Related papers: Homology, Hopf Algebras and Quantum Code Surgery
Quantum error correction (QEC) plays a crucial role in correcting noise and paving the way for fault-tolerant quantum computing. This field has seen significant advancements, with new quantum error correction codes emerging regularly to…
Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery…
Lattice surgery is a method to perform quantum computation fault-tolerantly by using operations on boundary qubits between different patches of the planar code. This technique allows for universal planar-code computation without eliminating…
The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses…
Surface quantum error-correcting codes are the leading proposal for fault-tolerance within quantum computers. We present OpenSurgery, a scalable tool for the preparation of circuits protected by the surface code operated through lattice…
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…
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow…
We observe that lattice surgery, a model of fault-tolerant qubit computation, generalises straightforwardly to arbitrary finite-dimensional qudits. The generalised model is based on the group algebras $\mathbb{C}\mathbb{Z}_d$ for $d \geq…
Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes, which generalises lattice surgery. In this work, we present a code surgery scheme, applicable to any qubit…
We demonstrate how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, we also improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits…
In this paper we outline a method for a compiler to translate any non fault tolerant quantum circuit to the geometric representation of the lattice surgery error-correcting code using inherent merge and split operations. Since the…
The emerging field of quantum resource estimation is aimed at providing estimates of the hardware requirements (`quantum resources') needed to execute a useful, fault-tolerant quantum computation. Given that quantum computers are intended…
Practical applications of quantum computing depend on fault-tolerant devices that employ error correction. A promising quantum error-correcting code for large-scale quantum computing is the surface code. For this code, Fault-Tolerant…
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…
The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates.…
Modular architectures are a promising approach to scaling quantum computers to fault tolerance. Small, low-noise quantum processors connected through relatively noisy quantum links are capable of fault-tolerant operation as long as the…
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an…
We introduce a framework for implementing logic in CSS quantum error correction codes, building on the surgery methods of Cowtan and Burton [CB24]. Our approach offers a systematic methodology for designing and analysing surgery protocols.…
Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation…
Future quantum computers will require quantum error correction for faithful operation. The correction capabilities come with an overhead for performing fault-tolerant logical operations on the encoded qubits. One of the most resource…