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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…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
Quantum states can quickly decohere through interaction with the environment. Quantum error correction is a method for preserving coherence through active feedback. Quantum error correction encodes the quantum information into a logical…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous…
Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Z\'emor can correct a constant fraction of random errors with very high probability.…
The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled…
We describe a method to use measurements and correction operations in order to implement the Clifford group in a stabilizer code, generalising a result from [Bombin,2011] for topological subsystem colour codes. In subsystem stabilizer codes…
Recently, automorphism ensemble decoding (AED) has drawn research interest as a more computationally efficient alternative to successive cancellation list (SCL) decoding of polar codes. Although AED has demonstrated superior performance for…
We propose an error correction coding algorithm for continuous quantum variables. We use this algorithm to construct a highly efficient 5-wavepacket code which can correct arbitrary single wavepacket errors. We show that this class of…
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the…
In this article, we present the unbalanced quantum error correcting codes(one-party-QECC), a novel idea for correcting unbalanced quantum errors. In some quantum communication tasks using entangled pairs, the error distributions between two…
Estimating many-body Hamiltonians has wide applications in quantum technology. By allowing coherent evolution of quantum systems and entanglement across multiple probes, the precision of estimating a fully connected $k$-body interaction can…
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
We explore the effect of Shor state construction methods on logical state encoding and quantum error correction for the [[7,1,3]] Calderbank-Shor-Steane quantum error correction code in a nonequiprobable error environment. We determine the…