Non-adiabatic holonomic quantum computation in linear system-bath coupling.

Chunfang Sun,Haodi Liu,Chunfeng Wu,Xun-Li Feng,Kang Xue,Jing-Ling Chen,Gangcheng Wang

doi:10.1038/srep20292

Abstract

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.

Highlights

N decoherence, and its non-adiabatic property ensures less operation time
As shown in the literatures26–31, dynamical decoupling (DD) can be used to preserve arbitrary state in quantum memories, it is compatible with gate operations used for quantum information processing (QIP) in principle, essentially by designing DD operations that commute with the gate operations
To protect quantum information from both control imprecisions and the detrimental effects of the environment, the schemes hybridizing Holonomic quantum computation (HQC) with decoherence-free subspaces (DFSs) based on adiabatic evolution have been proposed5–7

Summary

Results

0((T∆c)t)==∏exj =p−0(1−gij†HU∆0(t∆). tT)hgejn≡thee−eiHveofflTuct,iwonheorfetHheefwf dheonleotseyssttehme limit of arbitrarily fast control T c → 0, Heff approaches H with DD resulting. The group algebra equivalent subspaces can (DFSs) is be written as able to encode (N − 2) logical qubits to make universal quantum computation. The -invariant subspace λ = {1,1,1,1}, representing a set of eigenvalues of decoupling group elements, is spanned by the N-qubit quantum states ( r + NOT(r) )/ 2 , with r containing an even number of1′s of length N. To implement two noncommuting holonomic single-logical-qubit gates and one nontrivial holonomic two-logical-qubit gate, one needs a set of operators to achieve the appropriate transitions so that the evolution stays within the DFS. To this end, we need to seek for the operators that commute with the decoupling group.

By the choosing action of

Methods

Additional Information