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Universal fault-tolerant quantum computation with only transversal gates and error correction.
Adam Paetznick1, Ben W Reichardt
1David R. Cheriton School of Computer Science and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Physical Review Letters
|September 17, 2013
Summary
Transversal gates are key for fault-tolerant quantum computation. This study shows triorthogonal stabilizer codes enable transversal controlled-controlled-Z gates, creating universal quantum computation without state distillation.
Area of Science:
- Quantum computation
- Quantum error correction
- Quantum information theory
Background:
- Transversal implementations of encoded unitary gates are crucial for fault-tolerant quantum computation.
- While transversal gates alone are not computationally universal, they can achieve universality when combined with distilled resource states.
Purpose of the Study:
- To demonstrate the transversal implementation of the controlled-controlled-Z gate using triorthogonal stabilizer codes.
- To construct a universal set of fault-tolerant quantum gates without relying on state distillation.
- To adapt existing distillation procedures for Toffoli gates.
Main Methods:
- Utilizing triorthogonal stabilizer codes for gate implementation.
- Combining transversal controlled-controlled-Z, transversal Hadamard, and fault-tolerant error correction.
- Adapting the Bravyi-Haah distillation procedure for Toffoli gates.
Main Results:
- Triorthogonal stabilizer codes admit transversal implementation of the controlled-controlled-Z gate.
- A universal set of fault-tolerant gates is constructed without state distillation.
- An improved Toffoli distillation scheme is developed.
Conclusions:
- Fault-tolerant quantum computation can be achieved without state distillation by leveraging specific transversal gates and error correction.
- The findings offer a more efficient pathway to universal quantum computation.
- The adapted Toffoli distillation scheme enhances existing methods.
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