Two-qubit quantum gate and entanglement protected by circulant symmetry

Area of Science:

• Quantum Information Science
• Quantum Computing
• Atomic Physics

Background:

• The quantum Fourier transform (QFT) is a fundamental quantum gate for many quantum algorithms.
• Implementing multi-qubit gates with high fidelity remains a significant challenge in quantum computing.

Purpose of the Study:

• To propose and numerically demonstrate a method for realizing the two-qubit quantum Fourier transform (QFT).
• To leverage circulant Hamiltonian symmetry for efficient QFT implementation in ion trap systems.

Main Methods:

• Utilizing a Hamiltonian with circulant symmetry, where eigenvectors are Fourier modes.
• Employing adiabatic transitions between spin product states and QFT superposition states.
• Simulating the process in ion traps by tuning spin-spin interactions.

Main Results:

• Achieved very high fidelity for the two-qubit QFT with realistic experimental parameters.
• Demonstrated that circulant symmetry is key, independent of Hamiltonian element magnitudes.
• Showcased the feasibility of implementing this QFT in ion trap systems.

Conclusions:

• The proposed method offers a viable route to high-fidelity two-qubit QFT implementation.
• Circulant symmetry provides a robust framework for quantum gate design in ion traps.
• The technique can be further accelerated using shortcut-to-adiabaticity methods.