I am mainly interested in applying tools from quantum information to apply to other areas of physics, such as condensed matter and many-body physics of atomic, molecular and optical systems. A major theme of my Ph.D research is that of computational complexity theory, and what statements we can make about physical systems using complexity theory.
“Entanglement Bounds on the Performance of Quantum Computing Architectures”, arXiv:1908.04802 (with Zachary Eldredge, Leo Zhou, Aniruddha Bapat, James Garrison, Frederic Chong, and Alexey Gorshkov).
This work has the same motivation as arXiv:1808.07876, where we evaluate graphs that prescribe how to wire up different modules of a quantum computer. We deal with the more general case of measurements and feedback here and show a lower bound on the time required to create highly-entangled states on graphs. We also show that this bound can be saturated up to a logarithmic factor in the number of qubits.
“Complexity phase diagram for interacting and long-range bosonic Hamiltonians”, arXiv:1906.04178 (with Nishad Maskara, Minh Tran, Adam Ehrenberg, Bill Fefferman, and Alexey Gorshkov).
This work is in the same vein as arXiv:1703.05332 (paper #3 below). We classify a family of bosonic Hamiltonians based on the complexity of simulating its time evolution on a classical computer and draw a “complexity phase diagram” for the system, a slice of which is shown in the paper. This illustrates how computational complexity theory may have something to say about phases in many-body physics.
“Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator”, arXiv:1906.02700 (with Guido Pagano, Aniruddha Bapat, Patrick Becker, Katherine Collins, Arinjoy De, Paul Hess, Harvey Kaplan, Antonis Kyprianidis, Wen-Lin Tan, Christopher Baldwin, Lucas Brady, Fangli Liu, Stephen Jordan, Alexey Gorshkov, and Christopher Monroe).
This work experimentally demonstrates a quantum approximate optimisation algorithm (QAOA) on an ion trap to find the ground state energy of the long-range transverse-field Ising model. On the theory side, we supplement this study with observations on how the optimal parameters in the algorithm behave with increasing system size and depth, and an extension of Farhi and Harrow’s proof of exact sampling hardness to the approximate case.
” Unitary Entanglement Construction in Hierarchical Networks”, Physical Review A 98 (6), 062328, arXiv:1808.07876 (with Aniruddha Bapat, Zachary Eldredge, James Garrison, Frederic Chong, and Alexey Gorshkov).
In this paper we examine the tradeoff between speed and cost when deciding how to wire together different modules of a quantum computer. We give a class of networks called “hierarchical networks” and show that they have favourable properties for creating large entangled states. The ease of describing these networks also leads to good strategies for deciding how to map algorithm qubits to machine qubits.
“Dynamical phase transitions in sampling complexity”, Physical Review Letters 121 (3), 030501, arXiv:1703.05332 (with Bill Fefferman, Minh Tran, Michael Foss-Feig, and Alexey Gorshkov).
In this paper we argue that studying quantum computational supremacy is useful in other areas of physics too- namely to delineate phases and identify phase transitions in many-body physics. This is because complexity theory inherently gives us a way of classifying systems into “easy” or “hard” (to simulate on a classical computer), and classification is ubiquitous in physics.
Also see coverage here.
“Lattice Laughlin states on the torus from conformal field theory”, Journal of Statistical Mechanics: Theory and Experiment 2016 (1), 013102, arXiv:1507.04335 (with Anne Nielsen).
Here we derive the analogue of Laughlin wavefunctions for lattices with periodic boundary conditions, and derive various properties of these states, such as the modular S-matrix (which describes the phases picked up by anyons upon braiding them around each other).
“Remote tomography and entanglement swapping via von Neumann–Arthurs–Kelly interaction”, Physical Review A 89 (5), 052107, arXiv:1308.2852 (with S. M. Roy and Nitica Sakharwade).
In this paper, we give a method to perform remote tomography on a particle (say photon) without sending or teleporting it directly. In order to transmit information about the particle of interest, we use a “von Neumann-Arthurs-Kelly interaction” between the particle and two other particles that are more amenable to long-distance communication over telecom wavelengths.