Programme:

The meeting will be held in Seminar room 3 of the new Postgraduate Center. The program will start at 1.00pm and finish by 5pm, perhaps earlier. Feel free to turn up somewhat earlier for informal discussion, lunch or a coffee together.

Ingo Kamleitner, Macquarie University, Sydney, will be speaking about open quantum systems, more specifically, a quantum-mechanical description of Brownian motion. Shashank Virmani, University of Strathclyde - will talk on Fault tolerance and the classical simulation of noisy quantum computers. Richard Warburton, Heriot-Watt University will also give a talk- title TBA, but most likely related to quantum dots. Mark Hillery from Hunter College, CUNY, will also be visiting at the time.

Attendance is free. If you would like to attend, please send an email to Erika at E.Andersson@hw.ac.uk by 15 June. If you register after this, attending is most probably also fine, but it would be good to know roughly how many people are coming. People from outside Scotland are very welcome, although we have very limited possibilities to offer travel support.

Talk Abstract: Collisional quantum Brownian motion in one dimension
Ingo Kamleitner, Macquarie University, Sydney

In classical Brownian motion, a random walk like trajectory can be assigned to the particle of interest. The free particle evolution is interrupted by random momentum “jumps" due to collisions with surrounding gas particles, a process which leads to momentum diffusion. There is no intrinsic position diffusion present (although the position does diffuse in the long term due to momentum uncertainty).

In collisional quantum Brownian motion (CQBM), various authors [1-3] find additional position diffusion and it is argued that any master equation describing quantum friction must include position diffusion in order be completely positive. This observation is somewhat counter intuitive as it corresponds to random position jumps, which are not even possible in classical dynamics.

We first refine the approach of Barnett and Cresser [4], and identify appropriate Kraus operators for a single collision undergone by the Brownian particle from an exact solution of the Schrödinger equation for a gas particle and the Brownian particle interacting via a hard-core potential. A Markovian master equation is then constructed, this step involves introducing a coarse grained time scale large compared to the collision time (as do [1-3]). We show that it is this approximative procedure which results in a master equation which gives the illusion of position diffusion taking place. A more detailed solution on a finer time scale (which would almost certainly result in a non-Markovian master equation) would therefore not be expected to contain such a term, as can be seen to be the case in the work of Hu et al [5].

We test our master equation by calculating equations of motion of the expectation values of the two lowest order moments of position and momentum. We recover the full set of
classical equations. If the Brownian particle’s velocity is comparable (or even large as in a cloud chamber) to the thermal velocity of the gas particles, this includes non-linear
friction.

[1] L. Diósi, Europhys. Lett. 30, 63 (1995).
[2] B. Vacchini, Phys. Rev. Lett. 84, 1374 (2000).
[3] K. Hornberger, Phys. Rev. Lett. 97, 060601 (2006).
[4] S. M. Barnett, J. Jeffers, and J. D. Cresser, Phys. Rev. A 72, 022107 (2005).
[5] B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992).

Talk Abstract: Noise Resistance and the Classical Simulation of Quantum Computers
Shashank Virmani, University of Strathclyde

An interesting open problem in QI is how much noise a quantum architecture can tolerate before it becomes incapable of acting as a quantum computer - the so called `fault tolerance threshold'. In this talk I discuss the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works this approach has been used to derive upper bounds to fault tolerance thresholds - usually by identifying a privileged resource, such as an entangling gate or a non-Clifford operation, and then deriving the noise levels required to make it `unprivileged'. In this work we consider extensions of this approach where noise is added to Clifford gates too, and then `commuted' around until it concentrates on attacking the non-Clifford resource. While commuting noise around is not always straightforward, we find that easy instances can be identified in popular fault tolerance proposals, thereby enabling sharper upper bounds to be derived in these cases. For some schemes this can be quite effective - in the case of Knill's high threshold scheme for example, where the thresholds is conjectured to be higher than 3%, we can show that it is certainly no higher than around 13%, and this can probably be reduced further.

Directions
Heriot-Watt Campus Map, the Postgraduate Centre is building 8. Seminar room 3 where we will have the meeting is 3.04, on level 3.

This meeting is supported by SUPA and QQQ.