Extensions and Limitations of the Noisy Stabilizer Formalism
Matti, Jasmin
The stabilizer formalism is a central framework in quantum computing and one of the key building blocks for fault-tolerant quantum computers. According to the Gottesman–Knill theorem, we can efficiently simulate any quantum system consisting of stabilizer states, Clifford gates, and Pauli measurements on a classical computer. A key challenge in developing robust quantum technologies is that physical quantum systems are unavoidably affected by noise, which degrades quantum information. Accurate noise modeling is therefore essential. For stabilizer states, the noisy stabilizer formalism has recently been introduced as a framework for efficiently describing the evolution of graph states subject to Pauli-diagonal noise under Clifford operations and Pauli measurements. In this thesis, we explore and extend this formalism in two directions. First, we generalize the method from graph states to arbitrary stabilizer states, thereby extending the Gottesman-Knill theorem to noisy scenarios. Second, we extend the formalism to handle noise models beyond Pauli-diagonal channels. Moreover, we study the applicability of the noisy stabilizer formalism to entanglement purification protocols.
•Jan 1, 2025•0 citations