Efficient quantum circuit simulation using a multi-qubit Bloch vector
representation of density matrices
- URL: http://arxiv.org/abs/2103.13962v2
- Date: Fri, 11 Feb 2022 10:25:21 GMT
- Title: Efficient quantum circuit simulation using a multi-qubit Bloch vector
representation of density matrices
- Authors: Qunsheng Huang and Christian B. Mendl
- Abstract summary: A generalization to $n$ qubits via tensor products represents a density operator by a real vector of length $4n$.
We study this approach for the purpose of quantum circuit simulation, including noise processes.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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