Error Suppression and Error Correction in Adiabatic Quantum Computation: Techniques and Challenges

Abstract

Adiabatic quantum computation (AQC) has been lauded for its inherent robustness to control imperfections and relaxation effects. A considerable body of previous work, however, has shown AQC to be acutely sensitive to noise that causes excitations from the adiabatically evolving ground state. In this paper, we develop techniques to mitigate such noise, and then we point out and analyze some obstacles to further progress. First, we examine two known techniques that leverage quantum error-detecting codes to suppress noise and show that they are intimately related and may be analyzed within the same formalism. Next, we analyze the effectiveness of such error-suppression techniques in AQC, identify critical constraints on their performance, and conclude that large-scale, fault-tolerant AQC will require error correction, not merely suppression. Finally, we study the consequences of encoding AQC in quantum stabilizer codes and discover that generic AQC problem Hamiltonians rapidly convert physical errors into uncorrectable logical errors. We present several techniques to remedy this problem, but all of them require unphysical resources, suggesting that the adiabatic model of quantum computation may be fundamentally incompatible with stabilizer quantum error correction.