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IEEE Dallas Circuits and Systems Conference (DCAS)

Hardware-Efficient Quantum Grid Sampling for Low-Latency Amplitude Estimation

Yu-Ting Kao, Haoyu Lu, Yeong-Jar Chang, Jason Gemsun Young, Chao-Hung Wang, Darsen D. Lu

Published Apr 10, 2026• 0 citations
Publisher

Abstract

High-performance computing heavily relies on Monte Carlo (MC) simulation, but achieving high precision imposes massive computational loads due to its low convergence rate. To overcome this classical bottleneck, Quantum Amplitude Estimation (QAE) has emerged as a powerful algorithmic alternative, theoretically offering a quadratic speedup by offloading these workloads to quantum accelerators. However, mitigating Quantum Fourier Transform (QFT) discretization errors typically require Maximum Likelihood Estimation (MLE). MLE introduces prohibitive iterative latency and struggles with shot-noise in low-measurement regimes. To address this, we propose a comprehensive, hardware-efficient framework that integrates uniform state preparation with a novel Peak Estimation Refinement (PER) readout technique. PER exploits the symmetric conjugate eigenvalues of the quantum operator to provide deterministic,${O}(\mathrm{1})$probability extraction. This eliminates classical iterative optimization, achieving an approximately$600 \times$reduction in post-processing latency while inherently amplifying the signal-to-noise margin to resist stochastic fluctuations in low-shot environments. Validated via an RTL-to-quantum compilation flow and a 10 -qubit$\pi$-estimation synthesis benchmark, we demonstrate an estimation error of 0.007 %, proving the viability of migrating complex probabilistic workloads to real-time quantum accelerators

DOI
10.1109/dcas69364.2026.11544432

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quant-pharXiv:2609.25992•Sep 23, 2026•0 citations
High-performance computing heavily relies on Monte Carlo (MC) simulation, but achieving high precision imposes massive computational loads due to its low convergence rate. To overcome this classical bottleneck, Quantum Amplitude Estimation (QAE) has emerged as a powerful algorithmic alternative, theoretically offering a quadratic speedup by offloading these workloads to quantum accelerators. However, mitigating Quantum Fourier Transform (QFT) discretization errors typically require Maximum Likelihood Estimation (MLE). MLE introduces prohibitive iterative latency and struggles with shot-noise in low-measurement regimes. To address this, we propose a comprehensive, hardware-efficient framework that integrates uniform state preparation with a novel Peak Estimation Refinement (PER) readout technique. PER exploits the symmetric conjugate eigenvalues of the quantum operator to provide deterministic,O(1){O}(\mathrm{1})O(1)probability extraction. This eliminates classical iterative optimization, achieving an approximately600×600 \times600×reduction in post-processing latency while inherently amplifying the signal-to-noise margin to resist stochastic fluctuations in low-shot environments. Validated via an RTL-to-quantum compilation flow and a 10 -qubitπ\piπ-estimation synthesis benchmark, we demonstrate an estimation error of 0.007 %, proving the viability of migrating complex probabilistic workloads to real-time quantum accelerators
Quantum amplitude estimation (QAE) can achieve a quadratic speedup for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too expensive, it can diminish the quantum advantage. Preparing arbitrary quantum states has exponential complexity with respect to the number of qubits, and thus, is not applicable. Currently known efficient techniques require problems based on log-concave probability distributions, involve learning an unknown distribution from empirical data, or fully rely on quantum arithmetic. In this paper, we introduce an approach to simplify state preparation, together with a circuit optimization technique, both of which can help reduce the circuit complexity for QAE state preparation significantly. We demonstrate the introduced techniques for a numerical integration example on real quantum hardware, as well as for option pricing under the Heston model, i.e., based on a stochastic volatility process, using simulation.
Quantum neural networks (QNNs) suffer from a fundamental sampling bottleneck since quantum measurements are probabilistic, requiring many circuit executions to estimate outputs with sufficient accuracy. Conventional Monte-Carlo (MC) inference exhibits an O(1/N)\mathcal{O}(1/\sqrt{N})O(1/N​) sampling error, rendering QNN inference and training costly on near-term quantum hardware, especially where each shot requires expensive qubit generation. This work introduces a "single-shot" QNN framework by integrating quantum amplitude estimation (AE) into the readout stage. By embedding a trained QNN as a state-preparation oracle within AE, outputs are estimated through coherent interference rather than repeated sampling. We demonstrate that AE-based QNN inference achieves an O(1/N)\mathcal{O}(1/N)O(1/N) error even with a single shot. We further analyze noise robustness and training feasibility, showing that AE can be a powerful primitive for overcoming the sampling overhead of QNNs. This highlights that when the model itself is quantum, quantum algorithms can enhance the computation efficiency.
The Quantum Amplitude Estimation (QAE) algorithm is a major quantum algorithm designed to achieve a quadratic speed-up. Until fault-tolerant quantum computing is achieved, being competitive over classical Monte Carlo (MC) remains elusive. Alternative methods have been developed so as to require fewer resources while maintaining an advantageous theoretical scaling. We compared the standard QAE algorithm with two Noisy Intermediate-Scale Quantum (NISQ)-friendly versions of QAE on a numerical integration task, with the Monte Carlo technique of Metropolis–Hastings as a classical benchmark. The algorithms were evaluated in terms of the estimation error as a function of the number of samples, computational time, and length of the quantum circuits required by the solutions, respectively. The effectiveness of the two QAE alternatives was tested on an 11-qubit trapped-ion quantum computer in order to verify which solution can first provide a speed-up in the integral estimation problems. We concluded that an alternative approach is preferable with respect to employing the phase estimation routine. Indeed, the Maximum Likelihood estimation guaranteed the best trade-off between the length of the quantum circuits and the precision in the integral estimation, as well as greater resistance to noise.
Monte Carlo methods are fundamental to finance, system verification, and scientific simulation, but converge slowly: achieving an additive error of є requires O (1/є 2 ) samples. Quantum Amplitude Estimation (QAE) offers a quadratic speedup by encoding the target probabilistic model into a quantum circuit. However, constructing such a circuit demands low-level quantum expertise, and existing tools for this task all sacrifice at least one of generality, usability, or efficiency. To address these, we design QPPL (Quantum Probabilistic Programming Language), a simple imperative language, and a compiler that translates probabilistic programs into quantum circuits. The key insight is that the circuit construction amounts to specifying a probability distribution, precisely the task that probabilistic programming addresses. QPPL achieves generality by supporting joint distributions, conditional updates, dynamic probabilities, and real-valued expectations in a single language; usability by offering a sequential, imperative syntax with named variables and direct arithmetic that hides all quantum details; and efficiency by modularly compiling each construct into reversible circuit primitives, achieving scalable circuit synthesis. We prove that the compilation is semantics-preserving. On benchmarks spanning finance and probabilistic model checking, QPPL is the only tool that covers all benchmarks, while producing circuits with up to 8.8× fewer gates and 26× shallower depth than existing tools.
Quantum Amplitude Estimation (QAE) is an important quantum algorithm that has the potential to quadratically speed up Monte Carlo based calculations.In this paper, we present a variant of the QAE without Phase Estimation Algorithm called Iterative Refinement QAE (IRQAE). IRQAE can refine the current estimation to a more accurate estimation iteratively, hence it can provide an estimation with arbitrary required accuracy ∊. The key idea of IRQAE is to use a rotation gate to create a quantum state for samplings with the current estimation. Using this idea, we show that IRQAE can provide a highly accurate estimation with lower classical computational complexity and with the same quantum computational complexity compared to state-of-the-art QAEs without phase estimation using numerical experiments. We prove that the computational complexity of IRQAE of the quantum part is O(1/∊) and the classical one is O(1/∊). The quantum cost gives a quadratic advantage over that of the classical Monte Carlo simulation.
Quantum Amplitude Estimation promises to accelerate Monte Carlo integration by replacing the classical ε∝N−1/2\varepsilon \propto N^{-1/2}ε∝N−1/2 sampling law with the Heisenberg-limited ε∝N−1\varepsilon \propto N^{-1}ε∝N−1 scaling, but whether any part of that advantage survives on present-day hardware is an empirical question. We report a systematic experimental benchmark of a Maximum-Likelihood Amplitude Estimation QMC pipeline on IonQ trapped-ion processors, comprising 60 hardware trials on IonQ Forte-1 across five settings(5 & 9 qubits, 100-200 shots per depth, linear & exponential amplification schedules, ~113 device-hours), together with 100 trials on IonQ Aria-1 & Forte-1 noise models at 5, 9 & 19 qubits. The pipeline combines controlled-RyR_yRy​ rotational state preparation, Grover-based amplitude amplification and maximum-likelihood inference and is benchmarked against bmax⁡−1 ⁣∫0bmax⁡ ⁣sin⁡2 ⁣x dxb_{\max}^{-1}\!\int_0^{b_{\max}}\!\sin^2\!x\,\mathrm{d}xbmax−1​∫0bmax​​sin2xdx with bmax⁡=π/5b_{\max}=π/5bmax​=π/5 ,given results emerge. First, the noiseless limit it attains ε∝N−0.88\varepsilon \propto N^{-0.88}ε∝N−0.88, close to the Heisenberg-scaling reference, reducing the error 54-74x over a 133x increase in oracle calls. Second, scaling does not survive on hardware. Every noisy backend saturates at an error floor of (2-5)x 10^{-2}, with fitted exponents of 0.04-0.15 on Forte-1 linear schedules and α≤ ⁣0α\le\!0α≤0 on the vendor noise models: beyond the optimal shallow depth, however, deeper amplification provides no sustained accuracy gain and instead returns to the noise floor. Forte-1 hardware also outperformed IonQ's own Aria-1 noise model at every depth m≥2m \ge 2m≥2, indicating that vendor noise models are bad predictors of MLAE accuracy. The practical implication for UQ is that on current devices the useful operating point is a shallow, schedule-tuned amplification depth chosen so that the deepest circuit lands near p~1/2 not the deepest schedule the coherence budget allows.