Related papers: Three-dimensional surface codes: Transversal gates…
Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low…
The development of quantum computing systems for large scale algorithms requires targeted error rates unachievable through hardware advancements alone. Quantum Error Correction (QEC) allows us to use systems with a large number of physical…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error-correcting code. The recent discovery…
We show how looped pipeline architectures - which use short-range shuttling of physical qubits to achieve a finite amount of non-local connectivity - can be used to efficiently implement the fault-tolerant non-Clifford gate between 2D…
We construct quantum codes that support transversal $CCZ$ gates over qudits of arbitrary prime power dimension $q$ (including $q=2$) such that the code dimension and distance grow linearly in the block length. The only previously known…
We study the use of triorthogonal codes for universal fault-tolerant quantum computation and propose two methods to circumvent the Eastin-Knill theorem, which prohibits any single quantum error-correcting code from supporting both…
The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in…
We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code switching protocol with (i) a recently discovered transversal…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
We use the recently introduced lifted product to construct a family of Quantum Low Density Parity Check Codes (QLDPC codes). The codes we obtain can be viewed as stacks of surface codes that are interconnected, leading to the name…
The failure susceptibility of the quantum hardware will force quantum computers to execute fault-tolerant quantum circuits. These circuits are based on quantum error correcting codes, and there is increasing evidence that one of the most…
Three dimensional (3D) toric codes are a class of stabilizer codes with local checks and come under the umbrella of topological codes. While decoding algorithms have been proposed for the 3D toric code on a cubic lattice, there have been…
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there…
Constructing quantum codes with good parameters and useful transversal gates is a central problem in quantum error correction. In this paper, we continue our work in arXiv:2502.01864 and construct the first family of asymptotically good…
We build on recent work by B. Brown (Sci. Adv. 6, eaay4929 (2020)) to develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes, which can be used to implement a transversal (non-Clifford)…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the…
Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC)…
We present an architecture for early fault-tolerant quantum computers based on the smallest interesting colour code (Earl Campbell, 2016). It realizes a universal logical gate set consisting of single-qubit measurements and preparations in…