Abstract
Adiabatic quantum computation (AQC) is known to possess some intrinsic robustness, though it is likely that some form of error correction will be necessary for large scale computations. Error handling routines developed for circuit-model quantum computation do not transfer easily to the AQC model since these routines typically require high-quality quantum gates, a resource not generally allowed in AQC. There are two main techniques known to suppress errors during an AQC implementation: energy gap protection and dynamical decoupling. Here we show that both these methods are intimately related and can be analyzed within the same formalism. We analyze the effectiveness of such error suppression techniques and identify critical constraints on the performance of error suppression in AQC, suggesting that error suppression by itself is insufficient for large-scale, fault-tolerant AQC and that a form of error correction is needed. We discuss progress towards implementing error correction in AQC and enumerate several key outstanding problems. This work is a companion paper to "Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics"', which provides a dynamical model perspective on the techniques and limitations of error suppression and error correction in AQC. In this paper we discuss the same results within a quantum information framework, permitting an intuitive discussion of error suppression and correction in encoded AQC.
Highlights
Adiabatic quantum computation (AQC) is expected to be inherently robust against certain errors, such as dephasing and energy relaxation [1,2]
Fault tolerance requires an additional mechanism to remove the entropy generated by errors that do occur in the encoded system—i.e., error correction
Since this thermodynamic argument is independent of the computational model, we reasonably expect that achieving fault-tolerant AQC will require some form of error correction
Summary
Adiabatic quantum computation (AQC) is expected to be inherently robust against certain errors, such as dephasing and energy relaxation [1,2] This robustness suggests the possibility of an easier route to scalable quantum computation than the conventional gate-based ‘‘circuit’’ model, with less stringent requirements for fault tolerance and fewer resources devoted to error suppression and correction. Known suppression strategies include energy-gap protection (EGP) [7], in which the addition of the stabilizer generators to the system Hamiltonian causes errors to incur large energetic penalties; dynamical decoupling (DD)[8], whereby stabilizer generators are applied periodically as unitary operators, refocusing errors much like traditional spin echos; and Zeno effect suppression [9], which prevents errors from accumulating through frequent measurements of the stabilizer generators These three techniques apparently operate by very different physical mechanisms. A companion paper entitled Error Suppression and Correction in Adiabatic Quantum Computation: Nonequilibrium Dynamics [11] develops a dynamical model for describing error suppression and correction in AQC, and discusses most of the results in this paper from a dynamical perspective
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