Related papers: Error Threshold for Color Codes and Random 3-Body …
Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware.…
Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the…
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be…
We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group…
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 color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error…
Utility-scale quantum computers require quantum error correcting codes with large numbers of physical qubits to achieve sufficiently low logical error rates. The performance of quantum error correction (QEC) is generally predicted through…
Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for…
We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla…
It is not so well-known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite the potential advantages of using such protocols in terms of the relaxation of accuracy,…
The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing…
The quantum error threshold is the highest (model-dependent) noise rate which we can tolerate and still quantum-compute to arbitrary accuracy. Although noise thresholds are frequently estimated for the Steane seven-qubit, distance-three…
We introduce a decoder for the 3D color code with boundaries, which is a variation of the restriction decoder introduced by Kubicka and Delfosse. Specifically, we adapt the lift procedure to efficiently find a correction on qubits adjacent…
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…
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…
We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a…
We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a…
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal…
A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a…