Quantum Circuits with Mixed States
Abstract
We define the model of quantum circuits with density matrices, where nonunitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be equivalent in computational power to standard quantum circuits. The main result in this paper is a solution for the subroutine problem: The general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations. We give a natural definition of using general subroutines, and analyze their computational power. We suggest convenient metrics for quantum computing with mixed states. For density matrices we analyze the so called ``trace metric'', and using this metric, we define and discuss the ``diamond metric'' on superoperators. These metrics enable a formal discussion of errors in the computation. Using a ``causality'' lemma for density matrices, we also prove a simple lower bound for probabilistic functions.
 Publication:

arXiv eprints
 Pub Date:
 June 1998
 DOI:
 10.48550/arXiv.quantph/9806029
 arXiv:
 arXiv:quantph/9806029
 Bibcode:
 1998quant.ph..6029A
 Keywords:

 Quantum Physics
 EPrint:
 20 pages, Latex. In ``Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computation (STOC)'', pages 2030, 1997