I’m currently a graduate student in the Quantum Science and Technologies Group in the Hearne Institute for Theoretical Physics at Louisiana State University under the supervision of Mark Wilde. Previously, I was a Master’s student at the Institute for Quantum Computing at the University of Waterloo under the supervision of Norbert Lütkenhaus.

My research is in the general area of quantum information theory. For the past couple of years my focus has been on quantum cryptography, specifically quantum key distribution. I am also interested in quantum networks as well as quantum computing, specifically applying machine learning methods to quantum algorithms for near-term applications. Check out my research for details on what I’ve been working on, as well as my Google Scholar page and my papers on arXiv. I’ve also compiled a list of introductory resources on the topics pertaining to my research and to physics in general.

You can contact me at skhatr5 [at] lsu [dot] edu.

## Latest Papers

### Noise Resilience of Variational Quantum Compiling

Abstract:

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e., the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM’s noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

### Practical figures of merit and thresholds for entanglement distribution in quantum networks

Abstract:

Before global-scale quantum networks become operational, it is important to consider how to evaluate their performance so that they can be suitably built to achieve the desired performance. In this work, we consider three figures of merit for the performance of a quantum network: the average global connection time, the average point-to-point connection time, and the average largest entanglement cluster size. These three quantities are based on the generation of elementary links in a quantum network, which is a crucial initial requirement that must be met before any long-range entanglement distribution can be achieved. We evaluate these figures of merit for a particular class of quantum repeater protocols consisting of repeat-until-success elementary link generation along with entanglement swapping at intermediate nodes in order to achieve long-range entanglement. We obtain lower and upper bounds on these three quantities, which lead to requirements on quantum memory coherence times and other aspects of quantum network implementations. Our bounds are based solely on the inherently probabilistic nature of elementary link generation in quantum networks, and they apply to networks with arbitrary topology.

### Extendibility of bosonic Gaussian states

Abstract:

Extendibility of bosonic Gaussian states is a key issue in continuous-variable quantum information. We show that a bosonic Gaussian state is k-extendible if and only if it has a Gaussian k-extension, and we derive a simple semidefinite program, whose size scales linearly with the number of local modes, to efficiently decide k-extendibility of any given bosonic Gaussian state. When the system to be extended comprises one mode only, we provide a closed-form solution. Implications of these results for the steerability of quantum states and for the extendibility of bosonic Gaussian channels are discussed. We then derive upper bounds on the distance of a k-extendible bosonic Gaussian state to the set of all separable states, in terms of trace norm and Rényi relative entropies. These bounds, which can be seen as “Gaussian de Finetti theorems,” exhibit a universal scaling in the total number of modes, independently of the mean energy of the state. Finally, we establish an upper bound on the entanglement of formation of Gaussian k-extendible states, which has no analogue in the finite-dimensional setting.