Quantum fault-tolerant circuits

I. S. Osborne

Hafiz Md. Hasan Babu

This part of the book describes some background and preliminary studies of quantum fault-tolerant circuits in this chapter. The approach for designing a fault tolerant quantum adder (full-adder) is given in this chapter. A design for a fault tolerant multiplier (signed multiplier) is also shown. Finally, the design procedure for a quantum fault-tolerant integer division circuit is introduced in this chapter. In this design a restoring division algorithm as well as quantum restoring integer division circuitry are introduced.

Yasunari Suzuki

David Y. Feinstein, Vivek Nair, Mitchell Aaron Thornton

We study developments in quantum computing (QC) testing and fault tolerance (FT) techniques and discuss several attempts to formalize quantum logic fault models. We illustrate the inherent need for fault tolerance in QC due to the decoherence problem. Further, we examine several ideas regarding random testing and examine the viability of built-in-system-test (BIST) in future QC circuits.

Alexander M. Dalzell, Sam McArdle, Mario Berta +10 more

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.