How many CNOT gates does it take to generate a three-qubit state ?

12/2007; DOI: 10.1103/PhysRevA.77.032320
Source: arXiv

ABSTRACT The number of two-qubit gates required to transform deterministically a three-qubit pure quantum state into another is discussed. We show that any state can be prepared from a product state using at most three CNOT gates, and that, starting from the GHZ state, only two suffice. As a consequence, any three-qubit state can be transformed into any other using at most four CNOT gates. Generalizations to other two-qubit gates are also discussed.

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    ABSTRACT: Part I. Fundamental Concepts: 1. Introduction and overview; 2. Introduction to quantum mechanics; 3. Introduction to computer science; Part II. Quantum Computation: 4. Quantum circuits; 5. The quantum Fourier transform and its application; 6. Quantum search algorithms; 7. Quantum computers: physical realization; Part III. Quantum Information: 8. Quantum noise and quantum operations; 9. Distance measures for quantum information; 10. Quantum error-correction; 11. Entropy and information; 12. Quantum information theory; Appendices; References; Index.
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