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We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We provide equivalence transformations for these boundary conditions that can be used to simplify fault-tolerant circuits and to derive circuit identities in a topological manner. The spatial dimensionality of the scheme can be reduced to two by converting one spatial axis of the cluster into time. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors. The operational overhead is poly-logarithmic in the circuit size.
We review an approach to fault-tolerant holonomic quantum computation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the information remains protected.
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest level of
In the framework quotient algebra partition, a general methodology is introduced to construct fault tolerant encodes for an arbitrary action in an error-correcting code.
We extensively test a recent protocol to demonstrate quantum fault tolerance on three systems: (1) a real-time simulation of five spin qubits coupled to an environment with two-level defects, (2) a real-time simulation of transmon quantum computers,
We consider the problem of fault tolerance in the graph-state model of quantum computation. Using the notion of composable simulations, we provide a simple proof for the existence of an accuracy threshold for graph-state computation by invoking the t