Related papers: Three-dimensional surface codes: Transversal gates…
Quantum error correction is a cornerstone of reliable quantum computing, with surface codes emerging as a prominent method for protecting quantum information. Surface codes are efficient for Clifford gates but require magic state…
Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Qubit shuttling has become an indispensable ingredient for scaling leading quantum computing platforms, including semiconductor spin, neutral-atom, and trapped-ion qubits, enabling both crosstalk reduction and tighter integration of control…
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%,…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
We introduce a class of 3D color codes, which we call stacked codes, together with a fault-tolerant transformation that will map logical qubits encoded in two-dimensional (2D) color codes into stacked codes and back. The stacked code allows…
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales.…
Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…
This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to…
Surface codes can protect quantum information stored in qubits from local errors as long as the per-operation error rate is below a certain threshold. Here we propose holonomic surface codes by harnessing the quantum holonomy of the system.…
Two-level quantum systems, qubits, are not the only basis for quantum computation. Advantages exist in using qudits, d-level quantum systems, as the basic carrier of quantum information. We show that color codes, a class of topological…
Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the…
We introduce transversal dimension jump, a code-switching protocol for lifted product (LP) quantum low-density parity-check (qLDPC) codes across different chain-complex dimensions, enabling universal fault-tolerant quantum computation with…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome…
Surface codes are quantum error correcting codes normally defined on 2D arrays of qubits. In this paper, we introduce a surface code design based on the fact that the severity of bit flip and phase flip errors in the physical quantum…
Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the…