Abstract Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations. Here, we propose a low-depth implementation of a class of Hadamard test circuits, complemented by the development of a parameterized quantum ansatz specifically tailored for variational algorithms that exploit the underlying Hadamard test framework. Our findings demonstrate a significant reduction in single- and two-qubit gate counts, suggesting a reliable circuit architecture for noisy intermediate-scale quantum devices. Building on this foundation, we tested our low-depth scheme to investigate the expressive capacity of the proposed parameterized ansatz in simulating nonlinear Burgers’ dynamics. The resulting variational quantum states faithfully capture the shockwave feature of the turbulent regime and maintain high overlaps with classical benchmarks, underscoring the practical effectiveness of our framework. Furthermore, we evaluate the effect of hardware noise by modeling the error properties of real quantum processors and by executing the variational algorithm on a trapped-ion-based IBEX Q1 device. The outcomes of our demonstrations highlight the resilience of our low-depth scheme in the turbulent regime, consistently preparing high-fidelity variational states that exhibit strong agreement with classical benchmarks. Our work contributes to the advancement of resource-efficient strategies for quantum computation, offering a robust framework for tackling a range of computationally intensive problems across numerous applications.
Abstract Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations. Here, we propose a low-depth implementation of a class of Hadamard test circuits, complemented by the development of a parameterized quantum ansatz specifically tailored for variational algorithms that exploit the underlying Hadamard test framework. Our findings demonstrate a significant reduction in single- and two-qubit gate counts, suggesting a reliable circuit architecture for noisy intermediate-scale quantum devices. Building on this foundation, we tested our low-depth scheme to investigate the expressive capacity of the proposed parameterized ansatz in simulating nonlinear Burgers’ dynamics. The resulting variational quantum states faithfully capture the shockwave feature of the turbulent regime and maintain high overlaps with classical benchmarks, underscoring the practical effectiveness of our framework. Furthermore, we evaluate the effect of hardware noise by modeling the error properties of real quantum processors and by executing the variational algorithm on a trapped-ion-based IBEX Q1 device. The outcomes of our demonstrations highlight the resilience of our low-depth scheme in the turbulent regime, consistently preparing high-fidelity variational states that exhibit strong agreement with classical benchmarks. Our work contributes to the advancement of resource-efficient strategies for quantum computation, offering a robust framework for tackling a range of computationally intensive problems across numerous applications.
Resource-efficient computation is of central importance in the noisy intermediate-scale quantum (NISQ) era, where decoherence, gate errors, and restricted qubit connectivity severely limit the reliable execution of quantum algorithms. In this work, we demonstrate that incorporating circuit design considerations is crucial for developing resource-efficient variational quantum algorithms. By focusing on the Hadamard test circuit architecture, hardware-aware qubit connectivity, and problem-specific adaptive framework, we analyze how circuit design constraints can systematically reduce the measurement overhead associated with repeated evaluations of the candidate gate pool in adaptive algorithms. Specifically, we demonstrate reductions in the required measurement resources ranging from at least 25% to as high as 50% - 55%. To assess the effectiveness of our approach, we investigate the ground state problem of the nonlinear Schrödinger equation. Overall, our work contributes to resource-friendly strategies for quantum computation and underscores that algorithmic frameworks should systematically integrate circuit design constraints with hardware-aware and problem-specific structures to enhance the practical feasibility of quantum devices in the NISQ era.
A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we probe the ability of such approach to capture the ground state of the nonlinear Schr\"odinger equation for a range of parameters on real superconducting quantum processors. Specifically, we study the expressivity of real-amplitude, hardware-efficient Ansatz to capture the ground state of this nonlinear system across various interaction regimes and implement different noise scenarios in both simulators and cloud processors. Our investigation reveals that although quantum hardware noise impairs the evaluation of the energy cost function, certain small instances of the problem consistently converge to the ground state. We test and demonstrate a variety of cases on IBM Q superconducting devices and analyze the discrepancies in the energy cost function evaluation due to quantum hardware noise. These discrepancies are absent in the state fidelity estimation because of the shallow state preparation circuit. Our comprehensive analysis offers valuable insights into the practical implementation and advancement of the variational algorithms for nonlinear problems.
Abstract Noisy Intermediate-Scale Quantum (NISQ) devices are near-term quantum computing devices that inherently suffer from imperfect gate implementation, decoherence, and measurement noise. The main type of variational quantum algorithms(VQAs) is based on Parameterized Quantum Circuits (PQCs), which, however, face practical challenges due to optimization instability of optimization caused by noise and reduced performance. In this paper, we suggest a comprehensive noise-resilient optimization framework for PQCs, which explicitly incorporates noise-resilient circuit architecture design, incorporating noise-aware training strategies into the variational optimization loop. The framework uses circuit structures that are efficient in depth and are hardware compatible in addition to adaptive optimizer choice, stochastic optimization, and averaging as a part of repeated measurement to reduce the impacts of realistic noise. Large-scale experiments are performed with different amounts of qubits, depths of the circuit and noise strengths with realistic noise models. The findings indicate that the convergence rate is faster, the stability is increased, the variability of run-to-run variability is minimized, and other robustness is better than the noise-unaware optimization techniques. Moreover, systematic studies determine optimal operating regions that optimally trade-off expressibility and noise tolerance to offer useful design advice on trusted implementation of VQAs with near-term quantum hardware.
Abstract Accurately characterizing and mitigating the impact of noise is essential for improving the fidelity of quantum simulations on Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we introduce a circuit-structure-preserving error-mitigation framework designed for parameterized quantum circuits. Unlike conventional approaches that alter circuit topology or require heavy post-processing, our method preserves the native architecture while systematically diagnosing gate noise. This structure-preserving feature enables robust, high-fidelity simulations even in the presence of significant hardware noise, making the approach particularly effective for small-scale circuits executed at high sampling rates, such as those used in variational algorithms and quantum neural networks. To benchmark its performance, we apply the method to variational quantum simulations of a non-Hermitian ferromagnetic transverse-field Ising chain implemented on IBM Quantum processors. The mitigated results exhibit excellent agreement with exact theoretical predictions across a wide range of noise conditions. Thus, our framework provides a scalable and hardware-efficient strategy for the current hardware.
In quantum computing, state preparation techniques for loading classical data into quantum states can be resource-intensive and error-prone, especially on Noisy Intermediate-Scale Quantum (NISQ) devices. This work applies variational learning to compress quantum circuits for state preparation, transforming resource-heavy techniques into hardware-efficient ansatzes suitable for current quantum architectures. This approach enhances the efficiency of state preparation, broadening the applicability of quantum algorithms. We demonstrate significant reductions in circuit size and depth compared to the explicit circuit of the FF-QRAM state preparation. Additionally, we show that the learned ansatzes perform better in noisy environments, with significant fidelity improvements over the explicit state preparation technique under analysis.
Variational Quantum Circuits (VQCs) have emerged as a cornerstone of hybrid quantum–classical algorithms designed to harness the computational potential of near-term quantum devices. By combining parameterized quantum gates with classical optimization, VQCs provide a flexible framework for tackling machine learning, chemistry, and optimization problems intractable for classical methods. This review comprehensively overviews VQC design principles, ansatz structures, optimization strategies, and real-world applications. Furthermore, we discuss fundamental challenges such as barren plateaus, the expressibility–trainability trade-off, and current noisy intermediate-scale quantum (NISQ) hardware limitations. Finally, we highlight emerging directions that could enable scalable, noise-resilient, and physically interpretable variational quantum models for future quantum computing applications