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Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in…
In this work we explore the accuracy of quantum error correction depending of the order of the implemented syndrome measurements. CSS codes require bit-flip and phase flip-syndromes be measured separately. To comply with fault tolerant…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
In this dissertation, I present a general method for studying quantum error correction codes (QECCs). This method not only provides us an intuitive way of understanding QECCs, but also leads to several extensions of standard QECCs,…
The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse…
We simulate the implementation of a T-gate, or $\frac{\pi}{8}$-gate, for a [7,1,3] encoded logical qubit in a non-equiprobable error environment. We demonstrate that the use of certain non-fault tolerant methods in the implementation may…
We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant quantum computers (EFTQCs) in the context of models of their implementations on a surface code architecture. We estimate the logical and physical…
We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
We study a comprehensive list of quantum codes as candidates of codes to be used at the bottom, physical, level in a fault-tolerant code architecture. Using the Aliferis-Gottesman-Preskill (AGP) ex-Rec method we calculate the…
Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. Given that the overhead of such error correction is often formidable, autonomous quantum error correction (AQEC)…
We investigate the use of modern code-agnostic decoders to convert CA-SCL from an incomplete decoder to a complete one. When CA-SCL fails to identify a codeword that passes the CRC check, we apply a code-agnostic decoder that identifies a…
Standard quantum process tomography on a $d$-dimensional input is performed by preparing several states of an input probe that then evolve under the action of the quantum channel corresponding to the progress. The final states of the probe…
Quantum error correcting code can diagnose potential errors and correct them based on measured outcomes by leveraging syndrome measurement. However, mid-circuit measurement has been technically challenging for early fault-tolerant quantum…
In quantum error correction, the description of noise channel cannot be completely accurate, and fluctuation always appears in noise channel. It is found that when fluctuation of physical noise channel is considered, the average effective…
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an…
We develop a simple and general post-selection strategy for high-rate quantum codes that is transferrable across decoders. After an initial baseline run, the decoder is re-run once per logical observable, and forced in these latter runs to…
Stall patterns are known to cause an error floor in hard decision decoding of the OFEC code. We propose a novel stall pattern removal algorithm that lowers the error floor of state-of-the-art algorithms by an order of magnitude