Variational quantum dynamics simulations (VQDS) provide a promising route to simulate real- and imaginary-time quantum dynamics on noisy intermediate-scale quantum devices using fixed-depth circuits. However, their practical performance is strongly limited by sampling noise arising from a finite number of circuit measurements. In this work, we systematically investigate the impact of sampling noise on VQDS, with a focus on ground-state preparation in one-dimensional Ising spin models using imaginary time evolution. We compare different regularization strategies for stabilizing the equations of motion and show that Tikhonov regularization provides robust performance in noisy imaginary-time evolution. We then benchmark measurement-distribution strategies that allocate shots by minimizing a cost function that characterizes the error in solving the equation of motion. Using noisy circuit simulations, we demonstrate that such optimized shot allocation can significantly improve state fidelity and reduce the total measurement cost by more than a factor of two compared to uniform shot distributions. We observe that the best results are found if a sufficiently large number of measurements is guaranteed for all circuits, suggesting that a finite fraction of shots should be distributed evenly. Our results provide practical guidelines for implementing measurement-efficient variational quantum dynamics and ground-state preparation on near-term quantum hardware.
Variational quantum dynamics simulations (VQDS) provide a promising route to simulate real- and imaginary-time quantum dynamics on noisy intermediate-scale quantum devices using fixed-depth circuits. However, their practical performance is strongly limited by sampling noise arising from a finite number of circuit measurements. In this work, we systematically investigate the impact of sampling noise on VQDS, with a focus on ground-state preparation in one-dimensional Ising spin models using imaginary time evolution. We compare different regularization strategies for stabilizing the equations of motion and show that Tikhonov regularization provides robust performance in noisy imaginary-time evolution. We then benchmark measurement-distribution strategies that allocate shots by minimizing a cost function that characterizes the error in solving the equation of motion. Using noisy circuit simulations, we demonstrate that such optimized shot allocation can significantly improve state fidelity and reduce the total measurement cost by more than a factor of two compared to uniform shot distributions. We observe that the best results are found if a sufficiently large number of measurements is guaranteed for all circuits, suggesting that a finite fraction of shots should be distributed evenly. Our results provide practical guidelines for implementing measurement-efficient variational quantum dynamics and ground-state preparation on near-term quantum hardware.
Near-term quantum algorithms are a promising route to solving partial differential equations, but gauging their true potential requires separating algorithmic performance from sampling and hardware noise. We benchmark a ground-state variational quantum eigensolver (VQE), cast as a variational quantum linear solver, against the Trotterization, variational quantum imaginary time evolution, and adaptive variational quantum dynamics simulation methods applied to the one-dimensional advection-diffusion equation in the recent quantum-dynamics study by Alipanah et al. [Phys. Rev. Res. 7, 043318 (2025)2643-156410.1103/ndc3-bdwt] at matched grid and problem size. On a noiseless state-vector simulator the N=4 VQE drives the final-time infidelity to a numerical floor (∼10^{-14}) once the depth reaches L≈5, an algorithmic ceiling set by exact expectation values. Evaluating the same solver with a finite number S of measurement shots, still without hardware noise, makes the infidelity sampling limited, following 1-f≈c/S (a best-case readout-sampling estimate, with the solution's signs assumed known), providing a regime-matched comparison with the shot-based emulator of Alipanah et al. and explaining the gap to their noisy hardware runs (>10^{-1}). The benchmark thus decomposes the near-term error budget into algorithmic, sampling, and hardware contributions, with a matched-depth resource comparison. The formulation applies without modification across N=4,5,6 qubits and to a two-dimensional (eight-qubit, 16×16) problem evolved to t=1, where the state-vector VQE holds a ∼10^{-7} algorithmic-ceiling infidelity against the sampling-limited ∼10^{-5} of the corresponding shot-based simulation, a difference of measurement regime rather than algorithmic superiority.
For quantum algorithms to achieve their full potential, we need methodologies to optimize them, such as reaching a given output accuracy with minimal resource costs. Here, we develop such a methodology for a class of Noisy Intermediate-Scale Quantum (NISQ) algorithms. We leverage simulations of a Variational Quantum Eigensolver (VQE) to propose a phenomenological model of such algorithms that captures the complex relationship between algorithmic accuracy, algorithmic resource costs, and the noise that exists in realistic quantum hardware. For this, we take the algorithmic resource cost to be the total number of quantum gate-operations in the algorithm; minimizing this cost typically makes the algorithm faster and more energy-efficient. We consider the subtle trade-off between quantum circuit size (small circuits are too imprecise, but large ones are too noisy), and the number of iterations of that quantum circuit for the full algorithm to sufficiently converge. Using a noise-metric-resource methodology, we identify the sweet spot (of circuit size versus iterations) that minimizes the algorithmic resource costs for a desired algorithm accuracy. It also gives the circuit size that maximizes algorithm accuracy for a fixed resource cost. Our methodology provides a practical guideline for near-term deployment of variational algorithms on realistic noisy hardware, including hardware that uses error mitigation.
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.
We experimentally study error mitigation and finite-shot sampling on superconducting quantum hardware under a constrained execution budget. The study combines calibration-aware qubit selection, circuit-depth scaling, zero-noise extrapolation, dynamical decoupling, readout-error mitigation, and repeated-shot estimation on an IBM Quantum processor. Experiments are organized across ideal simulation, noise-model simulation, and physical-device execution to separate sampling uncertainty from device-induced error. We investigate how mitigation performance changes with circuit depth, effective noise scale, qubit connectivity, and measurement budget, and quantify accuracy using expectation-value error, mean-squared error, statistical uncertainty, and mitigation gain. A fixed hardware-execution budget is used to evaluate shot allocation strategies and repeated measurements without relying on unlimited sampling. The resulting analysis provides a hardware-aware characterization of when mitigation improves expectation-value estimation and when finite-shot fluctuations offset the benefit of additional mitigation overhead. The implementation uses contemporary Qiskit and IBM Quantum Runtime workflows and is designed to provide reproducible experimental evidence for error-mitigation studies on current quantum processors.
The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an exponentially large wave function, quantum computers are emerging as a promising platform for this task. However, variational approaches, suitable for near-term quantum computers, struggle with a prohibitive number of measurements and impractical runtimes for relevant system sizes. Here, we suggest a stochastic approach to variational quantum imaginary-time evolution, which allows a significant reduction in runtimes. Our approach allows trading off invested resources and accuracy, which makes it also suitable for ground state preparation, where simulating the exact dynamics is not required. We demonstrate the efficiency of our algorithm in simulations and show a hardware experiment performing the imaginary-time evolution of the transverse field Ising model on 27 qubits.