Quasi-Chaotic Oscillators Based on Modular Quantum Circuits

Secure communication has always relied on the ability to transform information into signals that are difficult to predict, reconstruct, or imitate. In classical digital systems, quasi-chaotic generators offer one way to achieve this goal: they use modular arithmetic to produce sequences that behave like noise, while still being generated by deterministic rules. This combination of structure and apparent randomness makes them especially interesting for encryption and signal protection. We bring this idea into the quantum domain. Instead of building quasi-chaotic oscillators with conventional digital circuits, the approach reconstructs their internal modular operations through quantum gates, creating a quantum version of a residue-based oscillator designed to generate pseudo-random, noise-like sequences.

The starting point is a nonlinear digital filter whose behaviour is governed by modular addition and multiplication. In classical implementations, this type of structure can be used to encode a signal into a quasi-chaotic sequence, with the filter coefficients acting as a form of encryption key. The proposed quantum design preserves this architecture, replacing its arithmetic core with quantum modular operations. A single section of the filter is implemented through quantum addition, quantum bit shifting, and quantum modular multiplication. These elementary components are assembled into a modular quantum block that can be repeated to form the full oscillator.

The quantum oscillator is constructed as an unrolled sequence of modular quantum sections. Each section receives a coefficient, an input value, and a delayed state, then computes the next value of the sequence using reversible quantum logic. Because quantum computation cannot simply erase intermediate information, auxiliary qubits are used to store temporary values. Uncomputing is then applied to restore part of these qubits and make them reusable. This detail is essential: the design is not only a direct translation of the classical system, but a careful adaptation to the constraints of quantum computation. The resulting architecture is modular, scalable in principle, and conceptually aligned with the parallelism offered by quantum superposition.

The validation is carried out through quantum circuit simulations using Qiskit. First, a single modular section is tested across input configurations, showing that its output matches the expected classical modular behaviour. Then, a complete oscillator response is generated and compared with the corresponding classical quasi-chaotic oscillator. The comparison shows an almost perfect overlap between the ideal quantum response and the classical reference, confirming that the quantum circuit reproduces the intended dynamics. The analysis is then extended by introducing bit-flip measurement errors, observing how increasing noise progressively degrades the generated sequence.

A further test examines the autocorrelation of the generated sequence, showing a behaviour close to that of an uncorrelated noise signal, one of the key properties expected from a quasi-chaotic generator intended for secure communication scenarios. The broader implication is that quantum modular circuits could enable fast, multi-channel encryption and decryption schemes. By exploiting superposition, a quantum oscillator may process multiple configurations in parallel, opening the possibility of evaluating many keys or signal paths simultaneously within a larger quantum algorithm. This direction remains exploratory, especially because current quantum hardware is still limited by noise, qubit availability, and circuit depth. Yet the proposed design shows that a classical idea from modular digital signal processing can be meaningfully reinterpreted in a quantum framework. In this perspective, quasi-chaotic generation becomes more than a tool for producing pseudo-random signals. It becomes a bridge between secure communication, modular arithmetic, and the future architecture of quantum information processing.