Between 2006 and 2010, I wrote a PhD thesis on quantum control theory in the Department for Applied Mathematics and Theoretical Physics at Cambridge University, UK.
Working with my supervisor Sophie Schirmer and Alastair Kay, I published a series of papers addressing the following questions:
- If you produce a quantum system, can you efficiently work out what you have made without measuring all parameters independently? (Hamiltonian system identification)
- Can you control a large quantum system even if you can only interact with a small part of it? (controllability)
- How much of a simple quantum system do you need to control in order to make it capable of all computations of a certain class? (computational complexity)
These questions have some very surprising answers - see my papers for details!
Papers
Perfect Quantum Routing in Regular Spin Networks
Peter J. Pemberton-Ross and Alastair Kay, Phys. Rev. Lett. 106, 02050
Computation on spin chains with limited access
Alastair Kay and Peter J. Pemberton-Ross, Phys. Rev. A 81, 010301(R)
Fast high-fidelity information transmission through spin-chain quantum wires
S. G. Schirmer and Peter J. Pemberton-Ross, Phys. Rev. A 80, 030301(R)
Quantum control theory for state transformations: Dark states and their enlightenment
Peter J. Pemberton-Ross, Alastair Kay, and Sophie G. Schirmer, Phys. Rev. A 82, 042322
Global controllability with a single local actuator
S. G. Schirmer, I. C. H. Pullen, and Peter J. Pemberton-Ross, Phys. Rev. A 78, 062339
Symmetry and Subspace Controllability for Spin Networks With a Single-Node Control
Xiaoting Wang ; Pemberton-Ross, P. ; Schirmer, S.G., IEEE Transactions on Automatic Control, 57, Issue 8