Simulating Quantum Operations with Mixed Environments

B. Terhal


One of the possible applications of a future quantum computer is the study of the behavior of open quantum systems and the nature of decoherence. For these tasks the quantum computer must be prepared to perform quantum operations that in general will involve an ``environment'', i.e., a quantum system is discarded at some point in the calculation. We study the space-efficiency of the implementation of such quantum operations in terms of the dimension of the environment. In particular, we study a class of quantum operations on a qubit input, the generalized depolarizing channel, for which we show that qutrit environment is sufficient to implement any channel in this class, whereas not all of these channels can be implemented using a qubit environment. The ``2 Pauli'' channel is one such channel that cannot be implemented with a qubit-environment and an explicit proof using the Gröbner-basis technique is given for this case.