Quantum Control in the Presence of Relaxation

1. Quantum Control in the Presence of Relaxation Benjamin Recht MIT Media Lab, 2002 Collaborators: Yael Maguire Seth Lloyd Isaac Chuang Neil Gershenfeld

2. Decoherence and Relaxation Quantum Classical Order Disorder

3. Correcting relaxation in NMR • Red: 90 pulse • Green: Spins Relax • Orange: Control Pulse • Push the spins back into the plane Induced signal with and without correction pulses

4. Recht Angle vs Ernst Angle • A new interpretation of an old result on steady-state NMR • In the limit where T1=T2 our schemes produce larger NMR signals and use smaller RF pulses

5. Waveform Shaping Spins Ringing Control Pulses We can write arbitrary envelopes on the spins using control pulses Zooming in, the spins process at their natural rate and we push them around

6. Preserving Entangled States We have numerically demonstrated the preservation of quantum information using only unitary operations Even under restrictive assumptions, we can store one third of an “ebit”