🧠 Trace Estimation via Quantum Circuits

📍 EPFL – Bachelor in Communication Systems, Year 3 (2023)
👥 Team: Matthias Wyss, Sofia Taouhid
🔗 Final Report: Report

In this project, we explore how quantum circuits can be used to estimate the trace of large unitary matrices—a task that becomes computationally expensive on classical systems as the number of qubits increases.

After studying the theoretical foundation (Bell states, controlled operations, trace estimation circuits), we designed and implemented a quantum protocol that computes the real and imaginary parts of the normalized trace of an unknown unitary operator ( U ).

We implemented the trace estimation circuit using Qiskit, generating random unitaries and validating our approach on IBM quantum simulators. We further analyzed how the number of shots and confidence interval parameters influence estimation accuracy. Finally, we applied the circuit to a “mystery gate” to estimate an unknown angle ( \theta ) and validated our predictions with theoretical values.

🛠 Tools & Libraries:

🧠 Techniques: