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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…
Current quantum processors are fragile, noisy and fairly limited in both quantity and quality with tens of qubits and physical error rates of around 10^-3. To realize practical quantum applications, however, error rates need to be below…
We propose modifying topological quantum error correcting codes by incorporating space-time defects, termed ``time vortices,'' to reduce the number of physical qubits required to achieve a desired logical error rate. A time vortex is…
Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that even…
The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the…
Floquet codes are a novel class of quantum error-correcting codes with dynamically generated logical qubits arising from a periodic schedule of non-commuting measurements. We utilize the interpretation of measurements in terms of…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
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,…
A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3% for the {4,5}-hyperbolic surface code in a phenomenological noise model (as compared to…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
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…
This paper explores a new approach to fault-tolerant quantum computing (FTQC), relying on quantum polar codes. We consider quantum polar codes of Calderbank-Shor-Steane type, encoding one logical qubit, which we refer to as $\mathcal{Q}_1$…