Related papers: Quantum convolutional data-syndrome codes
An arbitrarily reliable quantum computer can be efficiently constructed from noisy components using a recursive simulation procedure, provided that those components fail with probability less than the fault-tolerance threshold. Recent…
Quantum error correction can reduce the effects of noise in quantum systems, e.g. in metrology or most notably in quantum computing. Typically, this requires making measurements that provide information about the errors that have occurred…
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…
Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here I show that for suitable topological codes a single round of local measurements is…
We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
The aim of this paper is to propose an alternative method to solve a Fault Tolerant Control problem. The model is a linear system affected by a disturbance term: this represents a large class of technological faulty processes. The goal is…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
I report two general methods to construct quantum convolutional codes for quantum registers with internal $N$ states. Using one of these methods, I construct a quantum convolutional code of rate 1/4 which is able to correct one general…
This work is concerned with phrasing the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called "threshold theorems" on the possibility…
Protecting quantum information using quantum error correction (QEC) requires repeatedly measuring stabilizers to extract error syndromes that are used to identify and correct errors. Syndrome extraction data provides information about the…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block.…
Quantum computers have advanced rapidly in qubit count and gate fidelity. However, large-scale fault-tolerant quantum computing still relies on quantum error correction code (QECC) to suppress noise. Manually or experimentally verifying the…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design,…
This work addresses the open question of implementing fault-tolerant QRLCs with feasible computational overhead. We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. A first…