Two-bit gates are universal for quantum computation

Two-bit gates are universal for quantum computation

June 24, 1994 | David P. DiVincenzo
The paper discusses the universality of two-bit gates in quantum computation, a key step towards building a practical quantum computer. The author, David P. DiVincenzo, from IBM Research Division, argues that while three-bit gates were previously shown to be sufficient for constructing any quantum network, two-bit gates are more feasible to implement in physical systems due to their simpler nature. Two-bit gates can be realized using magnetic resonance operations on pairs of electronic or nuclear spins, and the proposed "quantum gearbox" design aims to achieve long phase coherence times by isolating individual spins during operations. DiVincenzo provides a proof using Lie group theory that two-bit gates are sufficient to generate any arbitrary quantum network. He demonstrates this by showing how a specific three-bit gate can be realized using a sequence of two-bit gates, and further extends this to prove that all necessary three-bit operations can be executed using two-bit gates. This proof is crucial for understanding the feasibility of quantum computing and the potential for practical quantum logic design. The paper also highlights the challenges in realizing quantum computers, such as the need for long phase coherence times and the difficulty in error correction. Despite these challenges, the author emphasizes the importance of quantum computing in addressing complex computational problems, particularly in areas like prime factorization and graph isomorphisms. The work concludes by suggesting new physics experiments that could be conducted using two-bit gates, such as studying quantum entanglement and teleportation.The paper discusses the universality of two-bit gates in quantum computation, a key step towards building a practical quantum computer. The author, David P. DiVincenzo, from IBM Research Division, argues that while three-bit gates were previously shown to be sufficient for constructing any quantum network, two-bit gates are more feasible to implement in physical systems due to their simpler nature. Two-bit gates can be realized using magnetic resonance operations on pairs of electronic or nuclear spins, and the proposed "quantum gearbox" design aims to achieve long phase coherence times by isolating individual spins during operations. DiVincenzo provides a proof using Lie group theory that two-bit gates are sufficient to generate any arbitrary quantum network. He demonstrates this by showing how a specific three-bit gate can be realized using a sequence of two-bit gates, and further extends this to prove that all necessary three-bit operations can be executed using two-bit gates. This proof is crucial for understanding the feasibility of quantum computing and the potential for practical quantum logic design. The paper also highlights the challenges in realizing quantum computers, such as the need for long phase coherence times and the difficulty in error correction. Despite these challenges, the author emphasizes the importance of quantum computing in addressing complex computational problems, particularly in areas like prime factorization and graph isomorphisms. The work concludes by suggesting new physics experiments that could be conducted using two-bit gates, such as studying quantum entanglement and teleportation.
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[slides and audio] Two-bit gates are universal for quantum computation.