AQUIRE: Adaptive Acquisition in Research

Updated 4 July 2026

AQUIRE is a family of domain-specific adaptive acquisition methods that optimize information gathering under uncertainty across quantum, inverse, and power system research.
In quantum computing, AQUIRE allocates measurements adaptively to reduce variance while accounting for hardware noise, achieving notable shot-efficiency improvements.
In inverse problems and power systems, AQUIRE adapts sensing actions or simulates rich datasets to enhance reconstruction accuracy and enable robust uncertainty quantification.

Searching arXiv for papers and usages of “AQUIRE” to ground the article and confirm the term’s multiple research-specific meanings. AQUIRE is a research term used in multiple, domain-specific ways rather than a single universally standardized framework. In the cited arXiv literature, it denotes: a qudit-native protocol for Adaptive Quantum Measurements with Real-time Error-awareness in quantum computing; an adaptive acquisition framework for inverse problems that sequentially chooses measurements by reinforcement learning; and an acquisition step in power-system modeling that generates a rich Monte Carlo dataset for quantile-based dynamic equivalents of active distribution grids (Simon et al., 1 May 2026, Silvestri et al., 2024, Vorwerk et al., 2022). In adjacent machine-learning literatures, closely related work on adaptive acquisition includes learning acquisition functions online in active learning and oracle-based nongreedy active feature acquisition (Haussmann et al., 2019, Valancius et al., 2023).

1. Scope and research usages

The term is best understood as a family of acquisition-centered constructs whose common element is adaptive information gathering under uncertainty, but whose mathematical objects, objectives, and operating constraints differ substantially across fields.

Paper	Domain	Meaning of AQUIRE
(Simon et al., 1 May 2026)	Quantum computing	Adaptive Quantum Measurements with Real-time Error-awareness
(Silvestri et al., 2024)	Inverse problems	Adaptive acquisition framework for sequential measurements
(Vorwerk et al., 2022)	Power systems	Dataset-acquisition stage for quantile dynamic equivalents

In the quantum-computing usage, AQUIRE is a measurement-allocation protocol for estimating observables on qudit-based quantum computers while reporting both the mean and an error bar that includes hardware-noise effects (Simon et al., 1 May 2026). In inverse problems, AQUIRE is a reinforcement-learning framework that builds the sensing matrix online by choosing each measurement sequentially from past observations and reconstructions (Silvestri et al., 2024). In power systems, the AQUIRE step is not itself the final predictor; it is the stage that deliberately generates a rich distribution of possible DN responses through Monte Carlo dynamic simulations so that later quantile models can predict intervals rather than a single mean trajectory (Vorwerk et al., 2022).

A common misconception is to treat these as variants of one method. The cited literature does not support that interpretation. The shared term “AQUIRE” marks a common concern with acquisition, uncertainty, and adaptivity, but the concrete implementations are field-specific.

2. AQUIRE in quantum observable estimation

In "An Error-aware and Adaptive Method for the Estimation of Quantum Observables on Qudit-Based Quantum Computers" (Simon et al., 1 May 2026), AQUIRE is defined as Adaptive Quantum Measurements with Real-time Error-awareness. Its stated goal is to estimate both the expectation value of an observable and the uncertainty of that estimate on qudit-based quantum computers, while using as few measurements as possible and accounting for hardware imperfections and experimental noise.

The observable is decomposed into generalized Pauli strings,

$\hat{O} = \sum_{i=1}^{p} c_i \hat{P}_i, \qquad \hat{P}_i = \bigotimes_{j=1}^{q} \hat{X}_{d_j}^{r_j}\hat{Z}_{d_j}^{s_j},$

and the central variance quantity is written as

$(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$

This formulation is explicitly designed for qubits, qudits, and mixed qubit–qudit systems (Simon et al., 1 May 2026).

The protocol has two core components. The first is adaptive shot allocation: AQUIRE continuously updates estimates of means and covariances from accumulated data and then allocates the next batch of shots to the clique that yields the largest reduction in the estimated variance. The second is error-aware estimation: it augments statistical uncertainty from finite sampling with an additional contribution caused by device noise, rather than reporting a purely sampling-based error bar (Simon et al., 1 May 2026).

Its Bayesian layer begins with a posterior over the outcome probabilities of each Pauli string,

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$

with the uniform prior $a_{i\mu}=1$ . The posterior mean estimate is

$\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$

and the observable estimate is

$\widetilde O = \sum_i c_i \widetilde P_i.$

The technically distinctive step is the treatment of off-diagonal covariances for overlapping commuting groups. AQUIRE constructs a joint posterior over the relevant probability variables and uses MCMC / Metropolis-Hastings to approximate the covariance integral in the physically allowed region $R$ (Simon et al., 1 May 2026).

Measurement allocation is organized through a commutation graph whose vertices are Pauli strings and whose edges connect commuting pairs. The protocol forms a clique cover and distinguishes BC (bitwise commutation) from GC (general commutation). A central improvement is overlap grouping, in which cliques are allowed to share Pauli strings and the resulting covariances are handled explicitly rather than ignored (Simon et al., 1 May 2026).

The noise-aware layer introduces an error probability $\xi_i$ for each measured Pauli string and writes the total variance as

$(\widetilde{\Delta O}_{\rm e})^2 = (\widetilde{\Delta O})^2 + (\widetilde{O}_{\rm e}-\widetilde O)^2.$

The paper estimates $\xi_i$ by stabilizer measurements on modified versions of the same diagonalizing circuits used for observable estimation, and for simulated experimental noise uses the circuit-level depolarizing model

$(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 0

For the trapped-ion experiment, the fitted values were approximately

$(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 1

These values reflect the asymmetry between local-gate and entangling-gate fidelities reported in the experiment (Simon et al., 1 May 2026).

The numerical benchmarks compare GC + adaptive, GC + non-adaptive, BC + adaptive, and BC + non-adaptive. The main reported finding is that GC + adaptive is always best among the tested settings. On the LiH benchmark, AQUIRE reaches the same accuracy as AEQuO with roughly 40% fewer shots when comparing estimated variances and 60% fewer shots when comparing exact variances (Simon et al., 1 May 2026). The protocol was also implemented on a trapped-ion qudit quantum processor based on $(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 2 ions, where it was used to measure an open plaquette Hamiltonian encoded on four qubits and one qutrit, and a periodic plaquette Hamiltonian encoded on three qutrits (Simon et al., 1 May 2026).

3. AQUIRE in inverse problems

In "Reinforcement Learning of Adaptive Acquisition Policies for Inverse Problems" (Silvestri et al., 2024), AQUIRE is an adaptive acquisition framework for inverse problems. Rather than fixing a sensing matrix or sampling pattern before measurement, it chooses each new measurement sequentially based on what has already been observed and how well the signal is currently being reconstructed.

The forward model is written in the linear case as

$(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 3

where $(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 4 is composed of rows $(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 5 that represent individual measurement actions. The paper contrasts this with the non-adaptive compressed-sensing setting in which all rows of $(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 6 are chosen beforehand. Its motivation is explicitly strongest when the acquisition horizon is short and measurements are scarce or costly (Silvestri et al., 2024).

The method is cast as a POMDP $(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 7. The hidden state is the signal $(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 8, treated as stationary:

$(\widetilde{\Delta O})^2 = \sum_{i,j=1}^{n} c_i c_j\,\widetilde{\mathcal C(\hat P_i,\hat P_j)}.$ 9

and each observation is

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 0

The reward directly measures reconstruction improvement,

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 1

with SSIM used in experiments (Silvestri et al., 2024).

The reconstruction model is an encoder-decoder architecture with a recurrent encoder. A GRU processes the history of actions and observations, produces a latent representation $p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 2, and a decoder maps that latent state to a reconstruction:

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 3

The reconstruction objective sums error over all time steps,

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 4

The acquisition model is a policy $p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 5 acting on the latent belief state:

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 6

Policy learning uses Vanilla Policy Gradient (VPG) with reward-to-go and a learned baseline (Silvestri et al., 2024).

A notable aspect of this AQUIRE is its support for continuous action spaces. In the Gaussian measurement space, actions are continuous-valued vectors and the measurement is

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 7

with the policy outputting parameters of a Gaussian distribution over actions. In the Radon measurement space, the action is a continuous angle $p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 8, the observation is a Radon projection, and the policy outputs parameters of a Von Mises distribution (Silvestri et al., 2024).

The paper also introduces a probabilistic latent-state design. The encoder becomes a belief model

$p_i(\vec{\theta}_i \mid \vec{s}_i) \propto \prod_{\mu=0}^{d_P-1} \theta_{i\mu}^{\,s_{i\mu}+a_{i\mu}},$ 9

with

$a_{i\mu}=1$ 0

and optimizes an ELBO-like objective. This variational formulation is used to explain why empirical gains from adaptive sensing do not contradict classical worst-case compressed-sensing lower bounds: the method targets average-case performance on data distributions and uses a probabilistic policy rather than the deterministic constructions assumed in the cited lower-bound arguments (Silvestri et al., 2024).

Empirically, AQUIRE is evaluated on MNIST and MAYO low-dose CT images. The baselines are AE-R, AE-P, and AE-E2E, with variational versions VAE-R and VAE-E2E. The paper’s headline result is that adaptive acquisition is most beneficial when the measurement budget is small, especially for Radon measurements. A representative reported result is MAYO Radon: AE-E2E around 0.623 SSIM vs AE-R around 0.444 SSIM (Silvestri et al., 2024). For Gaussian measurements, the gains are less consistent, and random sensing can remain stronger on higher-resolution data.

4. AQUIRE as a dataset-acquisition stage in active distribution grids

In "Using Quantile Forecasts for Dynamic Equivalents of Active Distribution Grids under Uncertainty" (Vorwerk et al., 2022), AQUIRE is the dataset-acquisition stage used to build a transmission-network equivalent of an active distribution network under uncertainty. The motivation is that a standard aggregated model gives only a mean trajectory at the TN/DN interface, whereas the actual response can deviate substantially from that mean during transients and under rare but important disturbances.

The paper therefore uses Monte Carlo dynamic simulations to generate a rich distribution of possible DN responses, not just a single representative response. This is explicitly tied to quantile forecasting: later stages are intended to predict intervals of possible responses with predefined confidence, rather than a deterministic average alone (Vorwerk et al., 2022).

The time series are obtained from simulations of the CIGRE European 18-bus residential low-voltage network. The DN model includes standard lines, transformers, induction motors, and synchronous machines, as well as detailed active thermal load (ATL) models and detailed IBG models with grid-support and protection functions. The transmission-side equivalent is initially a strong grid with short-circuit power of 150 MVA and inertia of 6 s (Vorwerk et al., 2022).

Uncertainty is injected by random sampling of device parameters and initial operating conditions. The uncertain parameters include ATL parameters, IBG parameters, induction-machine parameters, static-load exponents $a_{i\mu}=1$ 1 and $a_{i\mu}=1$ 2, and the initial load distribution among static, dynamic, and thermal components. A uniform distribution is assumed because the actual statistical distribution is unknown (Vorwerk et al., 2022).

Each Monte Carlo parameterization is subjected to ten different frequency events. A load step is applied at the TN level at $a_{i\mu}=1$ 3 s, the step magnitude ranges within $a_{i\mu}=1$ 4 kW, and each simulation runs for 12 s. The dataset size is reported exactly: 100 random parameterizations, combined with 10 different load-step events, yielding 1000 time series in total. The simulations are implemented in PyRAMSES, and because a variable-step solver is used, each time series contains between 500 and 2000 points (Vorwerk et al., 2022).

The interface quantities are PCC voltage magnitude $a_{i\mu}=1$ 5, TN frequency $a_{i\mu}=1$ 6, active current $a_{i\mu}=1$ 7, and reactive current $a_{i\mu}=1$ 8. For the machine-learning stage, the targets are $a_{i\mu}=1$ 9 and $\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 0, while the inputs are interface voltage magnitude and frequency together with shifted past values and, in closed loop, former current predictions (Vorwerk et al., 2022).

Quantile forecasting is built by minimizing the pinball loss

$\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 1

with lower and upper quantiles chosen as

$\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 2

The reported interval metrics are REL, ACE, and AIS, where

$\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 3

$\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 4

and

$\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 5

The paper reports that GBT is the best overall point-forecast method, while NNs perform better for high-confidence intervals, especially for intervals that are not excessively narrow (Vorwerk et al., 2022).

A second study tests the trained models on a weaker TN with inertia reduced from 6 s to 1.5 s and short-circuit power reduced from 150 MVA to 75 MVA. The paper states that $\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 6 prediction is relatively robust, $\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 7 degrades substantially, and prediction intervals widen, reflecting increased uncertainty (Vorwerk et al., 2022). In this usage, AQUIRE is thus the stage that converts detailed DN dynamics into a training set sufficiently rich for uncertainty-aware quantile learning.

Although not themselves named AQUIRE, two adjacent papers are directly relevant to the broader acquisition literature because they formalize adaptive, dataset-specific acquisition in learning systems.

"Deep Active Learning with Adaptive Acquisition" (Haussmann et al., 2019) proposes RAL (Reinforced Active Learning). Its central claim is that the acquisition function in active learning should be learned online rather than fixed a priori. RAL uses a Bayesian neural network predictor, a bootstrap acquisition function, a probabilistic state representation, and a Bayesian policy network. It first ranks unlabeled samples using Maximum Entropy Sampling, then thins the ranking by taking every $\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 8-th point until it has $\widetilde P_i = \sum_{\mu=0}^{d_P-1}\widetilde\theta_{i\mu}\,\omega_{d_P}^{\mu},$ 9 candidates, and finally learns a policy to warp the top portion of this ranking. The reward is

$\widetilde O = \sum_i c_i \widetilde P_i.$ 0

and the policy is updated with episodic REINFORCE using discount factor $\widetilde O = \sum_i c_i \widetilde P_i.$ 1 (Haussmann et al., 2019). On MNIST, FashionMNIST, and CIFAR-10, the final error rates after labeling 400 points are reported as: MNIST $\widetilde O = \sum_i c_i \widetilde P_i.$ 2, FashionMNIST $\widetilde O = \sum_i c_i \widetilde P_i.$ 3, and CIFAR-10 $\widetilde O = \sum_i c_i \widetilde P_i.$ 4, with the paper concluding that RAL always matches or beats the best fixed heuristic on these benchmarks (Haussmann et al., 2019).

"Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisition" (Valancius et al., 2023) proposes the Acquisition Conditioned Oracle (ACO) for active feature acquisition (AFA). ACO replaces the usual direct policy-learning view with subset-level search:

$\widetilde O = \sum_i c_i \widetilde P_i.$ 5

The approximation is nonparametric, using nearest neighbors:

$\widetilde O = \sum_i c_i \widetilde P_i.$ 6

The paper positions ACO against RL-based AFA, surrogate generative models, and greedy policies, and emphasizes that ACO is effective when useful information is combinatorial, as in the “pointer” example where a routing feature tells the model which other feature to inspect next (Valancius et al., 2023).

These works are relevant because they sharpen the meaning of “adaptive acquisition” in machine learning: the acquired object may be labels, features, or measurements, but the central design question is the same—how to value the next acquisition under uncertainty and limited budget.

6. Cross-domain structure and distinctions

Taken together, these papers suggest that AQUIRE-style systems are organized around three recurring components: a representation of current uncertainty, a mechanism for selecting the next acquisition, and a criterion for quantifying improvement or risk. In the quantum protocol, uncertainty is encoded in Bayesian posteriors over generalized Pauli outcomes and covariances, acquisition corresponds to shot allocation across commuting cliques, and improvement is defined through reduction of estimated variance including hardware-noise effects (Simon et al., 1 May 2026). In inverse problems, uncertainty is encoded in a latent recurrent state or variational belief model, acquisition is the next sensing action, and improvement is measured by stepwise reconstruction gains such as SSIM (Silvestri et al., 2024). In active distribution grids, uncertainty is represented by a Monte Carlo-generated distribution of DN responses, acquisition is scenario generation during dataset construction, and evaluation is based on interval reliability, coverage error, and sharpness (Vorwerk et al., 2022).

This comparison also clarifies what AQUIRE is not. It is not a single transferable algorithm with one shared loss, one shared architecture, or one shared probabilistic model. The quantum version is Bayesian, overlap-aware, and explicitly hardware-noise-aware (Simon et al., 1 May 2026). The inverse-problem version is reinforcement-learning-based, sequential, and designed for continuous acquisition spaces such as Gaussian projections and Radon angles (Silvestri et al., 2024). The power-system version uses acquisition in the literal sense of acquiring a required rich dataset by Monte Carlo simulation before quantile models are fitted (Vorwerk et al., 2022).

A plausible implication is that the usefulness of the AQUIRE label lies less in a fixed formal definition than in a methodological orientation: do not commit to a single static observation plan when uncertainty, limited budget, and downstream error estimation make adaptive or distribution-aware acquisition materially different from averaging or heuristic selection. In that limited but technically important sense, the term links several otherwise separate research programs.