Quantum computers have the potential to solve several interesting problems in polynomialtime for which no polynomial time classical algorithms have been found. However,one of the major challenges in building quantum devices is that quantum systems are verysensitive to noise arising from undesired interactions with the environment. Noise can leadto errors which can corrupt the results of the computation. Quantum error correction isone way to mitigate the effects of noise arising in quantum devices.With a plethora of quantum error correcting codes that can be used in various settings,one of the main challenges of quantum error correction is understanding how well variouscodes perform under more realistic noise models that can be observed in experiments.This thesis proposes a new decoding algorithm which can optimize threshold values oferror correcting codes under different noise models. The algorithm can be applied toany Markovian noise model. Further, it is shown that for certain noise models, logicalClifford corrections can further improve a code's threshold value if the code obeys certainsymmetries.Since gates and measurements cannot in general be performed with perfect precision,the operations required to perform quantum error correction can introduce more errorsinto the system thus negating the benefits of error correction. Fault-tolerant quantumcomputing is a way to perform quantum error correction with imperfect operations whileretaining the ability to suppress errors as long as the noise is below a code's threshold.One of the main challenges in performing fault-tolerant error correction is the high resourcerequirements that are needed to obtain very low logical noise rates. With the use of flag qubits, this thesis develops new fault-tolerant error correction protocols that are applicableto arbitrary distance codes. Various code families are shown to satisfy the requirementsof flag fault-tolerant error correction. We also provide circuits using a constant number ofqubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewerqubits than previous fault-tolerant error correction protocols.It is often the case that the noise afflicting a quantum device cannot be fully characterized.Further, even with some knowledge of the noise, it can be very challenging to useanalytic decoding methods to improve the performance of a fault-tolerant scheme. Thisthesis presents decoding schemes using several state of the art machine learning techniqueswith a focus on fault-tolerant quantum error correction in regimes that are relevant to nearterm experiments. It is shown that even in low noise rate regimes and with no knowledgeof the noise, noise can be further suppressed for small distance codes. Limitations of machinelearning decoders as well as the classical resources required to perform active errorcorrection are discussed.In many cases, gate times can be much shorter than typical measurement times ofquantum states. Further, classical decoding of the syndrome information used in quantumerror correction to compute recovery operators can also be much slower than gate times.For these reasons, schemes where error correction can be implemented in a frame (knownas the Pauli frame) have been developed to avoid active error correction. In this thesis, wegeneralize previous Pauli frame schemes and show how Clifford frame error correction canbe implemented with minimal overhead. Clifford frame error correction is necessary if thelogical component of recovery operators were chosen from the Clifford group, but couldalso be used in randomized benchmarking schemes.
【 预 览 】
附件列表
Files
Size
Format
View
New methods in quantum error correction and fault-tolerant quantum computing
PDF
download
878987797
028-85220240
