Universal fault-tolerant measurement-based quantum computation

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 any protocol 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.

A fault-tolerant non-Clifford gate for the surface code in two dimensions

“…History has shown that the gates a given model is able to achieve is connected with the macroscopic properties of a system, not its microscopic details. Developing our understanding of measurement-based quantum computation in three dimensions by decomposing it in terms of its topological degrees of freedom (16,29) is likely to be a promising route toward better models of two-dimensional fault-tolerant quantum computation.…”

“…There are several constraints the system must satisfy if we realize a controlledcontrolled-phase gate with a two-dimensional system. We first point out that the orientation of boundaries of the topological cluster state is important for the transmission of logical information (29). More precisely, they constrain the temporal directions of the model.…”

“…It is worth remarking that the method we have discussed here enables us to produce other three-dimensional structures that go beyond foliation (38). Much research has sought to map quantum error-correcting codes into measurement-based schemes (29,39) through a system called "foliation" to access favorable properties of exotic quantum error-correcting codes. Conversely, some fault-tolerant measurement-based schemes have been developed that are not expected to have a description in terms of a quantum error-correcting code.…”

“…Further, we can initialize the surface code in an arbitrary state fault tolerantly if, before face measurements are made, we replace the unentangled qubits on one side of one boundary of the lattice with an encoded surface code, for instance, the gray face shown to the left of Fig. 1B (29). We refer to this face as the initial face.…”

Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer

“…Other lattices such as non-foliated lattices [85][86][87] or non-CSS codes [88] can also be considered, including possibly new lattice designs tailored to errors in CV quantum computing.…”