Regensburg 2022 – scientific programme
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QI: Fachverband Quanteninformation
QI 4: Poster: Quantum Information
QI 4.29: Poster
Monday, September 5, 2022, 18:00–20:00, P2
A multi-qubit Bloch vector representation of density matrices in Julia — •Qunsheng Huang and Christian Mendl — Technische Universität München. Fakultät für Informatik. Boltzmannstraße 3. 85748 Garching
In the Bloch sphere picture, one finds the coefficients for expanding a single-qubit density operator in terms of the identity and Pauli matrices. A generalization to n qubits via tensor products represents a density operator by a real vector of length 4n, conceptually similar to a statevector.
The tensor structure leads to computationally efficient algorithms for applying circuit gates and performing few-qubit quantum operations. In view of variational circuit optimization, we study backpropagation through a quantum circuit and gradient computation based on this representation, and generalize our analysis to the Lindblad equation for modeling the (non-unitary) time evolution of a density operator.