Quantum
computation through quantum control
Over the past several
years, it has become clear that the physical implementation of logical
gates in
quantum information processing (QIP) may be facilitated by using the methods of optimal control theory (OCT). My work in this area consists of identifying and studying the control fields that implement these gates with maximal fidelity in diverse classes of quantum systems. We have developed numerical algorithms for control field search as well as design principles governing the best choice of quantum system for the implementation of a particular logical gate.
Prior work on the implementation of quantum gates using OCT has been directed toward discrete quantum information processing, as hypothetically carried out on the so-called quantum spin computers originally discussed by Benioff and Feynman.
quantum information processing (QIP) may be facilitated by using the methods of optimal control theory (OCT). My work in this area consists of identifying and studying the control fields that implement these gates with maximal fidelity in diverse classes of quantum systems. We have developed numerical algorithms for control field search as well as design principles governing the best choice of quantum system for the implementation of a particular logical gate.
Prior work on the implementation of quantum gates using OCT has been directed toward discrete quantum information processing, as hypothetically carried out on the so-called quantum spin computers originally discussed by Benioff and Feynman.
Optimal control theory for continuous variable quantum gates
R. Wu, and R. Chakrabarti and H. Rabitz, Phys. Rev. A 77, 052303 (2008) (13 pages).
Eprint arXiv:0708.2118 [quant-ph]
Quantum information can also be carried by continuous (infinite-dimensional) systems, such as a harmonic oscillator, rotor, or modes of the electromagnetic field.Compared to discrete QIP, continuous-variable QIP has several practical advantages, originating for example in the high bandwidth of continuous degrees of freedom, that have spurred substantial interest in its generic properties. Significant advances have recently been made in the experimental implementation of continuous quantum information processing, including the demonstration of quantum teleportation over continuous variables
As experimental methodologies improve, it becomes important to consider how such implementations could be enhanced through the systematic application of OCT. In this paper, we investigate the implementation of continuous variable quantum gates via OCT. We apply the methodology of optimal control theory to the problem of implementing quantum gates in continuous variable systems with quadratic Hamiltonians.
In this paper, the optimal control of several quantum computing gates, as well as that of algorithms composed of these primitives, is investigated using several typical physical models and compared for discrete and continuous quantum systems. Numerical simulations indicate that the optimization of generic CV quantum gates can be routinely achieved for all the major classes of computing primitives.
Next steps
Two outstanding challenges in quantum gate control theory are: 1) control in the presence of quantum decoherence; 2) the development of algorithms capable of systematically searching families of control fields that implement the gate of interest, for those that minimize auxiliary physically costs on the control field or total dynamical time. These tasks (in particular 2) are facilitated by foundational studies of the properties of quantum control landscapes. The proposal "Optimal control landscapes for quantum information processing" explains how.