2026-08-14 –, Room 3
Quantum computing, communication, and sensing technologies rely on precise knowledge of quantum states. Quantum states cannot be directly measured. Quantum state tomography (QST) reconstructs these states from indirect measurements, similar to how CT imaging combines multiple 2D projections into a 3D model. In QST, the goal is to minimize the statistical discrepancy between experimentally observed data and predictions from quantum theory. This optimization problem is nonlinear and subject to physical constraints on the states. We present a Julia implementation that efficiently and robustly minimizes this statistical distance while enforcing these constraints. Our work provides a practical, extensible toolkit for QST and a comparative guide to choosing optimizer based on accuracy, speed, and robustness.
In quantum mechanics, the full quantum state is represented by a density matrix. It cannot be directly measured. Only partial information, obtained through different measurement is accessible. Quantum state tomography (QST) reconstructs the complete state from these measurement that yield a measurement statistics. Quantum theory provides predicted statistics for any assumed state, and QST identifies the state whose predicted statistics best match the observed data by minimizing a suitable statistical distance.
We present a Julia implementation of a QST pipeline that reconstructs density matrices while ensuring physicality: each density matrix must be positive semi-definite and have unit trace. Our approach minimizes a residual between predicted and measured statistics and supports both least-squares and log-likelihood formulations. Physical constraints are enforced through Cholesky parameterization or projection methods. We benchmark on simulated data several optimization strategies, like projected Gauss–Newton, L-BFGS, and trust-region solvers. The benchmarks evaluate reconstruction accuracy, scaling with the number of qubits, convergence speed, and stability, offering practical guidance for selecting optimizer in QST applications.
During my previous studies, I theoretically investigated and optimized quantum optical and measurement systems using tools from quantum information theory. Since 2025, I have been a PhD student in physics at Charles University in Prague, where my theoretical research focuses on fast and reliable quantum state tomography. My work emphasizes developing and implementing improved methods that enable efficient tomography even for high‑dimensional systems.