Related papers: The domain wall color code
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,…
Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors,…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
Leveraging noise bias, where phase-flip errors dominate over bit-flips, can drastically reduce the hardware overhead of fault-tolerant quantum computation, but existing approaches require bias-preserving CNOT gates whose implementation…
We formulate a scheme for fault-tolerant quantum computation that works effectively against highly biased noise, where dephasing is far stronger than all other types of noise. In our scheme, the fundamental operations performed by the…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
We demonstrate that small quantum memories, realized via quantum error correction in multi-qubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…
Bosonic codes encode quantum information into a single infinite-dimensional physical system endowed with error correction capabilities. This reduces the need for complex management of many physical constituents compared with standard…
The topological color code and the toric code are two leading candidates for realizing fault-tolerant quantum computation. Here we show that the color code on a $d$-dimensional closed manifold is equivalent to multiple decoupled copies of…
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…
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…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…