Bharath Hebbe Madhusudhana

On paper, the quantum control of N qubits is a 2^N x 2^N unitary matrix. But in our labs, it is always something non-unitary, due to errors. Unitaries are a 4^N dim manifold and general quantum maps are a 16^N dimensional manifold (i.e., the set of completely positive trace-preserving maps). There is a lot of “space” outside the set of unitary operations, which can be classified into Markovian and non-Markovian processes (Fig). 

The goal of this line of research is to develop a set of tools, which would allow us to look at an experimental dataset and determine what forms of errors are present in the experiment and in what proportion. 

RCM tomography is one such tool. See this paper and this paper.  A quantum process acting on N-qubits is represented by a 4^N x 4^N Choi matrix. We define the reduced Choi matrix (RCM) corresponding to a subset of the N qubits as the corresponding partial trace of the Choi matrix. Intuitively, the RCM represents the process as seen by the subsystem.

I am also interested in finding practical quantum advantages (PQA) of near-term quantum devices, based on ultracold atoms. That is, to find computational tasks that satisfy three conditions: (i) useful, (ii) can be accomplished on a near-term device and (iii) for which we currently don't have an efficient classical algorithm. Finally, I am also interested in addressing the logistical problem of building increasingly complex ultracold atoms labs, within an academic setting.  Accordingly, I have the below objectives:

• Use a quantum simulator to develop quantum certified approximations (QCA) for many-body problems that don't have an efficient classical algorithms (see this paper and Applications to many-body physics for more details.)

Tweezer

Neutral atoms in a tweezer array are a very versatile platform, in particular to address the likes of the questions discussed above;  and it versatility is enhanced by having more lasers through the high resolution objectives in the setup. Adding laser post-build up of the experiment comes with two challenges: (i) projection through the high resolution objectives is extremely sensitive to mechanical alignment and (ii) the high resolution objective maynot be designed for all wavelengths and may introduce small aberrations. To address these challenges, in this work, we explore automation of mechanical alignment using a new algorithm — the modified AM algorithm, inspired by the cross-walking of laser beams.