DyPP: Dynamic Parameter Prediction to Accelerate Convergence of Variational Quantum Algorithms

TL;DR

DyPP tackles slow convergence and high shot costs in variational quantum algorithms by predicting future parameter values from a short history of past weights using a quadratic surrogate $f(x)=a x^2+ b x + c$, with two strategies NaP and AdaP to modulate the prediction distance $d$. It demonstrates speedups up to $3.1\times$ for VQE and $2.91\times$ for QAOA, and up to $2.25\times$ for QNN, alongside substantial shot reductions (up to $3.33\times$) and resilience to noise. The method is a lightweight, plug-in approach that relies only on previously computed weights and simple curve-fitting, avoiding gradient computations during prediction steps. This makes DyPP practical for NISQ-era hardware and broadly applicable to a range of hybrid quantum-classical algorithms.

Abstract

The exponential run time of quantum simulators on classical machines and long queue times and high costs of real quantum devices present significant challenges in the efficient optimization of Variational Quantum Algorithms (VQAs) like Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA) and Quantum Neural Networks (QNNs). To address these limitations, we propose a new approach, DyPP (Dynamic Parameter Prediction), which accelerates the convergence of VQAs by exploiting regular trends in the parameter weights to update parameters. We introduce two techniques for optimal prediction performance namely, Naive Prediction (NaP) and Adaptive Prediction (AdaP). Through extensive experimentation and training of multiple QNN models on various datasets, we demonstrate that DyPP offers a speedup of approximately $2.25\times$ compared to standard training methods, while also providing improved accuracy (up to $2.3\%$ higher) and loss (up to $6.1\%$ lower) with low storage and computational overheads. We also evaluate DyPP's effectiveness in VQE for molecular ground-state energy estimation and in QAOA for graph MaxCut. Our results show that on average, DyPP leads to speedup of up to $3.1\times$ for VQE and $2.91\times$ for QAOA, compared to traditional optimization techniques, while using up to $3.3\times$ lesser shots (i.e., repeated circuit executions). Even under hardware noise, DyPP outperforms existing optimization techniques, delivering upto $3.33\times$ speedup and $2.5\times$ fewer shots, thereby enhancing efficiency of VQAs.

Figures (11)

• Figure 1: Optimizers update parameters to follow a regular trend as depicted in the plot. DyPP uses this data to predict future weight based on prior trends. Error in predictions are recovered by intermediate optimization using generic optimizers which allows DyPP to make multiple predictions at regular intervals during a training process leading to faster convergence of VQAs.
• Figure 2: (a) Schematic of a 4-qubit hybrid QNN architecture. Classical features ($f_1, .., f_4$) are encoded as angles of quantum rotation gates ($RZ$ in this case). The PQC transforms encoded states to explore the search space and entangle features. The resulting expectation values are then fed into a classical linear layer for final prediction. (b) A generic QAOA parameterized circuit in which $U_C$ represents the cost layer/unitary with parameters $\gamma_i$ and $U_M$ represents the mixer layer/unitary with parameters $\beta_i$, where $i$ represents the depth of the circuit. Higher depth ($p$) circuit results in a more accurate approximation.
• Figure 3: VQAs involve encoding the necessary problem as a cost function into a PQC and evolving the state over time using a set of tunable quantum gates in order to minimize or maximize the expected output. (a) The generalized approach is to use a classical optimizer to update the parameters of the PQC for $x$ iterations to get the required result. (b) DyPP updates the parameters using a prediction function after fitting it with previously calculated weights for each parameter after every $p$ epoch (i.e., when $i \% p = 0$) to accelerate the optimization process.
• Figure 4: Weight evolution of different quantum parameters of a PQC when training a QNN under both noiseless and noisy environment.
• Figure 5: Accuracy and loss of a hybrid QNN model with various starting prediction distance $d_0$ for NaP when training a QNN for 50 epochs on a reduced MNIST 3-class dataset. NaP consistently outperforms original naive training, especially when $d_0$ is in the range [3, 4).