Evolutionary Vulnerability Surfaces in Hybrid Quantum-Classical Architectures: A Unified Formalism

AUTHOR Rakshas Intl. Unltd. • August 15, 2026

Abstract

This paper formalizes a multi-objective evolutionary simulation framework targeting cross-stack vulnerabilities in hybrid quantum-classical computing systems. By treating the computational stack—from the underlying physics of the qubits to the classical microkernel control plane—as a continuous topological surface, we mathematically define mutation kernels capable of evolving cascading fault pathways. Specifically, we detail three critical exploitation vectors: classical timing desynchronization via Advanced Dimension Interconnect (ADI) contention, memristive Hamiltonian drift in superconducting transmons, and Rydberg blockade violations in neutral atom arrays.

1. Classical Control Plane: Vector-based IPC Contention in YuKKi OS

The timing of control pulses sent to the quantum cryostat is highly deterministic. To break this determinism from the classical software layer, the evolutionary algorithm targets the spatial manifold engine within the YuKKi OS microkernel. The objective is to mutate routing paths within the Advanced Dimension Interconnect (ADI) protocol to force artificial network-on-chip (NoC) contention, thereby delaying the arrival of pulse instructions by a critical margin ($\Delta t$).

Let an ADI vector packet $\vec{v}_i$ encode a control pulse destined for cryostat controller node $k$. The arrival time is given by:

$$t_{\text{arrival}} = t_0 + \sum_{n \in \mathcal{P}} \tau_n(\vec{v}_i)$$

where $\mathcal{P}$ is the routed path through the spatial manifold. The evolutionary mutation kernel applies a routing perturbation matrix $\mathbf{M}_{\text{route}}$ to force multiple vector packets into a bottleneck queue.

The induced latency $\Delta t$ at a specific interconnect node $n$ follows a non-linear workload accumulation function. If we define the vector payload size as $S(\vec{v}_i)$ and the ADI node processing bandwidth as $B_n$, the contention delay is modeled as:

$$\Delta t_{\text{induced}} = \sum_{n \in \mathcal{P}} \left( \frac{S(\vec{v}_i)}{B_n} + f_{\text{queue}}(\mathbf{M}_{\text{route}}) \right) + \epsilon_{\text{mTLS}}$$

where $\epsilon_{\text{mTLS}}$ represents the cryptographic overhead injected via mutual TLS handshaking stalls. If $\Delta t_{\text{induced}}$ exceeds the physical qubit's coherence threshold (e.g., $T_2^\ast$), a dynamic phase error is mathematically guaranteed before the physical microwave generator can fire.

2. Superconducting Transmons: Memristive Hamiltonian Mutation

For superconducting architectures (e.g., Willow), the genome evolves hysteresis-like noise pathways. Instead of treating hardware noise as Markovian (memoryless), we model the qubit parameters as drifting over time based on the integral of past pulse sequences, formally defined via memristive state integration.

The standard interacting transmon Hamiltonian is:

$$H_0 = \sum_i \left( \omega_i a_i^\dagger a_i - \frac{\alpha_i}{2} a_i^\dagger a_i^\dagger a_i a_i \right) + \sum_{\langle i,j \rangle} J_{ij} (a_i^\dagger a_j + a_i a_j^\dagger)$$

To inject evolutionary memristive faults, we perturb the qubit frequency $\omega_i$ and the anharmonicity $\alpha_i$ through a state variable $w(t)$. The evolution of this memristive state is governed by the driving field amplitude $\Omega_d(t)$:

$$\frac{dw(t)}{dt} = -\gamma w(t) + \beta |\Omega_d(t)|^2$$

where $\gamma$ is the relaxation rate and $\beta$ is the memristive coupling constant. The mutated, time-dependent Hamiltonian thus becomes:

$$H(t) = H_0 + \sum_i \delta\omega_i(w_i(t)) a_i^\dagger a_i$$

The evolutionary algorithm maximizes the fitness of the mutation vector by finding the specific pulse history $\Omega_d(\tau)$ that pushes $\delta\omega_i(w_i(t))$ close to the cross-resonance collision frequency. By mapping this drift via simulated graphene resistive hyper-sensors, the algorithm identifies the exact threshold where the population leaks from the computational $\vert{}1\rangle$ state into the $\vert{}2\rangle$ state.

3. Neutral Atom Arrays: Rydberg Blockade Exploitation

In neutral atom quantum processors, entanglement relies on exciting atoms to a high-principal-quantum-number Rydberg state $\vert{}r\rangle$. This excitation depends on the Van der Waals interaction $V_{ij}$ between atoms $i$ and $j$, which scales with the inverse sixth power of the inter-atomic distance $R_{ij}$.

The ideal blockade requires that $V_{ij} \gg \hbar \Omega$ (where $\Omega$ is the Rabi frequency of the excitation laser). The interaction potential is:

$$V_{ij} = \frac{C_6}{R_{ij}^6}$$

The mutation kernel targets the acoustic-optic deflectors (AODs) guiding the optical tweezers. By injecting minute positional jitter $\delta \vec{r}(t)$, the mutated position of the atom becomes $\vec{r}_i(t) = \vec{r}_{i,0} + \delta \vec{r}_i(t)$.

The mutated inter-atomic distance is $R_{ij}(t) = \vert{}\vec{r}_i(t) - \vec{r}_j(t)\vert{}$. The Hamiltonian governing the two-atom system under laser excitation $\Omega_i(t)$ with detuning $\Delta_i$ is:

$$H(t) = \sum_{k \in \{i,j\}} \left( \frac{\Omega_k(t)}{2} \sigma_x^{(k)} - \Delta_k n_k \right) + V_{ij}(t) n_i n_j$$

The evolutionary engine searches for specific vibrational harmonics in $\delta \vec{r}_i(t)$ such that the expected minimum distance $R_{\text{min}}$ is periodically exceeded. When the mutated interaction $V_{ij}(t_{gate})$ dips below the $\hbar \Omega$ threshold during a gate operation, the Rydberg blockade is violated. This results in the simultaneous excitation to $\vert{}r_i r_j\rangle$, creating a lethal parity error that evades standard physical-layer error mitigation.

4. Synthesis: The Unified Cross-Stack Fitness Function

To evolve these faults concurrently, the global genome $\vec{V} = [\mathbf{\Omega}_{\text{phys}}, \mathbf{E}_{\text{qec}}, \mathbf{T}_{\text{ctrl}}]$ is evaluated using a unified fitness function.

Let $\mathcal{U}_{\text{ideal}}$ be the ideal unitary evolution of the quantum circuit, and $\mathcal{E}_{\text{sim}}(\vec{V})$ be the completely positive trace-preserving (CPTP) map of the system undergoing the simulated attack vector across the YuKKi OS, memristive, and Rydberg parameters.

The algorithm maximizes the trace distance between the ideal and corrupted logical states, penalized by the classical syndrome detectability $D_{\text{detect}}$:

$$\mathcal{F}(\vec{V}) = \frac{1}{2} \left\Vert \mathcal{E}_{\text{sim}}(\vec{V})[\rho_0] - \mathcal{U}_{\text{ideal}} \rho_0 \mathcal{U}_{\text{ideal}}^\dagger \right\Vert_1 - \lambda D_{\text{detect}}(\mathbf{E}_{\text{qec}})$$

By maximizing $\mathcal{F}(\vec{V})$, the simulation reliably isolates the exact combinations of software-level ADI latency and hardware-level Hamiltonian drift required to induce catastrophic, uncorrectable logical failures in any targeted quantum modality.

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Saturday, August 15, 2026

Towards debugging quantum computing.