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Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, including…
In the evolving landscape of quantum computing, determining the most efficient parameters for Quantum Error Correction (QEC) is paramount. Various quantum computers possess varied types and amounts of physical noise. Traditionally,…
Topological quantum error correction codes are known to be able to tolerate arbitrary local errors given sufficient qubits. This includes correlated errors involving many local qubits. In this work, we quantify this level of tolerance,…
Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process---it is the algorithm which computes…
Achieving high-fidelity entangling operations between qubits consistently is essential for the performance of multi-qubit systems and is a crucial factor in achieving fault-tolerant quantum processors. Solid-state platforms are particularly…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
We construct rotated logical states by applying rotation operators to stabilizer states, extending the logical basis and modifying stabilizer generators. Rotation operators affect the effective code distance $d_R$, which decays…
In the shallow sub-threshold regime, fault-tolerant quantum computation requires a tremendous amount of qubits. In this paper, we study the error correction in the deep sub-threshold regime. We estimate the physical error rate for achieving…
The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels…
We study the dependence of the fidelity of the surface code in the presence of a single finite-temperature massless bosonic environment after a quantum error correction cycle. The three standard types of environment are considered:…
Encoding quantum information in a quantum error correction (QEC) code enhances protection against errors. Imperfection of quantum devices due to decoherence effects will limit the fidelity of quantum gate operations. In particular, neutral…
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…
Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…
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…
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems…
When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free…
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…