Quantum information processing by nuclear magnetic resonance spectroscopy

Abstract

Three-qubit nuclear magnetic resonance quantum information processing with a single-crystal solid Toward quantum information processing by nuclear magnetic resonance: Pseudopure states and logical operations using selective pulses on an oriented spin 3/2 nucleus Nuclear magnetic resonance ͑NMR͒ is a direct macroscopic manifestation of the quantum mechanics of the intrinsic angular momentum of atomic nuclei. It is best known for its extraordinary range of applications, which include molecular structure determination, medical imaging, and measurements of flow and diffusion rates. Most recently, liquid-state NMR spectroscopy has been found to provide a powerful experimental tool for the development and evaluation of the coherent control techniques needed for quantum information processing. This burgeoning new interdisciplinary field has the potential to achieve cryptographic, communications, and computational feats far beyond what is possible with known classical physics. Indeed, NMR has made the demonstration of many of these feats sufficiently simple to be carried out by high school summer interns working in our laboratory ͑see the last two authors͒. In this paper the basic principles of quantum information processing by NMR spectroscopy are described, along with several illustrative experiments suitable for incorporation into the undergraduate physics curriculum. These experiments are spin-spin interferometry, an implementation of the quantum Fourier transform, and the quantum simulation of a harmonic oscillator.

Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds

“…This allows also to relax the requirement of commutativity of the measured observables and in fact we shall assume to have a complete knowledge of the density operator for all times. Although physically this set up is realistic only for some applications (typically nuclear spin ensembles [14,23]), it is of widespread use for the purposes of model-based quantum control (often under the name "tracking control" [12,38]), as it allows to generate control fields in spite of the high complexity of open loop control [10,16,34]. Furthermore, while the formulation comes from quantum control, our motivations for this work are mostly mathematical, namely feedback design and convergence analysis for a class of bilinear control systems living on a particular family of compact manifolds and evolving isospectrally.…”

Feedback Control of Spin Systems

“…These systems exhibit most of the essential features of quantum mechanical systems, like the state space of tensorial type (providing exponential growth of the degrees of freedom available) and natural coupling mechanisms between spins, which guarantee the nonclassical nonlocality characteristic of quantum evolutions. For the purposes of state manipulation, over the last 40 years the field of NMR has developed an extremely versatile and universally accepted set of tools, in the form of sequences of electromagnetic pulses [9,12,16]. In terms of classical control theory, these would be classified as open loop control methods.…”

Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups

“…(81) for varying periods of time, and the results {ρ out k } K k=1 determined by state tomography [2,3,25,26,27]. Assuming that the input states span the space of single-qubit Hermitian operators, this allows us to determine the propagators at each time point according to…”