One Clean Qubit

The One Clean Qubit model of computation is performed an ${\displaystyle n}$ qubit system with one pure state and ${\displaystyle n-1}$ maximally mixed states.^[1] This model was motivated by highly mixed states that are prevalent in Nuclear magnetic resonance quantum computers. It's described by the density matrix ${\displaystyle \rho =\left|0\right\rangle \langle 0|\otimes {\frac {I}{2^{n-1}}}}$, where ${\displaystyle I}$ is the identity matrix. In computational complexity theory, DQC1; also known as the Deterministic quantum computation with one clean qubit is the class of decision problems solvable by a one clean qubit machine in polynomial time, upon measuring the first qubit, with an error probability of at most 1/poly(n) for all instances.^[2]