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Related Concept Videos

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR 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...
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

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Related Experiment Video

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Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots
15:47

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

Published on: November 1, 2013

Universal set of quantum gates for double-dot spin qubits with fixed interdot coupling.

Ronald Hanson1, Guido Burkard

  • 1Center for Spintronics and Quantum Computation, University of California, Santa Barbara, California 93106, USA.

Physical Review Letters
|March 16, 2007
PubMed
Summary

We present universal gate operations for singlet-triplet qubits using electrical bias in double quantum dots. This method avoids complex time-dependent controls for robust quantum computing.

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Area of Science:

  • Quantum computing
  • Solid-state physics
  • Quantum information science

Background:

  • Singlet-triplet qubits utilize two-electron spins in double quantum dots.
  • Implementing universal gate operations is crucial for quantum computation.
  • Existing methods often require complex time-dependent control of tunnel coupling.

Purpose of the Study:

  • To propose a set of universal gate operations for singlet-triplet qubits.
  • To achieve these operations using only electrical bias.
  • To avoid time-dependent control of tunnel coupling.

Main Methods:

  • Analysis of two-electron spin dynamics in a double quantum dot.
  • Utilizing a fixed inhomogeneous magnetic field.
  • Applying electrical bias to switch potential offset between dots.

Main Results:

  • Demonstrated that all gate operations can be achieved by electrical bias.
  • Calculated effective qubit rotation angles based on applied electric bias.
  • Presented explicit gate sequences for single-qubit rotations and a CNOT gate.

Conclusions:

  • A universal gate set for singlet-triplet qubits is achievable with electrical bias.
  • This approach simplifies qubit control and enhances robustness.
  • The proposed method contributes to the development of practical quantum computers.