Compare Papers
Paper 1
A Quantum Complexity Lowerbound from Differential Geometry
Adam R. Brown
- Year
- 2021
- Journal
- arXiv preprint
- DOI
- arXiv:2112.05724
- arXiv
- 2112.05724
The Bishop-Gromov bound -- a cousin of the focusing lemmas that Hawking and Penrose used to prove their black hole singularity theorems -- is a differential geometry result that upperbounds the rate of growth of volume of geodesic balls in terms of the Ricci curvature. In this paper, I apply the Bishop-Gromov bound to Nielsen's complexity geometry to prove lowerbounds on the quantum complexity of a typical unitary. For a broad class of penalty schedules, the typical complexity is shown to be exponentially large in the number of qubits. This technique gives results that are tighter than all known lowerbounds in the literature, as well as establishing lowerbounds for a much broader class of complexity geometry metrics than has hitherto been bounded. For some metrics, I prove these lowerbounds are tight. This method realizes the original vision of Nielsen, which was to apply the tools of differential geometry to study quantum complexity.
Open paperPaper 2
Stochastic optimization for learning quantum state feedback control
Ethan N. Evans, Ziyi Wang, Adam G. Frim, Michael R. DeWeese, Evangelos A. Theodorou
- Year
- 2021
- Journal
- arXiv preprint
- DOI
- arXiv:2111.09896
- arXiv
- 2111.09896
High fidelity state preparation represents a fundamental challenge in the application of quantum technology. While the majority of optimal control approaches use feedback to improve the controller, the controller itself often does not incorporate explicit state dependence. Here, we present a general framework for training deep feedback networks for open quantum systems with quantum nondemolition measurement that allows a variety of system and control structures that are prohibitive by many other techniques and can in effect react to unmodeled effects through nonlinear filtering. We demonstrate that this method is efficient due to inherent parallelizability, robust to open system interactions, and outperforms landmark state feedback control results in simulation.
Open paper