Abstract With the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training.
Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization heuristics that ensure rapid and consistent convergence to local minima of the parameterized quantum circuit landscape. In this work, we train classical neural networks to assist in the quantum learning process, also know as meta-learning, to rapidly find approximate optima in the parameter landscape for several classes of quantum variational algorithms. Specifically, we train classical recurrent neural networks to find approximately optimal parameters within a small number of queries of the cost function for the Quantum Approximate Optimization Algorithm (QAOA) for MaxCut, QAOA for Sherrington-Kirkpatrick Ising model, and for a Variational Quantum Eigensolver for the Hubbard model. By initializing other optimizers at parameter values suggested by the classical neural network, we demonstrate a significant improvement in the total number of optimization iterations required to reach a given accuracy. We further demonstrate that the optimization strategies learned by the neural network generalize well across a range of problem instance sizes. This opens up the possibility of training on small, classically simulatable problem instances, in order to initialize larger, classically intractably simulatable problem instances on quantum devices, thereby significantly reducing the number of required quantum-classical optimization iterations.
The capability of the quantum approximate optimization algorithm (QAOA) in solving combinatorial optimization problems has been intensively studied in recent years due to its application in the quantum-classical hybrid regime. Despite having difficulties that are innate in the variational quantum algorithms (VQA), such as barren plateaus and the local minima problem, QAOA remains one of the applications that is suitable for the recent noisy intermediate scale quantum (NISQ) devices. Recent works have shown that the performance of QAOA largely depends on the initial parameters, which motivate parameter initialization strategies to obtain good initial points for the optimization of QAOA. On the other hand, optimization strategies focus on the optimization part of QAOA instead of the parameter initialization. Instead of having absolute advantages, these strategies usually impose trade-offs to the performance of the optimization problems. One such example is the layerwise optimization strategy, in which the QAOA parameters are optimized layer by layer instead of the full optimization. The layerwise strategy costs less in total compared to the full optimization, in exchange of lower approximation ratio. In this work, we propose the iterative layerwise optimization strategy and explore the possibility for the reduction of optimization cost in solving problems with QAOA. Using numerical simulations, we found that by combining the iterative layerwise strategy with proper initialization strategies, the optimization cost can be significantly reduced in exchange for a minor reduction in the approximation ratio. We also show that in some cases, the approximation ratio given by the iterative layerwise strategy is even higher than that given by the full optimization.
Quantum Neural Networks (QNNs) represent a compelling convergence of quantum mechanics and machine learning, yet their practical deployment remains constrained by noise, limited qubit counts, and the cost of full quantum execution. Hybrid quantum-classical (HQC) training offers a pragmatic path forward: parameterized quantum circuits (PQCs) process information in exponentially large Hilbert spaces while classical optimizers update parameters via gradient methods accessible on today's hardware. We present a modular HQC training framework, formalising the parameter-shift rule for hardware-compatible gradient estimation, characterising the barren-plateau phenomenon through a variance-decay analysis, and introducing noise-aware training strategies for NISQ devices. Empirical results from state-vector and shot-based simulation confirm measurable quantum advantage on quantum-structured tasks, with the phase classification benchmark improving +12.1% over a classical MLP baseline. The accompanying open-source library provides a clean abstraction between quantum simulation and classical optimisation, serving as a foundation for near-term quantum machine learning research.
Training quantum neural networks (QNNs) on near-term hardware remains hampered by two compounding difficulties: the exponential vanishing of gradient variance known as the barren plateau, and the
O(L⋅2n) time and memory cost of differentiating through an
n-qubit,
L-layer circuit. We propose RLQ-Grad, a reinforcement-learning-based optimizer in which a classical policy
πφ (a spectrally-normalized PPO agent) learns to propose parameter updates directly, conditioned on the QNN's current parameters, loss, accuracy, and previous update. Because the surrogate gradient is emitted by a classical network rather than obtained by differentiating through the unitary
U(θ), its variance is not constrained by the barren plateau concentration bound, and its cost scales with the number of trainable parameters rather than the Hilbert-space dimension. We prove these properties formally and verify them on a hardware-efficient ansatz across four supervised benchmarks with up to
n=20 qubits. RLQ-Grad preserves a near-flat gradient-variance curve where backpropagation, parameter-shift, and adjoint differentiation decay by 1 to 2 orders of magnitude. Accounting for the full training pipeline (PPO rollouts, actor-critic updates, and optimizer states), RLQ-Grad needs under 2 MB of memory and runs
2490×,
7876×, and
673× faster per iteration than these three methods at
n=20. It improves top-1 accuracy by up to
+10% over gradient-based baselines on circuits of up to 12 qubits, and matches dedicated barren plateau mitigation methods on CIFAR-10 at 14 to 20 qubits, where evolutionary and gradient-free optimizers collapse to chance.
Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. In turn, this makes some of the most compact ansätze usable in practice, which was not possible before even for rather basic problems. We show empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method.
There is increasing interest in the development of gate- based quantum circuits for the training of machine learning models. Yet, little is understood concerning the parameters of circuit design, and the effects of noise and other measurement errors on the performance of quantum machine learning models. In this paper, we explore the practical implications of key circuit design parameters (number of qubits, depth etc.) using several standard machine learning datasets and IBM's Qiskit simulator. In total we evaluate over 6500 unique circuits with n ≈ 120700 individual runs. We find that in general shallow (low depth) wide (more qubits) circuit topologies tend to outperform deeper ones in settings without noise. We also explore the implications and effects of different notions of noise and discuss circuit topologies that are more / less robust to noise for classification machine learning tasks. Based on the findings we define guidelines for circuit topologies that show near-term promise for the realisation of quantum machine learning algorithms using gate-based NISQ quantum computer.