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It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
Quantum Error Correction (QEC) is an essential field of research towards the realization of large-scale quantum computers. On the theoretical side, a lot of effort is put into designing error-correcting codes that protect quantum data from…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under code capacity…
Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone…
In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of…
Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error…
Local decoders, also known as cellular-automaton decoders, offer a promising path toward real-time quantum error correction by replacing centralized classical decoding, with inherent hardware constraints, by a natively parallel and…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
Recently, low-resolution LDPC decoders have been introduced that perform mutual information maximizing signal processing. However, the optimal quantization in variable and check nodes requires expensive non-uniform operations. Instead, we…
The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
We present a fault-tolerant universal quantum computing architecture based on a code concatenation of biased-noise qubits and the parity architecture. The parity architecture can be understood as an LDPC code tailored specifically to obtain…
Fault-tolerant quantum computing relies on Quantum Error Correction, which encodes logical qubits into data and parity qubits. Error decoding is the process of translating the measured parity bits into types and locations of errors. To…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes we analytically compute the effective logical channel that results when…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can…