InterQnet: Dual Facet in Control & Quantum Networks

• InterQnet is a context-dependent term with dual meanings: one as a DQN approximator in reinforcement-learning based intermittent control and the other as a multidisciplinary quantum networking project.
• In the control framework, InterQnet employs a 4-layer MLP to approximate the scheduler’s Q-function, optimizing communication-control trade-offs in discrete-time stochastic linear systems.
• In quantum networking, InterQnet integrates device innovation, error management, and network architecture to advance scalable, heterogeneous quantum communications.

InterQnet is a context-dependent research term with two distinct 2025 usages. In one usage, within the reinforcement-learning framework “InterQ: A DQN Framework for Optimal Intermittent Control,” “InterQnet” is an Editor’s term for the deep Q-network that approximates the scheduler’s Q-function in a communication-control co-design problem for discrete-time stochastic linear systems (Aggarwal et al., 12 Apr 2025). In a second usage, “InterQnet” denotes a multidisciplinary project on scalable heterogeneous quantum communications that combines device development, error handling, and network architecture through the paired programs InterQnet-Achieve and InterQnet-Scale (Chung et al., 23 Sep 2025). These usages concern different technical domains—optimal intermittent control and quantum networking—which suggests that the term should be interpreted strictly from local research context.

1. Terminological scope and disambiguation

In the control-theoretic usage, the paper itself refers to the overall algorithm as “InterQ,” and the detailed explanation introduces “InterQnet” only to denote the DQN approximator used to learn the scheduling policy (Aggarwal et al., 12 Apr 2025). The object being approximated is the scheduler’s action-value function over a continuous estimation-error state and a binary transmission action. In this sense, InterQnet is not a separate framework from InterQ; it is the neural component inside it.

In the quantum-networking usage, InterQnet is the formal project name of a “heterogeneous, full-stack approach to scaling quantum networks,” with explicit emphasis on heterogeneous platforms, long-distance operation, application diversity, and orchestration under realistic constraints (Chung et al., 23 Sep 2025). Here the term refers not to a neural network but to an architectural and experimental program spanning physical devices, control planes, error mitigation, and systems modeling.

A common source of confusion is therefore nominal rather than conceptual. One InterQnet is a DQN approximator for scheduling in stochastic control, while the other is a heterogeneous quantum-network initiative. Related literature in packet quantum networking, quantum interconnects, recursive quantum internet architectures, and metropolitan testbeds provides background for the latter usage, but does not redefine the term itself (Yu et al., 2019, Awschalom et al., 2019, Meter et al., 2021, Chung et al., 2022).

2. InterQnet in optimal intermittent control

The control-theoretic InterQ setting studies a discrete-time stochastic linear plant

$x_{k+1} = A x_k + B u_k + W_k,$

where $W_k$ is zero-mean, independent across time, and has covariance $K_W$ (Aggarwal et al., 12 Apr 2025). The scheduler continuously observes the true state $x_k$ and chooses a binary scheduling action $s_k \in \{0,1\}$, where $s_k = 1$ means transmit and $s_k = 0$ means no transmit. When transmission occurs, the controller receives the current state perfectly; otherwise it relies on its internal estimate $\hat{x}_k$.

The architecture has two sequential decision-makers. The scheduler $S$ observes $x_k$ continuously and decides $W_k$0, while the controller $W_k$1 receives $W_k$2 only when $W_k$3 and otherwise computes control from $W_k$4. The information structure is partially nested, with $W_k$5 for all $W_k$6, so the scheduler sees everything the controller sees and more. The paper states that this yields a separation principle, no dual effect for control, and certainty equivalence (Aggarwal et al., 12 Apr 2025).

The stage cost is

$W_k$7

with $W_k$8 and $W_k$9, and the communication cost is $K_W$0 with $K_W$1 per transmission. The discounted infinite-horizon objective is

$K_W$2

with $K_W$3 (Aggarwal et al., 12 Apr 2025). Under the partially nested structure, the optimal controller is certainty-equivalent LQR on $K_W$4, with discounted Riccati solution

$K_W$5

and gain

$K_W$6

so that

$K_W$7

The controller’s estimator predicts

$K_W$8

and updates according to

$K_W$9

With estimation error $x_k$0, the dynamics reduce to

$x_k$1

and the covariance evolves as

$x_k$2

After substituting the certainty-equivalence controller into the objective, the joint design reduces to a scheduler-only optimization,

$x_k$3

with

$x_k$4

The scheduler therefore faces an MDP with state $x_k$5, action $x_k$6, transition $x_k$7, and per-step cost $x_k$8 (Aggarwal et al., 12 Apr 2025).

3. DQN architecture, training, and scheduling structure

In this control usage, InterQnet approximates $x_k$9 for a continuous state $s_k \in \{0,1\}$0 and binary action $s_k \in \{0,1\}$1 (Aggarwal et al., 12 Apr 2025). Its input is $s_k \in \{0,1\}$2, and in the reported experiments $s_k \in \{0,1\}$3. The output head returns two scalar Q-values, $s_k \in \{0,1\}$4, one per action.

The architecture is an MLP with 4 hidden layers, each with 100 units, using GeLU activations and a linear output layer with 2 units. No normalization or feature engineering is specified; raw $s_k \in \{0,1\}$5 is fed to the network. The training loss for a minibatch of transitions $s_k \in \{0,1\}$6 is

$s_k \in \{0,1\}$7

with target-network weights $s_k \in \{0,1\}$8. The update is an Adam step,

$s_k \in \{0,1\}$9

and the paper also reports improved stability with Huber loss in place of MSE to reduce sensitivity to outliers in stochastic noise (Aggarwal et al., 12 Apr 2025).

The reported training mechanisms are standard DQN stabilizers: an experience replay buffer of capacity $s_k = 1$0 storing tuples $s_k = 1$1, minibatch size $s_k = 1$2, uniform random sampling, a target network with periodic hard update $s_k = 1$3, and $s_k = 1$4-greedy exploration with $s_k = 1$5, $s_k = 1$6 per step, and $s_k = 1$7. The optimizer is Adam with learning rate $s_k = 1$8, and the discount factor is $s_k = 1$9. The description explicitly notes that no double DQN, dueling, reward clipping, or prioritized replay are reported (Aggarwal et al., 12 Apr 2025).

A notable qualitative result is the geometry of the learned scheduling landscape. The authors prove sufficient conditions for regions in estimation-error space. No-transmit is strictly optimal if

$s_k = 0$0

while transmit is strictly optimal if

$s_k = 0$1

Empirically, the learned decision boundary aligns with an ellipse between these sufficient bounds. This indicates that the DQN is not merely producing an opaque policy but is recovering structure consistent with the analytical scheduling geometry derived from the error-state formulation (Aggarwal et al., 12 Apr 2025).

4. Empirical behavior, complexity, and limitations of the control usage

The reported numerical study uses an unstable two-dimensional system with

$s_k = 0$2

$s_k = 0$3, $s_k = 0$4, $s_k = 0$5, and $s_k = 0$6 (Aggarwal et al., 12 Apr 2025). The Riccati solution is reported as

$s_k = 0$7

and $s_k = 0$8 is numerically reported as approximately $s_k = 0$9 as the effective weighting in the quadratic error term. The InterQnet hyperparameters are the same 4×100 GeLU MLP with Adam, replay memory $\hat{x}_k$0, batch size $\hat{x}_k$1, and the stated $\hat{x}_k$2-greedy schedule.

The baselines are a multi-period periodic scheduling policy, which transmits every $\hat{x}_k$3 steps, and an event-triggered policy defined by $\hat{x}_k$4 if $\hat{x}_k$5, else $\hat{x}_k$6, with several thresholds tested (Aggarwal et al., 12 Apr 2025). Across tested $\hat{x}_k$7 values such as $\hat{x}_k$8 and $\hat{x}_k$9, the reported Pareto curves show InterQ dominating both baselines: lower cumulative control-plus-communication cost for a given communication rate. The same qualitative advantage is reported when Gaussian process noise is replaced by uniform noise in $S$0.

The paper also reports that Huber loss improves training stability compared to MSE, and that replay memory size influences robustness to rare outlier experiences. A practical point stated in the description is that a smaller replay memory can improve stability in unbounded continuous state spaces by flushing rare catastrophic samples; the authors found $S$1 worked well (Aggarwal et al., 12 Apr 2025).

Per decision step, the forward pass complexity is given as

$S$2

for 4 hidden layers of width 100 plus the 2-output head, which is summarized as roughly $S$3 multiplies per step. Action selection computes two Q-values and chooses the minimum, while training requires a single forward/backward pass per minibatch and is described as lightweight on modern hardware (Aggarwal et al., 12 Apr 2025).

The stated limitations are equally specific. The framework assumes linear dynamics and quadratic costs; although the process noise need not be Gaussian, the derivations hinge on linearity and the separation principle under partially nested information. The formulation also assumes known $S$4 to compute $S$5 and $S$6, and immediate perfect updates when $S$7. This suggests that model mismatch, delays, and out-of-order packets fall outside the present theory and would require adaptive observers, online Riccati estimation, extended filters, or POMDP formulations (Aggarwal et al., 12 Apr 2025).

5. InterQnet as a heterogeneous quantum-networking program

In the quantum-networking literature, InterQnet is a multidisciplinary project aimed at scalable quantum communications through a “comprehensive approach that improves devices, error handling, and network architecture” (Chung et al., 23 Sep 2025). The project targets scalability challenges associated with node count and topologies, heterogeneity of platforms, long distances, application diversity, and large user demand. The stated impact spans distributed quantum computing, secure communications, metrology, and sensing.

The program has a two-pronged strategy. InterQnet-Achieve is the “inner co-design loop,” intended to realize a three-node heterogeneous quantum network enabling communication between two distinct platforms via a third acting as a repeater node. Its components include a first-generation repeater based on Yb neutral atom arrays, solid-state $S$8 devices in nanophotonic cavities, superconducting microwave qubits including transmon and eNe devices interfaced via integrated piezo-optomechanical transducers, and optical quantum frequency converters (Chung et al., 23 Sep 2025). The error-handling components include Pauli Check Sandwiching, resource-aware correction, and finite-size distillation circuits compiled to hardware. The control system is a centralized automated controller with a modular orchestrator, gRPC device agents, hybrid clock distribution using 10 MHz and 1 PPS radio-over-fiber plus NTP alignment, polarization drift compensation services, and an on-demand entanglement service governed by a CAR model.

InterQnet-Scale is the “outer systems study.” Its purpose is to evaluate architectural choices for scalability and resilience, including centralized versus distributed control, in-band versus out-of-band signaling, continuous entanglement generation, and error-correction trade-offs (Chung et al., 23 Sep 2025). The modeling components include device-aware models in SeQUeNCe, tensor-network-accelerated optical simulations, Lindblad modeling of physical qubits, entanglement witnessing, ACP scheduling, and advanced coding strategies such as qLDPC and bosonic GKP with Petz recovery and concatenation. The Achieve and Scale components share measurements and models: physical parameters feed simulation, and simulation results inform device development and orchestration logic.

The quantum-networking InterQnet is therefore not merely a protocol stack or a device platform. It is explicitly described as full-stack co-design that links devices, protocols, control planes, and error handling under realistic constraints such as coexisting traffic, polarization drift, and timing derived from deployed-fiber data (Chung et al., 23 Sep 2025).

6. Platforms, orchestration, and error management in the quantum-networking usage

The platform heterogeneity in InterQnet is central to its design. The Yb neutral-atom platform offers telecom-band atomic transitions from the long-lived $S$9 “clock” state at 1390, 1480, and 1540 nm, demonstrated atom-photon time-bin entanglement at 1390 nm, and memory coherence times greater than 10 s (Chung et al., 23 Sep 2025). The $x_k$0 platform in $x_k$1 thin films on silicon provides a natural telecom transition near 1520–1530 nm, Purcell enhancement greater than 200 in nanophotonic crystal cavities, approximately 40% collection efficiency via fiber-to-chip coupling, an ensemble homogeneous linewidth of approximately 5 kHz, and spectral diffusion of approximately 27 kHz over 4 ms. The superconducting/eNe direction reports eNe qubit coherence of approximately 100 $x_k$2s, single-qubit gate fidelity greater than 99.97%, resilient operation up to 0.4 K, and an integrated piezo-optomechanical microwave–optical interface targeting conversion efficiency greater than 50% with sub-photon added noise. Optical QFCs based on $x_k$3 sum-frequency generation in periodically poled lithium niobate waveguides convert 1390/1520/1550 nm single photons to 745.7 nm for two-photon interference and Bell-state measurement, with pump temporal shaping used for photon-wavefunction engineering (Chung et al., 23 Sep 2025).

The control plane is organized into infrastructure, logical, and control-and-service planes. The orchestrator uses an SDN-like microservice architecture with gRPC device agents encapsulating EPS units, analyzers, time taggers, and polarization compensators; high-level protocol commands execute autonomously across nodes (Chung et al., 23 Sep 2025). Synchronization is provided by radio-over-fiber 10 MHz and 1 PPS distribution plus NTP alignment, and polarization stabilization uses machine-learning-based prediction with RMS error of approximately 0.072 per Stokes parameter even with at least 5 nm wavelength separation. Background entanglement generation is managed by ACP, which adapts neighbor selection to request traffic and can integrate distillation when available.

The project also formalizes several error-handling layers. For two-photon interference fringes, the visibility metric is

$x_k$4

and deployed-fiber experiments with coexisting classical traffic maintained visibilities of 59–68% (Chung et al., 23 Sep 2025). For coexistence-aware orchestration, the empirical coincidences-to-accidentals ratio is modeled as

$x_k$5

with $x_k$6 transmittance, $x_k$7 correlated photon pairs per pulse, $x_k$8 SpRS-induced noise photons, and $x_k$9 detector dark counts (Chung et al., 23 Sep 2025). The orchestrator uses this model to tune EPS pump power, detector bias, and classical intensities to meet target CAR.

Pauli Check Sandwiching is described analytically. For initial Bell fidelity $W_k$00 and postselection probability $W_k$01, PCS X checks give

$W_k$02

while PCS XZ checks give

$W_k$03

and

$W_k$04

Finite-size distillation based on the $W_k$05 code, qLDPC-based logical Bell-pair purification, and bosonic GKP encodings with near-optimal Petz recovery are presented as complementary layers in an error-management hierarchy (Chung et al., 23 Sep 2025).

On the systems side, ACP scheduling in a 200-node autonomous-system topology reduced time-to-serve versus UCP by more than 50%, with reductions up to 94% across scenarios, and ACP plus distillation improved end-to-end fidelity by approximately 0.05 (Chung et al., 23 Sep 2025). Experimental progress includes 4.38 km round-trip deployed-fiber coexistence experiments with quantum at 1550.10 nm and classical 10GBASE-LR at 1330 nm, coincidence rates of 120–155 s$W_k$06 with a 1 ns window, 4.3 km HOM interference with a maximum dip visibility of $W_k$07, and a plane-based orchestration abstraction deployed in a real testbed (Chung et al., 23 Sep 2025).

7. Relation to broader quantum-internet research and open directions

The quantum-networking usage of InterQnet sits within a broader lineage of quantum internet architecture, transport, and testbed research. Packet-level transport semantics for repeater-based, packet-switched internetworks were developed in “Protocols for Packet Quantum Network Intercommunication,” which proposed recursive quantum retransmission based on a $W_k$08 threshold QSS scheme and a quantum three-way handshake for full-duplex logical connections (Yu et al., 2019). In that framework, the expected total number of shares required to deliver one quantum message under per-share loss probability $W_k$09 is

$W_k$10

and the handshake false-accept probability is bounded by $W_k$11. These results are not part of InterQnet proper, but they define transport-layer constraints relevant to any packet-based quantum internetwork.

Architectural recursion and interdomain abstraction are treated in “A Quantum Internet Architecture,” which centers on QRNA, RuleSets, and two-pass connection setup (Meter et al., 2021). QRNA abstracts lower-layer subnetworks as virtual nodes and recommends qDijkstra with “seconds per Bell pair” as link cost. This provides a useful comparison point for InterQnet’s centralized automated orchestration and ACP scheduling. A plausible implication is that InterQnet’s Achieve/Scale split addresses many of the same scalability questions as QRNA—control placement, signaling models, and fidelity-aware service composition—but from the standpoint of heterogeneous device co-design and experimental integration rather than a single recursive control formalism.

The workshop summary “Development of Quantum InterConnects for Next-Generation Information Technologies” frames quantum interconnects as a grand challenge and defines the metrics commonly used for heterogeneous interfaces, including conversion efficiency $W_k$12, added noise $W_k$13, fidelity $W_k$14, cooperativity $W_k$15, Purcell factor $W_k$16, bandwidth $W_k$17, insertion loss $W_k$18, mode-matching $W_k$19, coherence times $W_k$20 and $W_k$21, and entanglement rate $W_k$22 (Awschalom et al., 2019). Those criteria are directly relevant to InterQnet’s emphasis on microwave–optical transduction, cavity-enhanced telecom memories, and frequency conversion. Likewise, the metropolitan repeaterless testbed IEQNET demonstrates a layered SDN-controlled architecture over deployed fiber, quantum–classical coexistence, transparent optical switching, and calibration workflows that form an immediate experimental context for InterQnet’s deployed-fiber automation and coexistence claims (Chung et al., 2022).

The open directions are explicit in both 2025 usages. For the control-theoretic InterQnet, proposed extensions include actor-critic variants, adaptive observers, online Riccati estimation under model uncertainty, communication delays, and nonlinear systems (Aggarwal et al., 12 Apr 2025). For the quantum-networking InterQnet, the current bottlenecks include photon collection for Yb, entanglement rates, Raman and multipair noise, transducer efficiency and added noise, fiber-coupling losses, pump-induced heating, long-term polarization stability, orchestrator scaling, robust swapping under realistic error budgets, and staged integration of qLDPC and GKP recovery (Chung et al., 23 Sep 2025). Taken together, these trajectories indicate that “InterQnet” currently names two active but unrelated research threads: one centered on certainty-equivalence control plus DQN-based scheduling, and one centered on heterogeneous full-stack co-design for scalable quantum networks.