Abstract
Certain physical systems that one might consider for fault-tolerant quantum computing where qubits do not readily interact, for instance photons, are better suited for measurement-based quantum-computational protocols. Here we propose a measurement-based model for universal quantum computation that simulates the braiding and fusion of Majorana modes. To derive our model we develop a general framework that maps any scheme of fault-tolerant quantum computation with stabilizer codes into the measurement-based picture. As such, our framework gives an explicit way of producing fault-tolerant models of universal quantum computation with linear optics using protocols developed using the stabilizer formalism. Given the remarkable fault-tolerant properties that Majorana modes promise, the main example we present offers a robust and resource efficient proposal for photonic quantum computation.
Highlights
Wherever there is ambiguity, we will refer to the qubits that lie in a cluster state as “physical qubits.”
We review here a foliated qubit where the physical qubits of the entangled chain are measured in the Pauli-X basis
The examples of resource states we have considered here are by no means exhaustive and other variations can be made following the general principles of foliation given in the previous section, but given the multitude of variations one could come up with we leave further experimentation to the reader
Summary
Considerable experimental effort [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] is being dedicated to the realization of linear optical quantum computation [19,20] due to the extensive coherence times that photonic qubits promise. Measurement-based quantum computation [29,30,31,32,33] provides a natural language to describe computational operations with flying qubits In this picture we initialize a specific manybody entangled resource state which is commonly known as a cluster state. Owing to its high threshold error rates [38,39,40] and simplicity in its design [20,41,42,43], the topological cluster state is the prototypical model for robust fault-tolerant measurement-based quantum computation [44]. We remark on recent work [64,65] on measurement-based quantum computation where the topological cluster-state model is generalized to find robust codes, and Refs. Appendix A describes an alternative type of foliated qubit, Appendix B gives proofs of technical theorems we state in the main text, Appendix C discusses foliated subsystem codes, and Appendix D gives a generalization of the foliated stabilizer codes we propose
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