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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…
An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomena of fragile temporal boundaries that arise during the standard logical state…
We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks,…
We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find…
Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the…
This paper outlines a three-step procedure for determining the low bit error rate performance curve of a wide class of LDPC codes of moderate length. The traditional method to estimate code performance in the higher SNR region is to use a…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the…
Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…
We refine an old idea for performing fault-tolerant error correction in topological codes by simulating confining interactions between excitations. We implement confinement using an array of local classical processors that measure…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research…
Quantum error correction is essential for reliable quantum computation, where surface codes demonstrate high fault-tolerant thresholds and hardware efficiency. However, noise in single-shot measurements limits logical readout fidelity,…
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…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
Developing space- and time-efficient logical magic state preparation protocols will likely be an essential step towards building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
We present a comprehensive and self-contained simplified review of the quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%,…
We study the performance of distance-three surface code layouts under realistic multi-parameter noise models. We first calculate their thresholds under depolarizing noise. We then compare a Pauli-twirl approximation of amplitude and phase…