Variational quantum algorithms (VQAs) have attracted remarkable interest over the past few years because of their potential computational advantages on near-term quantum devices. They leverage a hybrid approach that integrates classical and quantum computing resources to solve high-dimensional problems that are challenging for classical approaches alone. In the training process of variational circuits, constructing an accurate probability distribution for each epoch is not always necessary, creating opportunities to reduce computational costs through shot reduction. However, existing shot allocation methods that capitalize on this potential often lack adaptive feedback or are tied to specific classical optimizers, which limits their applicability to common VQAs and broader optimization techniques. Our observations indicate that the information entropy of a quantum circuit’s output distribution exhibits an approximately exponential relationship with the number of shots needed to achieve a target Hellinger distance. In this work, we propose a distribution-adaptive dynamic shot (DDS) framework that efficiently adjusts the number of shots per iteration in VQAs using the entropy distribution from the prior training epoch. Our results demonstrate that the DDS framework sustains inference accuracy while achieving an ∼ 50 % reduction in average shot count compared to fixed-shot training, and ∼ 60 % higher accuracy than recently proposed tiered shot allocation methods. Furthermore, in noisy simulations that reflect the error rates of actual IBM quantum systems, DDS achieves an ∼ 30 % reduction in the total number of shots compared to the fixed-shot method with minimal degradation in accuracy and offers ∼ 70 % higher computational accuracy than tiered shot allocation methods.
Variational quantum algorithms (VQAs) have attracted remarkable interest over the past few years because of their potential computational advantages on near-term quantum devices. They leverage a hybrid approach that integrates classical and quantum computing resources to solve high-dimensional problems that are challenging for classical approaches alone. In the training process of variational circuits, constructing an accurate probability distribution for each epoch is not always necessary, creating opportunities to reduce computational costs through shot reduction. However, existing shot allocation methods that capitalize on this potential often lack adaptive feedback or are tied to specific classical optimizers, which limits their applicability to common VQAs and broader optimization techniques. Our observations indicate that the information entropy of a quantum circuit’s output distribution exhibits an approximately exponential relationship with the number of shots needed to achieve a target Hellinger distance. In this work, we propose a distribution-adaptive dynamic shot (DDS) framework that efficiently adjusts the number of shots per iteration in VQAs using the entropy distribution from the prior training epoch. Our results demonstrate that the DDS framework sustains inference accuracy while achieving an ∼ 50 % reduction in average shot count compared to fixed-shot training, and ∼ 60 % higher accuracy than recently proposed tiered shot allocation methods. Furthermore, in noisy simulations that reflect the error rates of actual IBM quantum systems, DDS achieves an ∼ 30 % reduction in the total number of shots compared to the fixed-shot method with minimal degradation in accuracy and offers ∼ 70 % higher computational accuracy than tiered shot allocation methods.
The exponential runtime of quantum simulators on classical machines, along with long queue times and high costs associated with real quantum devices, presents significant challenges for the efficient optimization of Variational Quantum Algorithms (VQAs) such as the Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), and Quantum Neural Networks (QNNs). To address these limitations, we propose a novel approach, DyPP (Dynamic Parameter Prediction), which accelerates the convergence of VQAs by leveraging regular trends in the parameter weights to update parameters efficiently. We introduce two techniques for optimal prediction performance: Naive Prediction (NaP) and Adaptive Prediction (AdaP). Through extensive experimentation and training of multiple QNN models on various datasets, we demonstrate that DyPP achieves a speedup of approximately 2.25×compared to standard training methods, while also providing improved accuracy (up to 2.3% higher) and lower loss (up to 6.1% reduction) with minimal storage and computational overhead. We further 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 a speedup of up to 3.1× for VQE and 2.91× for QAOA compared to traditional optimization, while requiring up to 3.3× fewer shots (i.e., repeated circuit executions). Even in the presence of hardware noise, DyPP outperforms existing optimization techniques, delivering up to 3.33× speedup and requiring 2.5× fewer shots, thereby enhancing the efficiency of VQAs.
Variational Quantum Algorithms (VQAs) are a promising approach for practical applications like chemistry and materials science on near-term quantum computers as they typically reduce quantum resource requirements. However, in order to implement VQAs, an efficient classical optimization strategy is required. Here we present a new stochastic gradient descent method using an adaptive number of shots at each step, called the global Coupled Adaptive Number of Shots (gCANS) method, which improves on prior art in both the number of iterations as well as the number of shots required. These improvements reduce both the time and money required to run VQAs on current cloud platforms. We analytically prove that in a convex setting gCANS achieves geometric convergence to the optimum. Further, we numerically investigate the performance of gCANS on some chemical configuration problems. We also consider finding the ground state for an Ising model with different numbers of spins to examine the scaling of the method. We find that for these problems, gCANS compares favorably to all of the other optimizers we consider.
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× 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× for VQE and 2.91× for QAOA, compared to traditional optimization techniques, while using up to 3.3× lesser shots (i.e., repeated circuit executions). Even under hardware noise, DyPP outperforms existing optimization techniques, delivering upto 3.33× speedup and 2.5× fewer shots, thereby enhancing efficiency of VQAs.
Efficient classical optimizers are crucial in practical implementations of Variational Quantum Algorithms (VQAs). In particular, to make Stochastic Gradient Descent (SGD) resource efficient, adaptive strategies have been proposed to determine the number of measurement shots used to estimate the gradient. However, existing strategies overlook the overhead that occurs in each iteration. In terms of wall-clock runtime, significant circuit-switching and communication latency can slow the optimization process when using a large number of iterations. In terms of economic cost when using cloud services, per-task prices can become significant. To address these issues, we present an adaptive strategy that balances the number of shots in each iteration to maximize expected gain per unit time or cost by explicitly taking into account the overhead. Our approach can be applied to not only to the simple SGD but also its variants, including Adam. Numerical simulations show that our adaptive shot strategy is actually efficient for Adam, outperforming many existing state-of-the-art adaptive shot optimizers. However, this is not the case for the simple SGD. When focusing on the number of shots as the resource, our adaptive-shots Adam with zero-overhead also outperforms existing optimizers.
Variational quantum algorithms (VQAs) hold significant promise for solving complex problems across diverse fields. However, their practical implementation on near-term quantum devices is severely hampered by the pervasive effects of quantum noise. Traditional quantum circuit compilation techniques are largely static, failing to account for the unique noise profiles inherent in individual quantum hardware. This paper introduces a novel adaptive quantum circuit compilation framework designed to mitigate these limitations. The core concept centers around dynamically adjusting the circuit layout and gate decomposition in real-time, leveraging measurements of the quantum hardware's noise characteristics to optimize both the accuracy and circuit depth of the compiled quantum circuit. This approach represents a critical step towards unlocking the full potential of VQAs by enabling them to effectively operate within the constraints of noisy quantum computers. The framework incorporates feedback loops for continuous refinement, adapting to evolving noise conditions. The methodology is described, focusing on the key components: noise profiling, adaptive gate decomposition, and circuit re-optimization. Simulation results demonstrate the effectiveness of the adaptive approach in reducing circuit depth and improving the fidelity of VQA computations compared to static compilation methods. This work lays the foundation for robust and efficient VQA execution on future quantum hardware.
Any algorithm execution on quantum computers requires several repeated and costly executions (known as shots) to obtain reliable results. In this work, we propose a closed-form accurate analytical expression to determine optimal number of shots required for reliable execution of any algorithm on a quantum computer. We also present a theoretically grounded technique to distribute fixed shot budget across different partitions in a quantum circuit minimizing the total error. Our proposed analytical model helps to reduce the shots associated with reliable execution of quantum algorithms by about 58\% compared to current practice, in turn reducing the energy consumption by upto 62\%. Furthermore, our proposed optimal shot allocation technique across different partitions reduces total error by up to 73\% compared to conventional approaches.