|dc.date.accessioned||2018-10-22 20:07:06 (GMT)||
|dc.date.available||2018-10-22 20:07:06 (GMT)||
|dc.description.abstract||Quantum computers have the potential to solve several interesting problems in polynomial
time 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 very
sensitive to noise arising from undesired interactions with the environment. Noise can lead
to errors which can corrupt the results of the computation. Quantum error correction is
one 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 various
codes perform under more realistic noise models that can be observed in experiments.
This thesis proposes a new decoding algorithm which can optimize threshold values of
error correcting codes under different noise models. The algorithm can be applied to
any Markovian noise model. Further, it is shown that for certain noise models, logical
Clifford corrections can further improve a code's threshold value if the code obeys certain
Since gates and measurements cannot in general be performed with perfect precision,
the operations required to perform quantum error correction can introduce more errors
into the system thus negating the benefits of error correction. Fault-tolerant quantum
computing is a way to perform quantum error correction with imperfect operations while
retaining 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 resource
requirements 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 applicable
to arbitrary distance codes. Various code families are shown to satisfy the requirements
of flag fault-tolerant error correction. We also provide circuits using a constant number of
qubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewer
qubits 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 use
analytic decoding methods to improve the performance of a fault-tolerant scheme. This
thesis presents decoding schemes using several state of the art machine learning techniques
with a focus on fault-tolerant quantum error correction in regimes that are relevant to near
term experiments. It is shown that even in low noise rate regimes and with no knowledge
of the noise, noise can be further suppressed for small distance codes. Limitations of machine
learning decoders as well as the classical resources required to perform active error
correction are discussed.
In many cases, gate times can be much shorter than typical measurement times of
quantum states. Further, classical decoding of the syndrome information used in quantum
error 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 (known
as the Pauli frame) have been developed to avoid active error correction. In this thesis, we
generalize previous Pauli frame schemes and show how Clifford frame error correction can
be implemented with minimal overhead. Clifford frame error correction is necessary if the
logical component of recovery operators were chosen from the Clifford group, but could
also be used in randomized benchmarking schemes.||en
|dc.publisher||University of Waterloo||en
|dc.subject||Quantum error correction||en
|dc.subject||Fault-tolerant quantum computing||en
|dc.title||New methods in quantum error correction and fault-tolerant quantum computing||en
|uws-etd.degree.department||Physics and Astronomy||en
|uws-etd.degree.discipline||Physics (Quantum Information)||en
|uws-etd.degree.grantor||University of Waterloo||en
|uws-etd.degree||Doctor of Philosophy||en
|uws.contributor.affiliation1||Faculty of Science||en