Efficient simulation of controlled large quantum systems

Abstract

Engineers are looking to produce technologies that exploit the full quantum nature of a system, including quantum computing, quantum communication and quantum metrol- ogy. Quantum control allows engineers to modify the behaviour of the full quantum state of a system, which will be an important part of making these technologies commercially viable. If these technologies are to be competitive, they must be scaled up to large sizes. We produce a novel toolset which can be used to simulate large con- trolled quantum systems efficiently. We target this toolset at a large quantum system that can immediately benefit: Bose-Einstein Condensates (BECs). We first develop the Controlled Fokker-Planck Equation (CFPE), which allows scalable simulation of a controlled BEC. We find using coherent-state-based methods to generate a CFPE produces solutions with severely limited integration times, as monitoring of a BEC is intrinsically involves continuous 'number-like' measurements. To solve this problem, we develop a novel representation based on number state which acts in harmony with the measurement: the Number-Phase Wigner (NPW) representation. The NPW method efficiently and accurately simulates controlled BECs. It converges over 4 orders of mag- nitude longer than its closest coherent-state-based competitor. Using the NPW we are able to perform the first full-field analysis of a BEC under a cooling feedback control. We find that quantum noise produces heating in BECs that was not previously pre- dicted using approximate methods. We remove the effects of quantum noise with the creation of a novel control. Show more