Related papers: Phenomenological Noise Models and Optimal Threshol…
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting…
A toric code is an error-correcting code determined by a toric variety or its associated integral convex polytope. We investigate $4$- and $5$-dimensional toric $3$-fold codes, which are codes arising from polytopes in $\mathbf{R}^3$ with…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by…
Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select…
Subsystem quantum error-correcting codes typically involve measuring a sequence of non-commuting parity check operators. They can sometimes exhibit greater fault-tolerance than conventional subspace codes, which use commuting checks.…
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…
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a…
We study parallel fault-tolerant quantum computing for families of homological quantum low-density parity-check (LDPC) codes defined on 3-manifolds with constant or almost-constant encoding rate. We derive generic formula for a transversal…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
Concatenation of two quantum error correcting codes with complementary sets of transversal gates can provide a means towards universal fault-tolerant computation. We first show that it is generally preferable to choose the inner code with…
Toric codes and color codes are two important classes of topological codes. Kubica, Yoshida, and Pastawski showed that any $D$-dimensional color code can be mapped to a finite number of toric codes in $D$-dimensions. In this paper we…
Quantum error detection (QED) offers a promising pathway to fault tolerance in near-term quantum devices by balancing error suppression with minimal resource overhead. However, its practical utility hinges on optimizing design…
To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…