Noisy Quantum Communication and Computation
Final rept. 21 Apr 2003-20 Jul 2006
TUFTS UNIV MEDFORD MA
Pagination or Media Count:
Proposals for adiabatic quantum computation generated renewed interest and questions about the adiabatic approximation. We presented a simple proof of the adiabatic theorem in which we showed that the first order correction has the expected dependence on an energy gap however, determining the time scale needed to ensure a small error may require consideration of higher order terms. We also give a simple new proof of the key gap estimates needed to who that a quantum circuit can be approximated by adiabatic evolution in time polynomial in the number of gates our methods also improve one of the estimates. We obtained a number of new results about quantum channels, including several results about the conjugate channels obtained by reversing the roles of the system and environment. We considered several new classes of unital channels, one of which leads to the construction of new bound entangled states. We defined the concept of minimal conditional information of an channel and showed that it gives a measure of the extent to which channel breaks entanglement. We also proved some mathematical results about norms of channels with implications for channel capacity and error correction.
- Quantum Theory and Relativity
- Solid State Physics