I am documenting my journey through the IBM Quantum Learning course on Diagonalization. Below are the lab reports and engineering notes from this series.
| Date | Title | Description |
|---|---|---|
| Nov 26, 2025 | Challenge Accepted: Mastering Quantum Diagonalization (It’s Not Just for Molecules) | Yesterday, I attended a Qiskit Advocate seminar on Sample-Based Quantum Diagonalization (SQD). The session was a fascinating deep dive into how we can extract eigenvalues… |
| Nov 30, 2025 | The Variational Principle: A Linear Algebra Perspective | Exploring the linear algebra foundations of VQE and how finding the lowest eigenvalue translates to a quantum optimization problem. |
| Dec 2, 2025 | Encoding Math into Metal: Representing Vectors and Matrices on a QPU | How to translate classical linear algebra structures into quantum states and operators, and efficiently calculate expectation values using the Qiskit Estimator. |
| Dec 12, 2025 | Closing the Loop: From Fixed Angles to Optimization | Turning constants into variables: How to build a parameterized quantum circuit and use classical optimization to find the minimum eigenvalue and eigenvector. |
| Dec 19, 2025 | The Art of the Ansatz: Entanglement and the Hilbert Space Wall | Why our previous circuit failed, how adding a CNOT gate fixes it, and why even that isn’t enough for every matrix. |
| Jan 18, 2026 | Exploring the Ansatz Zoo: Heuristics and the Parameter Gap | We cannot search the entire Hilbert space. We explore the n-local blueprint, why we prefer 2-local circuits, and use RealAmplitudes to find the answer with exponentially fewer parameters. |
| Jan 21, 2026 | The Implicit Matrix: Scaling Max-Cut with Paulis | We use the Max-Cut problem to demonstrate how to transition from a classical matrix formulation to a quantum operator without ever building the full dense matrix. |
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