We introduce a new model of fault tolerance for Boolean circuits. We consider synchronized circuits and we allow an adversary to choose a small constant fraction of the gates at each level of the circuit to be faulty. We require that even in the presence of such faults the circuit compute a \loose version" of the given function. We show that every symmetric function has a small (size O(n), dept...

A major challenge for quantum computation in ion trap systems is scalable integration of error correction and fault tolerance. We analyze a distributed architecture with rapid high fidelity local control within nodes and entangled links between nodes alleviating long-distance transport. We demonstrate fault-tolerant operator measurements which are used for error correction and non-local gates. ...

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. The concatenation scheme exploits the transversal properties of two different codes, combining them to provide a means to protect against low-weight arbitrary errors. We give the required properties of the error correcting codes to ensure universal fault tolerance and discuss ...

An important task required to build a scalable, fault-tolerant quantum computer is to efficiently represent an arbitrary single-qubit rotation by fault-tolerant quantum operations. Traditionally, the method for decomposing a single-qubit unitary into a discrete set of gates is Solovay-Kitaev decomposition, which in practice produces a sequence of depth O(log(1/ )), where c ∼ 3.97 is the state-o...

This paper attempts to establish the connection among classifications of gapped boundaries in topological phases of matter, bosonic symmetry-protected topological (SPT) phases and faulttolerantly implementable logical gates in quantum error-correcting codes. We begin by presenting constructions of gapped boundaries for the d-dimensional quantum double model by using d-cocycles functions (d ≥ 2)...

Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gaugefixing. Combining 2D and 3Dgauge color codes in a 3Dqubit lattice, fault-tolerant quantum computation can be achievedwith constant time overhead on the number of logical gates, up to efficient global classical computation, using only loc...

Fault tree analysis (FTA), as one of the powerful tools in reliability engineering, has been widely used to enhance system quality attributes. In most fault tree analyses, precise values are adopted to represent the probabilities of occurrence of those events. Due to the lack of sufficient data or imprecision of existing data at the early stage of product design, it is often difficult to accura...

Quantum error correction requires the measurement of error syndromes to properly locate and identify errors. Here we compare three syndrome measurement strategies for the [[7,1,3]] quantum error correction code: Shor states, Steane states, and one ancilla qubit. The first two of these strategies are fault tolerant while the third is not. For each strategy we compare the fidelities of applying 5...

We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show ho...

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a CNOT gate is 8.3 × 10. We also compute the fidelities of Z, X, Swap, and Controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable...