Related papers: Fault-tolerant gates via homological product codes
We present a detailed description of an architecture for fault-tolerant quantum computation, which is based on the cluster model of encoded qubits. In this cluster-based architecture, concatenated computation is implemented in a quite…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
The $[[7,1,3]]$ Steane code and $[[23,1,7]]$ quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation. These two codes have transversal implementations of all Clifford gates, but…
A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize…
Majorana-based quantum computation in nanowires and neutral atoms has gained prominence as a promising platform to encode qubits and protect them against noise. In order to run computations reliably on such devices, a fully fault-tolerant…
We compare two different implementations of fault-tolerant entangling gates on logical qubits. In one instance, a twelve-qubit trapped-ion quantum computer is used to implement a non-transversal logical CNOT gate between two five qubit…
A quantum computer can solve hard problems - such as prime factoring, database searching, and quantum simulation - at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection, by…
High-fidelity logical \emph{T}-gate realization constitutes a core prerequisite for large-scale fault-tolerant quantum computing. However, conventional magic state distillation requires massive physical qubit overhead across successive…
Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…
Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to…
A novel scheme is presented for fault-tolerant quantum computation based on the cluster model. Some relevant logical cluster states are constructed in concatenation by post-selection through verification, without necessity of recovery…
Quantum computing holds the promise of solving classically intractable problems. Enabling this requires scalable and hardware-efficient quantum processors with vanishing error rates. This perspective manuscript describes how bosonic codes,…
We present a fault-tolerant universal gate set consisting of Hadamard and controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal non-Clifford gates on these codes are intriguing in that higher levels of the Clifford…
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical…
We discuss and implement experimentally a method for characterizing quantum gates operating on superpositions of coherent states. The peculiarity of this encoding of qubits is to work with a non-orthogonal basis, and therefore some…
Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…
A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates…