and derivative-free optimizers across combinatorial optimization using the Quantum Approximate Optimization Algorithm (QAOA), supervised quantum machine learning using Iris classification and a quantum convolutional neural network (QCNN) for binary MNIST classification, and quantum chemistry using the variational quantum eigensolver (VQE) for molecular hydrogen. By separating objective evaluations from sample-circuit costs under finite-shot simulation and physical execution on a 156-qubit processor, we compare optimizer behavior across workloads with different parameter counts and measurement requirements. Four selected simulator and hardware case studies report terminal and best observed objectives separately, alongside post-training classifier accuracies. The comparisons include selected MaxCut and hydrogen trajectories and illustrate workload-dependent objective changes and evaluation costs, while the simulator benchmark compares both peak and mean performance across three seeds. The hardware runs do not establish an optimizer ranking or isolate a causal effect of device noise.