Inspiration
What it does## Inspiration
As quantum computing transitions into the NISQ (Noisy Intermediate-Scale Quantum) era, bridging the gap between textbook quantum protocols and real-world hardware limitations is crucial. We were inspired to build a comprehensive Qiskit-based simulation framework to explore two pillars of quantum information science: E91 Quantum Key Distribution (QKD) with active eavesdropper detection, and Grover's Search performance under realistic noise. Our goal was to not only simulate ideal quantum mechanics but also rigorously analyze how statistical fluctuations, eavesdropping, and physical noise channels degrade quantum advantage.
What it does
- E91 QKD Protocol Simulator: Prepares Bell states ($\lvert \Phi^{+} \rangle$), performs arbitrary $x$-$z$ plane measurements, simulates an intercept-resend eavesdropper (Eve), and computes the Quantum Bit Error Rate (QBER).
- Entanglement Certification: Automatically evaluates the CHSH parameter ($S$) and its standard error ($\sigma_S$) to certify genuine quantum non-locality ($S > 2$).
- Disturbance Classification: Employs a custom Weighted Least Squares (WLS) regression model to mathematically distinguish between directional eavesdropper interference and isotropic depolarizing transmission noise.
- Noisy Grover Search: Implements phase oracles and diffusion operators without ancillas, evaluating success probabilities under both depolarizing $\mathcal{D}(p)$ and bit-flip $\mathcal{B}(q)$ noise models to find optimal iteration cutoffs.
How we built it
Built using Python, Qiskit 2.6, Qiskit Aer, NumPy, and Matplotlib.
- Developed custom circuit blocks for mid-measurement intercept-resend mechanisms (
add_intercept_resend). - Engineered analytical expectation value functions incorporating transmission parameters $p$ and $\lambda$.
- Integrated rigorous error-propagation formulas and customized heatmap visualizers for correlation data.
Challenges we ran into
- Noise vs. Amplification Trade-offs: Balancing deep Grover circuits against hardware noise where over-iteration leads to state decay rather than success.
- Statistical Rigor: Managing finite-shot variance ($\pm \sigma_S$) to ensure eavesdropper detection thresholds ($>5\sigma$) remained robust against normal statistical fluctuations.
- Matrix Alignment: Ensuring proper core dimension alignment when building weighted least-squares covariance matrices for disturbance classification.
What we learned
We gained deep insights into the practical challenges of QKD security—specifically, why a Bell violation certifies entanglement but a full security proof requires tracking QBER and classical post-processing. We also quantified how noise dampens amplitude amplification, highlighting the critical need for error mitigation in future quantum algorithms.
