Control problems in quantum systems

Abstract

The past decade or two has witnessed tremendous progress in theory and practice of quantum control technologies. Bridging different scientific disciplines ranging from fundamental particle physics to nanotechnology, the goal of quantum control has been to develop effective and efficient tools for common analysis and design, but more importantly would pave the way for future technological applications. This article briefly reviews basic quantum control theory from the perspective of modeling, analysis and design, as well as considers future research directions. quantum control, control theory, quantum physics Citation: Wu R B, Zhang J, Li C W, et al. Control problems in quantum systems. Chin Sci Bull, 2012Bull, , 57: 2194Bull, -2199Bull, , doi: 10.1007 Quantum control refers to the design of control strategies in systems that obey the principles of quantum mechanics, e.g. microscopic systems with few atoms or photons that were addressed early in the lecture "Plenty of Room at the Bottom" given by Richard Feynman in 1959 [1]. This dream has been pursued since 1960s right after the invention of lasers, which illuminated the hope to coherently control chemical reaction processes, but it was not until the end of 20th century when a burst of successes occurred in controlling ultrafast quantum dynamics. Nowadays, quantum control protocols are being introduced to more fields such as quantum information processing [2] and nanomaterials and nanodevices [3].The inherent power afforded quantum control results from the unique nonclassical features of quantum mechanics. Essentially, orthogonal eigenstates of a quantum observable (corresponding classically identifiable states) can form superpositions and thereby span a much larger space of quantum states available for coherent manipulation; quantum tunneling allows crossing of energy barriers without as much work as in classical mechanics, thus potentially improve sensitivity and controllability. However, there is no free lunch *Corresponding author (email: rbwu@tsinghua.edu.cn) on the other side; these advantages can only be exploited under extreme spatial (atomic or subatomic) and temporal (femtosecond and attosecond) physical scales. To realize the power of quantum control, vulnerable coherence and entanglement in quantum states need to be protected and measured before being destroyed by intermediate interacting environments. The earliest quantum control studies from the 1960s to the 1980s focused on (macroscopic) quantum ensembles in plasmas and laser devices, nuclear accelerators, and nuclear power plants [4] (mostly in former Soviet Union), in which the systems were modeled as quantum harmonic oscillators, which have little difference with those from classical systems [5, 6]. In the 1980s, Tarn's group completed a series of studies on general (linear or nonlinear) quantum systems in regard to modeling [7], controllability [8], invertibility [9], and quantum nondemolition filter problems [10]. In Europe, Belavkin's investigations [11][12][13] on the optimal estimat...

Quantum control modeling beyond semiclassical approximation

“…It should be indicated that, when the environment is initially prepared at coherent states with large photon numbers, the convolutionless model (1) is more precise than (2). However, in the case that fluctuation is comparable with the mean value, there are no much difference in precision between them.…”

“…To resolve quantum control problems [1][2][3][4], a good mathematical model must be built up for analysis and design. From the very beginning of quantum control theory [5], semi-classical control models had been broadly used, in which the control parameters (e.g., an electromagnetic field) are taken as classical variables and the plant to be controlled is quantum.…”

Exploring Trends and Opportunities in Quantum‐Enhanced Advanced Photonic Illumination Technologies

“…[ 6 ] However, a major obstacle is to mitigate the problems of noise and decoherence, which lead to defects in the processing of quantum information due to the entanglement of qubits with external systems. [ 7 ] It is also important to provide simplified and efficient tools for the analysis and design of quantum control systems. Quantum control theory aims to improve these capabilities and prepare the ground for the next generation of technological applications.…”

Creation of quantum correlations via the initial classical-mixed states

“…The dynamics of QD and entanglement of two qubits in contact with an environment have been studied in the last decade theoretically as well as experimentally. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] It was shown that entanglement is very fragile and entanglement sudden death can occur, [6] while QD is more robust under decoherence and only presents an instantaneous disappearance at some time points in a non-Markovian regime and asymptotic decay in a Markovian regime. In particular, QD can be completely unaffected by decoherence channels for certain initial states, and this phenomenon has been observed experimentally.…”