Fault-tolerant quantum computation with local interactions

Hwang, Yongsoo

We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes. To realize fault-tolerant quantum computing, the fault-tolerant quantum protocols should be transformed into executable quantum circuits based on the nearest-neighbor interaction. Unlike topological codes that are defined based on local operations fundamentally, for the concatenated codes, it is possible to obtain the circuits composed of the local operations by applying the quantum circuit synthesis. However, by the existing quantum circuit synthesis developed for ordinary quantum computational algorithms, the fault-tolerant of the protocol may not be preserved in the resulting circuit. Besides, we have to consider something more to implement the quantum circuit of universal fault-tolerant quantum computing. First, we have not to propagate quantum errors on data qubits when selecting a qubit move path (a sequence of \emph{SWAP} gates) to satisfy the geometric locality constraint. Second, the circuit should be self-contained so that it is possible to act independently regardless of the situation. Third, for universal fault-tolerant quantum computing, we require multiple fault-tolerant quantum circuits of multiple fault-tolerant quantum protocols acting on the same input, a logical data qubit. Last, we need to recall fault-tolerant protocols such as syndrome measure and encoder implicitly include classical control processing conditioned on the measurement outcomes, and therefore have to partition the quantum circuits in time flow to execute the classical control as the architect intended. We propose the circuit synthesis method resolving the requirements and show how to synthesize the set of universal fault-tolerant protocols for $[[7,1,3]]$ Steane code and the syndrome measurement protocol of $[[23, 1, 7]]$ Golay code.

Simon J. Devitt, Austin G. Fowler, Lloyd C. L. Hollenberg

Barbara M. Terhal, Guido Burkard

We derive a threshold result for fault-tolerant quantum computation for local non-Markovian noise models. The role of error amplitude in our analysis is played by the product of the elementary gate time ${t}_{0}$ and the spectral width of the interaction Hamiltonian between system and bath. We discuss extensions of our model and the applicability of our analysis.

Earl T. Campbell, Barbara M. Terhal, Christophe Vuillot

David Peter Divincenzo

Panos Aliferis, Barbara M. Terhal

We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage faults by using so-called leakage reduction units such as quantum teleportation. We describe ways to limit the use of leakage reduction while keeping the quantum circuits fault-tolerant. We also show that measurement-based computation is inherently tolerant against leakage faults. 1