Related Experiment Video
Updated: Jul 15, 2026
14:55
Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy
Published on: September 17, 2017
Quantum state tomography for quadrupolar nuclei using global rotations of the spin system
J Teles1, E R deAzevedo, R Auccaise
1Instituto de Física de São Carlos, Universidade de São Paulo, P.O. Box 369, São Carlos 13560-970, São Paulo, Brazil. jteles@ifsc.usp.br
The Journal of Chemical Physics
|April 28, 2007
Summary
This study introduces a faster quantum state tomography method using shorter radiofrequency pulses for complete density matrix reconstruction. The technique is validated for single spin systems and applied to the Deutsch algorithm implementation.
Area of Science:
- Quantum Information Science
- Magnetic Resonance Spectroscopy
- Quantum Computing
Background:
- Quantum state tomography is crucial for characterizing quantum systems.
- Previous methods often require long radiofrequency (rf) pulses, limiting experimental efficiency.
- Efficient reconstruction of the density matrix is essential for understanding and controlling quantum states.
Purpose of the Study:
- To develop a faster and more efficient quantum state tomography method.
- To enable complete density matrix reconstruction using global rotations and coherence selection.
- To reduce the time required for quantum state tomography, particularly for quantum algorithms.
Main Methods:
- Utilizing global rotations of the spin system combined with a coherence selection scheme.
- Employing shorter radiofrequency (rf) pulses for faster spin manipulation.
- Describing spin state rotations using the irreducible tensor formalism.
- Simulating the method for a single spin-1/2 nucleus and applying it experimentally.
Main Results:
- Demonstrated feasibility of the method for a single spin-1/2 nucleus via simulations.
- Successfully applied the method to perform tomography during the implementation of the Deutsch algorithm on a (23)Na quadrupole nucleus.
- Extended the tomography method for a 3-coupled homonuclear spin-1/2 system, requiring additional evolution under the internal Hamiltonian.
Conclusions:
- The developed quantum state tomography method offers significant time reduction compared to previous techniques.
- The method is versatile, applicable to single spins, quantum algorithms, and multi-spin systems.
- This advancement facilitates more efficient characterization and control of quantum states in various NMR-based quantum information processing applications.
Related Concept Videos
01:03Atomic Nuclei: Nuclear Spin State Overview
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
01:08NMR Spectroscopy: Spin–Spin Coupling
The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
01:05Atomic Nuclei: Magnetic Resonance
The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
01:23Atomic Nuclei: Nuclear Relaxation Processes
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...
01:08Atomic Nuclei: Nuclear Spin
All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to...
Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to...