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arXiv · 2103.13962

Efficient quantum circuit simulation using a multi-qubit Bloch vector representation of density matrices

Qunsheng Huang·Christian B. Mendl
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Abstract

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 $4^n$, conceptually similar to a statevector. Here, we study this approach for the purpose of quantum circuit simulation, including noise processes. 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.

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Qunsheng Huang, Christian B. Mendl. 2021-03-25. Efficient quantum circuit simulation using a multi-qubit Bloch vector representation of density matrices. https://doi.org/10.1103/physreva.105.022409

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