Related papers: Fault-tolerance of the [[8,1,3]] non-CSS code
We examine the transformation of noise under a quantum error correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
Two-dimensional color codes are a promising candidate for fault-tolerant quantum computing, as they have high encoding rates, transversal implementation of logical Clifford gates, and resource-efficient magic state preparation schemes.…
Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…
We investigate a family of fault-tolerant quantum error correction schemes based on the concatenation of small error detection or error correction codes with the three-dimensional cluster state. We propose fault-tolerant state preparation…
Quantum hardware rarely suffers equal amounts of bit-flip ($X$) and phase-flip ($Z$) errors; one type is often much more common than the other. A code that is ``bias-tailored'' can exploit this imbalance, lowering the fault-tolerance…
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…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error…
Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
Ancilla post-selection is a common means of achieving fault-tolerance in quantum error-correction. However, it can lead to additional data errors due to movement or wait operations. Alternatives to post-selection may achieve lower overall…
The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
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 investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing…
Channel capacities quantify the optimal rates of sending information reliably over noisy channels. Usually, the study of capacities assumes that the circuits which sender and receiver use for encoding and decoding consist of perfectly…