New Approach to Topological Quantum Computation Promises Scalability and Fault-Tolerance, Researchers Say

The article explores a new approach to topological quantum computation (TQC), a promising method for scalable, fault-tolerant quantum computation. The authors, Sam Roberts and Dominic J Williamson present a scheme for universal TQC based on Clifford-complete braiding and fusion of symmetry defects in the 3fermion anyon theory. They also discuss the Walker-Wang model’s contribution to TQC and the role of the 3Fermion anyon theory. This new approach provides a general framework for finding fault-tolerant resource states for universal computation, opening up new possibilities for scalable, fault-tolerant quantum computation and paving the way for future research.

What is the New Approach to Topological Quantum Computation?

The article discusses a new approach to topological quantum computation (TQC), could be a promising method for scalable, fault-tolerant quantum computation. The focus has been on TQC with Kitaev’s toric code due to its high threshold to noise and amenability to planar architectures with nearest-neighbor interactions. To encode and manipulate quantum information in the toric code, various techniques drawn from condensed-matter contexts have been utilized. Some of the efficient approaches for TQC with the toric code rely on creating and manipulating gapped boundaries, symmetry defects, and anyons of the underlying topological phase of matter.

The article was written by Sam Roberts from the Centre for Engineered Quantum Systems School of Physics at The University of Sydney and Dominic J Williamson from the Stanford Institute for Theoretical Physics at Stanford University. They present a scheme for universal TQC based on Clifford-complete braiding and fusion of symmetry defects in the 3fermion anyon theory supplemented with magic state injection. They also formulate a fault-tolerant measurement-based realization of this computational scheme on the lattice using ground states of the Walker-Wang model for the 3fermion anyon theory with symmetry defects.

How Does the Walker-Wang Model Contribute to TQC?

The Walker-Wang model provides a rich class of spin-lattice models in three dimensions, the boundaries of which can naturally be used to topologically encode quantum information. The 2D boundary phases of Walker-Wang models accommodate a richer set of possibilities than standalone 2D topological phases realized by commuting-projector codes. The Walker-Wang construction prescribes a Hamiltonian for a given input degenerate anyon theory, the ground states of which can be interpreted as a superposition over all valid world lines of the underlying anyons.

The authors focus on a particular instance of the Walker-Wang model based on the 3fermion anyon theory. They show that the associated ground states can be utilized for fault-tolerant measurement-based quantum computation (MBQC) via a scheme based on the braiding and fusion of lattice defects constructed from the symmetries of the underlying anyon theory. The resource states required for the computation can be prepared with a Clifford circuit acting on a 2D grid with only nearest-neighbor interactions.

What is the Role of the 3Fermion Anyon Theory in TQC?

The 3Fermion anyon theory, or 3Ftheory, is an interesting and nontrivial example of the power of the Walker-Wang model framework. Owing to the rich set of symmetries of the 3Ftheory, a universal scheme for TQC can be found where all Clifford gates can be fault-tolerantly implemented and magic states can be noisily prepared and distilled. In particular, the full Clifford group in this scheme can be obtained by braiding symmetry-twist defects. This is in contrast to the 2D toric code where only a subgroup of Clifford operators can be achieved by braiding symmetry-twist defects when using qubit encodings with fixed charge parity.

The 3FWalker-Wang model, and consequently the TQC scheme that is based on it, is intrinsically 3D as there is no commuting-projector (e.g., stabilizer) code in two dimensions that realizes the 3Ftheory. This improved computational capability is derived from the symmetries of the anyon theory, S3 for the 3Ftheory and Z2 for the toric code, as both the toric code and 3Fanyon theories consist of four anyons.

What is the Significance of this New Approach to TQC?

The new approach to TQC presented in the article is significant because it provides a general framework for finding fault-tolerant resource states for universal computation. For example, the well-known topological cluster-state scheme for MBQC is produced when the toric code anyon theory is used as input to the Walker-Wang construction. Therefore, the approach provides a generalization of the topological cluster-state scheme, which is based on the toric code anyon theory, to general Abelian anyon models.

Despite great advances, the overheads for universal fault-tolerant quantum computation remain a formidable challenge. It is therefore important to analyze the potential of TQC in a broad range of topological phases of matter and attempt to find new computational substrates that require fewer quantum resources to execute fault-tolerant quantum computation. The new approach to TQC presented in the article is a step in this direction.

What are the Future Implications of this Research?

The research presented in the article has important implications for the future of quantum computation. The new approach to TQC based on the Walker-Wang model and the 3Fermion anyon theory opens up new possibilities for scalable, fault-tolerant quantum computation. The approach provides a general framework for finding fault-tolerant resource states for universal computation, which is a significant step towards overcoming the formidable challenge of the overheads for universal fault-tolerant quantum computation.

The research also demonstrates how symmetry defects of the 3fermion anyon theory can be realized in a two-dimensional subsystem code due to Bombín making contact with an alternative implementation of the 3fermion defect-computation scheme via code deformations. This opens up new avenues for further research and development in quantum computation.