Decompositions of general quantum gates
Abstract
Quantum algorithms may be described by sequences of unitary transformations called quantum gates and measurements applied to the quantum register of n quantum bits, qubits. A collection of quantum gates is called universal if it can be used to construct any n-qubit gate. In 1995, the universality of the set of one-qubit gates and controlled NOT gate was shown by Barenco et al. using QR decomposition of unitary matrices. Almost ten years later the decomposition was improved to include essentially fewer elementary gates. In addition, the cosine-sine matrix decomposition was applied to efficiently implement decompositions of general quantum gates. In this chapter, we review the different types of general gate decompositions and slightly improve the best known gate count for the controlled NOT gates to (23/48)4^n in the leading order. In physical realizations, the interaction strength between the qubits can decrease strongly as a function of their distance. Therefore, we also discuss decompositions with the restriction to nearest-neighbor interactions in a linear chain of qubits.
Read the paper
Related studies
- In silico toxicology protocols
- QM7-X, a comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules
- Quantum Informed Machine-Learning Potentials for Molecular Dynamics Simulations of CO2's Chemisorption and Diffusion in Mg-MOF-74
- In-silico strategies in nano-drug design: Bridging nanomaterials and pharmacological applications
- mRNA codon optimization with quantum computers
- The computational power of the human brain
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.