InterQ: Adversarial, Quantum, & Control

• InterQ is a multifaceted term encompassing adversarial retrieval, quantum scheduling, and deep reinforcement learning-based intermittent control.
• In adversarial information retrieval, FSAP_InterQ leverages cross-topic harmful examples to generate adversarial documents with high Mean Help-Defeat Rates.
• In quantum computing and networked control, InterQ optimizes resource allocation and transmission scheduling using communication-aware algorithms and DQN frameworks.

InterQ is a term used in multiple, unrelated research contexts in 2025–2026. In the adversarial-information-retrieval literature, it denotes FSAP$_\text{InterQ}$, the inter-query mode of Few-Shot Adversarial Prompting, where harmful examples from unrelated queries are used to generate new adversarial documents for a target query (Bigdeli et al., 21 Aug 2025). In modular quantum computing, InterQ is a communication-aware scheduler for modular QPU architectures with heterogeneous classical and quantum communication models (Kulkarni et al., 18 May 2026). In networked control, InterQ is a deep Q-learning framework for optimal intermittent control in stochastic linear systems with costly communication (Aggarwal et al., 12 Apr 2025). The shared name therefore identifies distinct constructs rather than a single unified method.

1. Scope of the term

The three documented uses of the term span adversarial retrieval, modular quantum scheduling, and communication-constrained control.

Paper	Domain	Meaning of “InterQ”
"Adversarial Attacks against Neural Ranking Models via In-Context Learning" (Bigdeli et al., 21 Aug 2025)	Neural ranking attacks	FSAP$_\text{InterQ}$, the cross-query, cross-topic mode of FSAP
"InterQ: Communication-Aware Scheduling Across Modular QPUs with Classical and Quantum Links" (Kulkarni et al., 18 May 2026)	Modular quantum computing	A communication-aware scheduler for modular QPU architectures
"InterQ: A DQN Framework for Optimal Intermittent Control" (Aggarwal et al., 12 Apr 2025)	Networked control and RL	A DQN framework for learning intermittent scheduling policies

The overlap is nominal rather than conceptual. One usage concerns in-context generation of harmful documents for retrieval attacks; one concerns resource-aware fragmentation and placement of quantum circuits across modules; and one concerns state-transmission scheduling in a partially nested control architecture. Any technical discussion of “InterQ” therefore requires immediate disambiguation.

2. InterQ in adversarial neural retrieval

In "Adversarial Attacks against Neural Ranking Models via In-Context Learning," InterQ refers to inter-query prompting: harmful examples taken from other, different queries are used as few-shot demonstrations to guide an LLM to generate a new adversarial document for a new target query that may have no harmful documents of its own (Bigdeli et al., 21 Aug 2025). The paper instantiates this as FSAP$_\text{InterQ}$ under the assumption that the attacker has no harmful documents for the target query $q^*$, but does possess a cross-topic support set of harmful query–document pairs from unrelated topics: $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$ These pairs are concatenated into an adversarial prompt,

$$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$

and the LLM then generates

$$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$

This mode is contrasted with FSAP$_\text{IntraQ}$, where the support set contains multiple harmful documents from the same query $q^*$: $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$ The paper characterizes FSAP$_\text{InterQ}$0 as maximizing topic fidelity in single-topic attacks where harmful content already exists, whereas FSAP$_\text{InterQ}$1 is designed for generalization and low-resource attacks where no harmful examples exist for the target query. The only shared property between support examples and target generation in InterQ is the harmful style and stance; the support set is explicitly described as a cross-topic support set consisting of diverse query-document pairs drawn from unrelated topics.

Within the broader FSAP framework, InterQ is one branch of a black-box attack pipeline. The attacker has black-box access to an LLM $_\text{InterQ}$2 and a neural ranking model $_\text{InterQ}$3, a small support set of human-annotated harmful documents, and no gradient access or internal model instrumentation. The pipeline comprises support selection, prompt construction, LLM generation, ranking, and attack evaluation. InterQ is the default mode when no harmful documents are available for the target query, but the paper also evaluates it when same-query harmful examples do exist, in order to test transfer across queries and topics.

The formal attack objective is to generate $_\text{InterQ}$4 such that

$_\text{InterQ}$5

with expected indicator adversarial loss

$_\text{InterQ}$6

Attack strength is evaluated primarily through Mean Help-Defeat Rate (MHDR). For a query $_\text{InterQ}$7 with helpful documents $_\text{InterQ}$8 and adversarial documents $_\text{InterQ}$9,

$_\text{InterQ}$0

and

$_\text{InterQ}$1

Conceptually, FSAP$_\text{InterQ}$2 relies on in-context learning to transfer adversarial patterns rather than topic templates. The paper identifies persuasive tone, manipulative structure, harmful stance, and surface fluency as the relevant transferred properties. A plausible implication is that InterQ tests whether neural ranking models are vulnerable not merely to lexical perturbations but to rhetorically well-formed, newly synthesized misinformation.

3. Empirical profile and security implications of FSAP$_\text{InterQ}$3

The empirical evaluation uses the TREC 2020 Health Misinformation and TREC 2021 Health Misinformation tracks (Bigdeli et al., 21 Aug 2025). In TREC 2020, 46 COVID-19 topics are available and 22 with both helpful and harmful documents are used; helpful documents have preference code 4 and harmful documents have preference code $_\text{InterQ}$4. In TREC 2021, 35 topics are available and 27 with both helpful and harmful documents are used; helpful documents have preference scores $_\text{InterQ}$5 and harmful documents have scores $_\text{InterQ}$6 or $_\text{InterQ}$7. For InterQ, the support examples for a topic are taken from other topics in these collections, not from the target topic itself.

Four neural ranking models are used: MonoBERT, MonoT5, text-embedding-ada-002, and text-3-embedding-small. Documents are chunked into 512 tokens with stride 256, and the maximum chunk similarity is used as the query–document relevance score. In the main experiments, FSAP$_\text{InterQ}$8 fixes $_\text{InterQ}$9, and in the support-size analysis it varies $q^*$0.

The main quantitative result is that FSAP$q^*$1 achieves very high MHDR, often greater than 90\%. Peak reported values are 96.4\% MHDR on TREC 2020 using text-3-embedding-small and 97.2\% MHDR on TREC 2021 using MonoT5. The abstract summarizes the InterQ variant as achieving a Mean Helpful Defeat Rate of 90\% on average across various NRMs. Against baselines, InterQ often matches or exceeds IntraQ despite lacking same-topic examples, clearly outperforms Fact-Inversion with MHDR around 59–72\%, and exceeds Rewriter and Paraphraser, which are often below 50\% MHDR and sometimes worse than original harmful documents. Liar Attack can achieve slightly higher maximum MHDR, but the paper reports that it is more easily detected as adversarial.

The LLM study compares GPT-4o and DeepSeek-R1-claude3.7. On TREC 2021, DeepSeek FSAP$q^*$2 attains MHDR of 93.4–99.6\%, stance alignment of 75.1\%, and detection pass of 96.5\%, compared with GPT-4o stance alignment of 85.2\% and detection pass of 94.3\%. On TREC 2020, DeepSeek FSAP$q^*$3 attains MHDR of at least 94.9\%, stance alignment of 31.1\%, and detection pass of 97.9\%, compared with GPT-4o stance alignment of 67.9\% and detection pass of 82.9\%. The paper therefore concludes that InterQ attacks generalize across proprietary and open-source LLM families, with smaller models sometimes yielding better undetectability even when stance fidelity is weaker.

Qualitatively, the generated documents are described as grammatically fluent and stylistically natural, topically coherent with the target query despite cross-topic prompting, and difficult to distinguish from credible-looking misinformation. Stance alignment is measured by GPT-4o as a stance classifier, and adversarial detection pass is also measured via GPT-4o. For GPT-4o-generated FSAP$q^*$4 documents, approximately 82.9\% of TREC 2020 outputs and 94.3\% of TREC 2021 outputs are not flagged as adversarial. The paper characterizes this as a realistic and scalable threat to neural retrieval systems and highlights pool poisoning as a security implication: a small library of harmful examples from some health topics can be used to attack entirely new topics without model gradients or backend access.

The paper also notes limitations directly relevant to InterQ. It reports dependence on LLM quality, possible topic drift or stance drift, especially with smaller models, the absence of adversarial generalization theory for cross-topic attacks on neural rankers, and the lack of defenses tailored to cross-query pattern transfer. Future work is described in terms of robust defenses and game-theoretic modeling of attacker–defender dynamics.

4. InterQ as a communication-aware scheduler for modular QPUs

In "InterQ: Communication-Aware Scheduling Across Modular QPUs with Classical and Quantum Links," InterQ is a scheduler for modular quantum systems in which multiple QPUs, possibly heterogeneous, are connected by classical links, quantum links, or both (Kulkarni et al., 18 May 2026). The motivating premise is that scaling beyond monolithic processors requires modular architectures, and that scheduling in such settings must account not only for qubit capacity and parallel execution but also for communication-driven dependencies, circuit cutting, and shared interconnect resources.

For each job $q^*$5, the scheduler takes as input

$q^*$6

where $q^*$7 is the logical qubit requirement, $q^*$8 is approximate circuit depth, $q^*$9 is shot count, $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$0 is the interaction or dependency graph, and $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$1 is the set of admissible communication modes. Hardware inputs include a set of modules $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$2, with per-module qubit capacities $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$3, calibration profiles $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$4, and link parameters such as latency, bandwidth, Bell-pair rate, and success probability. InterQ outputs a partition $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$5 of each job into fragments, a placement function $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$6, and a schedule $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$7 specifying start times, communication operations, and precedence constraints.

The scheduler minimizes a communication-aware objective: $$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$8 with

$$\mathcal{S}_{\text{inter}}^- = \{(q_1, d_{q_1}^{-}), (q_2, d_{q_2}^{-}), \dots, (q_k, d_{q_k}^{-})\}.$$9

Here $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$0 is runtime imbalance within a parallel group,

$$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$1

$$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$2 is synchronization or precedence slack associated with LOCC execution, $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$3 is communication pressure on the module’s incident links, and $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$4 is cut-induced sampling overhead. The weights $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$5 tune the emphasis on makespan, communication, and cutting overhead.

A central feature is adaptive circuit cutting. InterQ may keep a job monolithic, cut it into LO fragments, cut it into LOCC fragments with real-time classical dependencies, or create QComm-based remote fragments using Bell pairs. It considers alternative partitions only if they reduce the global objective and preserve feasibility under cut budgets and communication budgets.

The framework distinguishes three execution regimes. In LO, circuit cutting produces fragments that execute independently, with offline reconstruction via quasi-probability decomposition: $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$6 For wire cuts, the sampling overhead scales as $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$7 for $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$8 cut wires. In LOCC, a cut wire is implemented through upstream measurement, classical transmission, and downstream conditional correction, reducing sampling overhead from $$\mathcal{P}_{\text{inter}} = \bigoplus_{i=1}^{k} \text{Format}(q_i, d_{q_i}^{-}),$$9 to $$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$0 in idealized models, but introducing timing constraints: $$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$1 InterQ also enforces the placement constraint

$$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$2

In QComm, remote operations consume Bell pairs and occupy shared quantum links. The remote-gate cost is modeled as

$$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$3

and remote-operation fidelity as

$$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$4

Link budgets are enforced through

$$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$5

The scheduler therefore treats qubit capacity, placement, grouping, communication latency, Bell-pair demand, and cutting overhead as jointly optimized quantities. This differs from approaches that assume a fixed communication model or treat communication as incidental rather than schedulable.

5. Architecture-specific instantiations and performance of the quantum InterQ scheduler

The modular-quantum InterQ framework is instantiated for three representative architectures and evaluated in a unified SimPy discrete-event simulation environment, with circuit construction and partitioning using Qiskit-based tools and Qiskit’s circuit-cutting addon (Kulkarni et al., 18 May 2026). Benchmarks include MQT Bench circuits such as Real Amplitudes, QFT, EfficientSU2, Deutsch-Jozsa, VQE, GHZ, Amplitude Estimation, and TwoLocal; QUEKO circuits; RevLib circuits; and random circuits. Reported metrics include average queue length, queue time $$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$6, average runtime $$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$7, average response time $$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$8, workload changes, and fidelity-oriented metrics LPST, TiIF, TRF, and TiRF.

For superconducting IBM-style LOCC, the modeled system uses multiple 127-qubit backends such as ibm_kawasaki and ibm_sherbrooke, with classical link latency $$\tilde{d}_{q^*}^{-} = \mathcal{M}_\theta(\mathcal{P}_{\text{inter}}, q^*).$$9 ns and dynamic-circuit overhead $_\text{IntraQ}$0 ns. For trapped-ion IonQ-style QComm, modules are Aria with 25 qubits and Forte with 36 qubits, with QComm link latency $_\text{IntraQ}$1 ns, classical feed-forward $_\text{IntraQ}$2 ns, remote-gate latency $_\text{IntraQ}$3 ns, Bell-pair generation rate $_\text{IntraQ}$4 Hz, and Bell-pair fidelity 0.99. For neutral-atom Atomic-style QComm, modules are ac1000 with 112 physical qubits, with QComm link latency $_\text{IntraQ}$5 ns, classical feed-forward $_\text{IntraQ}$6 ns, remote-gate latency $_\text{IntraQ}$7 ns, Bell-pair rate $_\text{IntraQ}$8 Hz, and Bell-pair fidelity 0.988.

In the 11-circuit workload containing a 142-qubit job, IBM LOCC hosts the oversized circuit by cutting across multiple 127-qubit modules and achieves average runtime approximately 2.95 with LPST $_\text{IntraQ}$9. IonQ QComm requires six QPUs and reaches average runtime approximately 20.96 with LPST $q^*$0. Atomic QComm reaches intermediate runtime approximately 7.55 with LPST $q^*$1. The paper interprets this workload as showing best makespan for superconducting, best estimated fidelity for neutral atom, and an intermediate fidelity–runtime profile for trapped ion.

In the MQT + QUEKO comparison between IBM LOCC and IonQ QComm, IBM LOCC yields average queue length 1.08 versus 2.25, average runtime 3.43 versus 16.47, better TRF and TiRF, and slightly worse LPST $q^*$2 versus $q^*$3. In scaling experiments, the MQT 133 jobs workload yields $q^*$4 and LPST $q^*$5 for IBM LOCC, $q^*$6 and LPST $q^*$7 for IonQ QComm, and $q^*$8 and LPST $q^*$9 for Atom QComm. For random 50 jobs, the reported totals are $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$0, LPST $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$1 for IBM LOCC; $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$2, LPST $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$3 for IonQ QComm; and $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$4, LPST $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$5 for Atom QComm.

The paper also compares adaptive cutting against a Serial Round Robin baseline with no cutting. In a 15-circuit workload containing a 142-qubit circuit, the baseline cannot schedule that oversized circuit at all, because no 127-qubit backend can host it monolithically. InterQ partitions the circuit into upstream and downstream LOCC fragments and improves average queue time from 3.43 to 2.97, average runtime from 2.79 to 2.58, average wait time from 6.22 to 5.55, TRF from 1.0 to 2.316, and TiRF from 1.0 to 1.227, at the cost of slightly lower fidelity, with average TiIF 0.968 versus 1.0 and LPST $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$6 versus $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$7.

The abstract summarizes the overall tradeoff as architecture dependent: neutral-atom modular QPUs achieve the highest fidelity, superconducting systems minimize runtime, and trapped-ion systems provide a balanced intermediate profile across fidelity and makespan. The detailed tables are workload dependent, but they consistently show that communication and cutting decisions materially reshape queueing, latency, and fidelity. The paper’s stated limitations are also substantial: the study is simulation-based, uses simplified noise and fidelity models, treats LO reconstruction cost primarily through sampling overhead, and uses heuristic or greedy optimization rather than a provably optimal global scheduler.

6. InterQ as a DQN framework for optimal intermittent control

In "InterQ: A DQN Framework for Optimal Intermittent Control," InterQ addresses communication–control co-design for a discrete-time stochastic linear system in which communication between a scheduler colocated with the plant and a remote controller is costly (Aggarwal et al., 12 Apr 2025). The plant is

$$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$8

where $$\mathcal{S}_{\text{intra}}^- = \{(q^*, d_{q^*}^{-(1)}), \dots, (q^*, d_{q^*}^{-(k)})\}.$$9, $_\text{InterQ}$00, and $_\text{InterQ}$01 is i.i.d., zero mean, with finite covariance $_\text{InterQ}$02. At each time $_\text{InterQ}$03, the scheduler chooses a binary action

$_\text{InterQ}$04

with $_\text{InterQ}$05 meaning transmit the state $_\text{InterQ}$06 and $_\text{InterQ}$07 meaning no transmission.

The stage cost combines quadratic control cost and communication cost: $_\text{InterQ}$08 and the discounted infinite-horizon objective is

$_\text{InterQ}$09

The information structure is partially nested. The controller’s information is

$_\text{InterQ}$10

while the scheduler’s information is

$_\text{InterQ}$11

so that $_\text{InterQ}$12 for all $_\text{InterQ}$13. Because the scheduler exclusively controls communication, the controller has no dual effect, which yields a certainty-equivalence structure and a separation in the optimization.

Under controllability of $_\text{InterQ}$14 and observability of $_\text{InterQ}$15, the paper derives a certainty-equivalent controller. Let $_\text{InterQ}$16 solve the discounted algebraic Riccati equation and define

$_\text{InterQ}$17

Then the optimal control law is

$_\text{InterQ}$18

where $_\text{InterQ}$19 is the least-squares estimate of the state. The estimator evolves as

$_\text{InterQ}$20

The remaining design problem is the scheduler. Defining the estimation error

$_\text{InterQ}$21

the error dynamics become

$_\text{InterQ}$22

so the error is reset to zero whenever a transmission occurs. The closed-loop cost reduces to

$_\text{InterQ}$23

with

$_\text{InterQ}$24

Hence the communication–control co-design problem becomes an optimal scheduling problem on the error process: $_\text{InterQ}$25

InterQ models this scheduling problem as an infinite-horizon discounted MDP with continuous state and binary action. The state is $_\text{InterQ}$26, the action set is $_\text{InterQ}$27, the transition is governed by the error dynamics, and the running cost is

$_\text{InterQ}$28

The optimal Q-function satisfies

$_\text{InterQ}$29

and the optimal policy is

$_\text{InterQ}$30

Because $_\text{InterQ}$31 is unknown and the state space is continuous, the paper proposes a Deep Q-Network approximation $_\text{InterQ}$32. The target for a sampled transition $_\text{InterQ}$33 is

$_\text{InterQ}$34

and the minibatch loss is

$_\text{InterQ}$35

Training uses experience replay, a target network updated every $_\text{InterQ}$36 episodes, and $_\text{InterQ}$37-greedy exploration with

$_\text{InterQ}$38

The experimental implementation uses a fully connected MLP with 4 hidden layers of size 100, GeLU activations, Adam optimizer, learning rate $_\text{InterQ}$39, replay memory size $_\text{InterQ}$40, batch size $_\text{InterQ}$41, $_\text{InterQ}$42, $_\text{InterQ}$43, and $_\text{InterQ}$44. The framework is released as open-source software at https://github.com/AC-sh/InterQ.

7. Scheduling geometry, empirical behavior, and limitations in intermittent control

The intermittent-control InterQ paper combines structural analysis with numerical evaluation on a 2D unstable system (Aggarwal et al., 12 Apr 2025). Defining the state value function

$_\text{InterQ}$45

the paper derives

$_\text{InterQ}$46

From this, it gives sufficient conditions for not scheduling

$_\text{InterQ}$47

and for scheduling

$_\text{InterQ}$48

A corollary states that if

$_\text{InterQ}$49

then it is optimal to always schedule. These results imply a threshold structure in the error space. The paper visualizes the learned decision regions and reports that they are well approximated by an ellipse

$_\text{InterQ}$50

with the learned boundary lying between the inner and outer theoretical ellipses.

The main experimental system uses

$_\text{InterQ}$51

with $_\text{InterQ}$52, $_\text{InterQ}$53, $_\text{InterQ}$54, and noise covariance

$_\text{InterQ}$55

The ARE solution is reported as

$_\text{InterQ}$56

and $_\text{InterQ}$57 in the reported scalar form.

InterQ is compared against two baselines. BS1 is periodic scheduling with period $_\text{InterQ}$58: $_\text{InterQ}$59 BS2 is an event-triggered norm-threshold rule: $_\text{InterQ}$60 For $_\text{InterQ}$61 and $_\text{InterQ}$62, the paper reports communication–control trade-off plots in which InterQ Pareto-dominates both baselines: for a given communication rate it achieves lower control cost, or for a given control cost it uses fewer transmissions. It also evaluates the method under non-Gaussian noise, specifically uniform noise in $_\text{InterQ}$63 per coordinate, and again reports that InterQ outperforms the baselines.

The paper also discusses practical training behavior. A larger replay buffer can improve sample diversity, but in continuous unbounded state spaces it can preserve rare large-error experiences that destabilize learning. A smaller buffer can help forget such experiences, improving stability. The authors further state that Huber loss is more stable than MSE in noisy settings because it is less sensitive to outliers in temporal-difference errors. The combination of experience replay, target networks, $_\text{InterQ}$64-greedy exploration, and robust loss is presented as necessary to stabilize DQN in this control setting.

The stated limitations are that the theory relies on linear dynamics and quadratic cost, the controller assumes known model matrices and solves the ARE analytically, the formulation is discounted infinite horizon, the scheduler observes the full state and knows all past controls, and InterQ learns only the scheduler rather than jointly learning controller and scheduler. The framework also does not encode no-communication events as additional information in the controller’s filter. Future directions include nonlinear systems, settings in which no-communication events are informative, multi-agent networked control, and joint treatment of model uncertainty and plant learning.

Taken together, the three uses of the term “InterQ” document independent lines of work on transfer-based adversarial prompting, communication-aware modular quantum scheduling, and reinforcement-learning-based intermittent control. The commonality is lexical, but each version formalizes coordination under communication or transfer constraints in a technically specific way.