General logical linear nearest neighbor (LLNN) architecture for fault-tolerant quantum computation

Abstract

We present a general scheme for implementing fault-tolerant quantum computation. We discuss a general two-dimensional architecture of qubits involving only linear nearest neighbor interactions. Between the qubits by using ancillas, we show how to implement gate operations for encoding, error correction, fault-tolerant quantum computation and decoding procedures in our design. The architecture is designed with two different coupling parameters ξ1and ξ2 between the qubits. A universal set of gate operations (Controlled-NOT, Hadamard, Phase, T) are performed on the encoded logical qubits fault tolerantly, by pulsing the bias on the target qubit to a certain value for a chosen time duration. Initially, we designed an architecture (discussed in Appendix A) for fault-tolerant computation that was capable of correcting errors, non fault-tolerantly. Since it is possible that the error correction circuit itself propagate errors, we designed an architecture that corrects errors, fault tolerantly. Finally, we compare our architecture to an existing architecture for fault-tolerant computation employing a linear one-dimensional nearest neighbor array of qubits and show how ours is more efficient. Even though all through this work we use the specific instance of the 7-qubit Steane code in describing our gate implementations, our method can be extended to all systems employing transversal gates for fault-tolerant quantum computation.