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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.
Classical simulations of quantum circuits are limited in both space and time when the qubit count is above 50, the realm where quantum supremacy reigns. However, recently, for the low depth circuit with more than 50 qubits, there are several methods
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite a
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such limits, but imp
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possib
The ability to simulate one Hamiltonian with another is an important primitive in quantum information processing. In this paper, a simulation method for arbitrary $sigma_z otimes sigma_z$ interaction based on Hadamard matrices (quant-ph/9904100) is g