Research / Manuscript in preparation
Quantum simulation & operator dynamics
What needs to be simulated when we only care about a particular observable?
The problem
A quantum state carries more information than a single measurement needs. My work at the University of Augsburg asks how the choice of observable can guide classical simulation of quantum dynamics.
The mathematical idea
In the Heisenberg picture, time dependence moves from the state to the observable:
Approximate Heisenberg propagation follows this operator in a structured basis. Pauli propagation, symmetry, and Lie-algebraic structure offer different ways of organizing the operators that can appear. The approximation should account for the final readout, rather than treating every operator component as equally useful.
Approach
The research explores structured operator bases and representation-theoretic methods, with particular attention to readout-aware approximation. The question is both computational and mathematical: which parts of the evolving representation matter for the quantity we want to estimate?
Scope and next questions
The manuscript, Readout-aware Approximate Heisenberg Propagation in Structured Operator Bases, is in preparation. This overview does not report benchmark results. A central question is how to balance a compact representation against error in the observable, especially when the operator dynamics leave a convenient subspace.