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Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits
Guanyu Zhu1, Ali Lavasani1, Maissam Barkeshli1
1Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA.
Physical Review Letters
|August 16, 2020
Summary
Quantum error correcting codes enable braiding non-Abelian anyons using constant-depth circuits. This advances universal quantum gate implementation without increasing space overhead, making braiding effectively instantaneous.
Area of Science:
- Quantum computation theory
- Quantum error correction
- Topological quantum computing
Background:
- Understanding space-time resource costs for universal quantum gates is crucial.
- Non-Abelian anyons are key for topological quantum computation.
- Current braiding methods are often adiabatic and resource-intensive.
Purpose of the Study:
- To determine efficient methods for braiding non-Abelian anyons in Turaev-Viro codes.
- To develop constant-depth local unitary quantum circuits for braiding operations.
- To assess the impact on space-time resource costs and error propagation.
Main Methods:
- Utilized Turaev-Viro quantum error correcting codes.
- Employed constant-depth local unitary quantum circuits for braiding anyons.
- Analyzed error string growth and space overhead scaling.
Main Results:
- Demonstrated braiding of non-Abelian anyons over distances of the code distance.
- Achieved universal logical gate sets using constant-depth circuits for the Fibonacci code.
- Showed that error string lengths grow by only a constant factor, ensuring protected gates.
Conclusions:
- Braiding in quantum error correcting codes can be achieved efficiently with constant-depth circuits.
- This approach does not increase asymptotic space overhead, offering a practical path to universal quantum computation.
- Reformulated braiding as an effectively instantaneous process, contrasting with traditional adiabatic methods.
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