CogRouter: Quantum & Cognitive Routing

• CogRouter is a dual-function concept that offers a coherent quantum routing element for QRAM through shallow TCG circuits and robust post-selection techniques.
• It employs qutrit state encoding to perform low-depth, deterministic conditional operations, drastically reducing gate counts compared to traditional methods.
• CogRouter also adapts LLM reasoning depth dynamically via two-stage training (CoSFT and CoPO), achieving state-of-the-art accuracy with reduced token consumption.

CogRouter is a term with two distinct high-impact technical meanings in recent research: (1) a coherent quantum routing element for bucket-brigade quantum random access memory (QRAM) realized via shallow transition-composite-gate (TCG) circuits on superconducting qutrits (Zhang et al., 20 May 2025), and (2) a framework for LLM agents that enables dynamic, step-level cognitive depth adaptation, grounded in hierarchical cognitive theory, for efficient and robust sequential decision-making (Yang et al., 13 Feb 2026). Both instantiations address the scalable realization of selective information transmission—either quantum or neural—by engineering efficient control over routing primitives.

1. CogRouter in Quantum Information: TCG-Engineered QRAM Routing

The quantum CogRouter is a scalable, coherent conditional routing element crucial for bucket-brigade QRAM architectures. These routers enable selective qubit pathing, foundational for quantum search and quantum machine learning protocols utilizing QRAM (Zhang et al., 20 May 2025). Experimental realization leverages the auxiliary $|2\rangle$ energy levels of superconducting transmon qutrits to achieve low-depth, deterministic conditional SWAP (CSWAP) operations with built-in error resilience.

Transition-Composite-Gate (TCG) Scheme

The TCG scheme implements a three-qubit CSWAP by utilizing the qutrit’s non-computational state $|2\rangle$ as a mediating auxiliary. In the relevant subspace $\{|11\rangle, |02\rangle\}$, the effective Hamiltonian is

$$H_{\mathrm{int}} = g(|11\rangle\langle 02| + |02\rangle\langle 11|) + \Delta |02\rangle\langle 02|,$$

where $g$ is the coupling and $\Delta$ the detuning. By pulsing $\Delta \rightarrow 0$ for $\tau = \pi/(2g)$, an iSWAP$_{02\leftrightarrow 11}$ gate swaps $\left|11\right\rangle$ and $|2\rangle$0, forming the backbone for $|2\rangle$1 gates in this architecture. The CSWAP is decomposed into a sequence of $|2\rangle$2 gates and single-qutrit $|2\rangle$3 rotations, drastically reducing both two-qubit gate count and circuit depth relative to Clifford-based approaches (see Table 1).

Scheme	Two-qubit Gates	One-qubit Gates	Depth
Clifford CSWAP	16	20	30
TCG non-eraser ($|2\rangle$4)	6	2	8
TCG eraser ($|2\rangle$5)	6	6	12

Eraser-Detection by Non-Adjacent Qutrit Encoding

Routing addresses are encoded in non-adjacent qutrit states: “Left” in $|2\rangle$6, “Right” in $|2\rangle$7, leaving the intermediate $|2\rangle$8 unused. Leakage into $|2\rangle$9 is detected and used for post-selection; erroneous shots are discarded, which improves routing fidelity. The postselected fidelity is renormalized as

$\{|11\rangle, |02\rangle\}$0

where $\{|11\rangle, |02\rangle\}$1 is the measured leakage into $\{|11\rangle, |02\rangle\}$2.

2. Circuit Implementations and Scaling

Single-layer CogRouter: Realized with three qutrits, the router implements

$\{|11\rangle, |02\rangle\}$3

With TCG eraser encoding, the circuit depth is $\{|11\rangle, |02\rangle\}$4 compared to $\{|11\rangle, |02\rangle\}$5 for Clifford decomposition. Preparation involves $\{|11\rangle, |02\rangle\}$6 rotations for address superpositions.

Multi-layer bucket-brigade networks: Extendable to multiple routing layers via triangular tiling in a superconducting 2D grid. For two layers (six qutrits), QRouters operate in parallel within a layer, yielding $\{|11\rangle, |02\rangle\}$7-layer circuits versus $\{|11\rangle, |02\rangle\}$8 for serial Clifford schemes. The architecture is scalable up to five layers before topological constraints induce router overlap.

3. Experimental Results and Fidelity Characterization

Quantum state tomography and random-access protocols validate the mechanism. Single-router fidelities reach $\{|11\rangle, |02\rangle\}$9 (with eraser post-selection), a substantial improvement over non-eraser baselines ($$H_{\mathrm{int}} = g(|11\rangle\langle 02| + |02\rangle\langle 11|) + \Delta |02\rangle\langle 02|,$$0). For a two-layer routing network, the average postselected RAT fidelity is $$H_{\mathrm{int}} = g(|11\rangle\langle 02| + |02\rangle\langle 11|) + \Delta |02\rangle\langle 02|,$$1. The eraser-detection mechanism mitigates the principal error mode—leakage-induced misrouting—without extra hardware, and TCG engineering enables depth reductions of $$H_{\mathrm{int}} = g(|11\rangle\langle 02| + |02\rangle\langle 11|) + \Delta |02\rangle\langle 02|,$$2 relative to conventional Clifford methods.

4. CogRouter as Step-Level Cognitive Depth Router for LLM Agents

Independently, CogRouter denotes a cognitive adaptation framework for LLM-based agents that selects the appropriate "reasoning depth" on a step-by-step basis in long-horizon environments (Yang et al., 13 Feb 2026). The approach, motivated by the ACT-R cognitive architecture, formalizes reasoning into four discrete levels: Instinctive Response (L1), Situational Awareness (L2), Experience Integration (L3), and Strategic Planning (L4). Agents dynamically choose the depth—balancing task complexity and token efficiency.

Two-stage Training: CoSFT and CoPO

Training proceeds as follows:

• Cognition-aware Supervised Fine-Tuning (CoSFT): Instills stable, level-specific reasoning chains by supervised learning over expert demonstrations, randomly distributed among the four cognitive levels.
• Cognition-aware Policy Optimization (CoPO): Reinforces adaptive level selection using step-level confidence-weighted RL. Log-probability-based confidence metrics are used to reweight advantage estimates for each candidate level at every step, efficiently credit-assigning trajectory-level rewards to step-wise cognitive depth choices.

The agent’s output tokens follow a structured template for cognitive level, "thinking" chain, and action, enabling explicit format supervision and credit assignment.

5. Empirical Performance and Analysis

Experiments on ALFWorld and ScienceWorld validate CogRouter’s step-level depth adaptation strategy:

Method	ALFW SR	SciW Score	SciW SR	Avg SR	Avg #Tokens
GPT-4o	61.5%	57.0	22.5%	42.0%	935.4
OpenAI-o3	74.0%	72.4	54.0%	64.0%	4737.5
GRPO	83.5%	71.1	53.0%	68.3%	4367.3
GiGPO	88.0%	67.3	47.0%	67.5%	3779.2
CogRouter (CoPO)	92.5%	84.6	72.0%	82.3%	1641.4

CogRouter achieves higher success rates with 62% fewer tokens compared to GRPO. Only multi-level, adaptive policies reach both high efficiency and state-of-the-art accuracy.

Ablation shows that single-level training trades performance for efficiency (“L1 only” achieves 76.5% SR at 357 tokens; “L4 only” achieves 86.5% SR at 4641 tokens). Average log-probability is the most reliable confidence weighting signal; using alternatives degrades results by 3–13 percentage points.

6. Limitations, Scalability, and Future Directions

For the quantum CogRouter, dominant limitations are decoherence and leakage at circuit depths beyond two layers ($$H_{\mathrm{int}} = g(|11\rangle\langle 02| + |02\rangle\langle 11|) + \Delta |02\rangle\langle 02|,$$3, $$H_{\mathrm{int}} = g(|11\rangle\langle 02| + |02\rangle\langle 11|) + \Delta |02\rangle\langle 02|,$$4), as well as crosstalk and frequency crowding in dense tilings. Further advances include short-path TCG variants, improved coherence, and hardware-aware layouts. For the LLM-based CogRouter, the current four-level hierarchy is fixed; extensions to continuous or learned hierarchies, multimodal agents, or curriculum-driven adaptation are proposed directions.

Both instantiations demonstrate that engineered dynamic routing—of quantum or cognitive resources—substantially increases scalability and efficiency in their respective domains, and provide modular blueprints for future large-scale applications in QRAM and embodied AI (Zhang et al., 20 May 2025, Yang et al., 13 Feb 2026).