Related papers: Comparison of memory thresholds for planar qudit g…
Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many…
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…
Quantum computers are highly vulnerable to noise, necessitating the use of error-correcting codes to protect stored data. Errors must be continuously corrected over time to counteract decoherence using appropriate decoders. Therefore, fast…
We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by…
Universal fault-tolerant quantum computation will require real-time decoding algorithms capable of quickly extracting logical outcomes from the stream of data generated by noisy quantum hardware. We propose modular decoding, an approach…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…
Threshold estimation is central to fault-tolerant quantum computing, but the reported threshold depends not only on the code and noise model, but also on the decoder used to interpret syndrome data. We study this dependence for surface-code…
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine…
Biased-noise qubits, in which one type of error (e.g. $X$- and $Y$-type errors) is significantly suppressed relative to the other (e.g. $Z$-type errors), can significantly reduce the overhead of quantum error correction. Codes such as the…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achieved by direct measurements of the stabilizers.…
Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner.…
Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the…
We investigate a scheme of fault-tolerant quantum computation based on the cluster model. Logical qubits are encoded by a suitable code such as the Steane's 7-qubit code. Cluster states of logical qubits are prepared by post-selection…
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…
Recent experimental advances have made it possible to implement logical multi-qubit transversal gates on surface codes in a multitude of platforms. A transversal controlled-NOT (tCNOT) gate on two surface codes introduces correlated errors…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
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…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…