Fault-tolerance Threshold Research Articles

Two-dimensional architectures for donor-based quantum computing

Through the introduction of a new electron spin transport mechanism, a 2D donor electron spin quantum computer architecture is proposed. This design addresses major technical issues in the original Kane design, including spatial oscillations in the exchange coupling strength and cross-talk in gate control. It is also expected that the introduction of a degree of non-locality in qubit gates will significantly improve the scaling fault-tolerant threshold over the nearest-neighbour linear array.

Error models for mode mismatch in linear optics quantum computing

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode-mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode-mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode-mismatch on its operation, and relate these error models to current fault tolerant threshold estimates.

Noise thresholds for optical cluster-state quantum computation

In this paper we do a detailed numerical investigation of the fault-tolerant threshold for optical cluster-state quantum computation. Our noise model allows both photon loss and depolarizing noise, as a general proxy for all types of local noise other than photon loss noise. We obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical quantum computing is possible in the combined presence of both noise types, provided that the loss probability is less than $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and the depolarization probability is less than ${10}^{\ensuremath{-}4}$. Our fault-tolerant protocol involves a number of innovations, including a method for syndrome extraction known as telecorrection, whereby repeated syndrome measurements are guaranteed to agree. This paper is an extended version of Dawson et al. [Phys. Rev. Lett. 96, 020501 (2006)].

A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing

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 estimates of the threshold are near some experimentally achieved gate fidelities. However, the landscape of threshold estimates includes pseudothresholds, threshold estimates based on a subset of components and a low level of the recursion. In this paper, we observe that pseudothresholds are a generic phenomenon in fault-tolerant computation. We define pseudothresholds and present classical and quantum fault-tolerant circuits exhibiting pseudothresholds that differ by a factor of $4$ from fault-tolerance thresholds for typical relationships between component failure rates. We develop tools for visualizing how reliability is influenced by recursive simulation in order to determine the asymptotic threshold. Finally, we conjecture that refinements of these methods may establish upper bounds on the fault-tolerance threshold for particular codes and noise models.

Noise Thresholds for Optical Quantum Computers

In this Letter we numerically investigate the fault-tolerant threshold for optical cluster-state quantum computing. We allow both photon loss noise and depolarizing noise (as a general proxy for all local noise), and obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical quantum computing is possible for photon loss probabilities <3 x 10(-3), and for depolarization probabilities <10(-4).

Local fault-tolerant quantum computation

We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter $r$ which characterizes the scale-up in the size of the circuit due to encoding. We carry out a detailed seminumerical threshold analysis for concatenated coding using the seven-qubit CSS code in the local and the `nonlocal' setting. First, we find that the threshold in the local model for the ⟦7,1,3⟧ code has a $1∕r$ dependence, which is in correspondence with our analytical estimate. Second, the threshold, beyond the $1∕r$ dependence, does not depend too strongly on the noise levels for transporting qubits. Beyond these results, we find that it is important to look at more than one level of concatenation in order to estimate the threshold and that it may be beneficial in certain places, like in the transportation of qubits, to do error correction only infrequently.

Classical simulability, entanglement breaking, and quantum computation thresholds

We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modeled classically. This question is useful for providing upper bounds on fault-tolerant thresholds, and for understanding the nature of the quantum-classical computational transition. We refine some previously known upper bounds using two different strategies. The first one involves the introduction of bientangling operations, a class of classically simulable machines that can generate at most bipartite entanglement. Using this class we show that it is possible to sharpen previously obtained upper bounds in certain cases. As an example, we show that under depolarizing noise on the controlled-NOT gate, the previously known upper bound of 74% can be sharpened to around 67%. Another interesting consequence is that measurement-based schemes cannot work using only two-qubit nondegenerate projections. In the second strand of the work we utilize the Gottesman-Knill theorem on the classically efficient simulation of Clifford group operations. The bounds attained using this approach for the $\ensuremath{\pi}∕8$ gate can be as low as 15% for general single-gate noise, and 30% for dephasing noise.

Lupus erythematosus and rheumatoid arthritis — Groups of defects in microdebridement (polygenetic defects exceeding the fault tolerance threshold — A consequence of natural defense mechanisms)

Lupus erythematosus (LE) and rheumatoid arthritis (RA) are groups of defects in microdebridement of tissue which includes removal of infectious agents and cellular debris. They are the phenotypic response to a number of polygenetic and/or induced defects. The recognized clinical patterns of these disorders are the responses to accumulated tissue debris and complications of secondary debridement mechanisms that cannot function properly due to basic defects in the debridement system. The series of events that occurs after infection or tissue damage is polygenetic and involve multiple pathways. Genetic polymorphism of this group of mechanisms increases survival against a wider variety of infections. An organism capable of bypassing or destroying a specific step in the host defense is still eliminated by the host in spite of the created defect (a fault tolerant system). However, a single mutant error of this same step creating the same defect will not disrupt the host to the point of clinical illness or death. The pathways are broad enough to bypass some mutant errors. It is the same fault tolerant system. Increased pressure on the system from infection or tissue damage or a combination of multiple genetic defects results in enough faults to exceed the threshold of fault tolerance and produce clinical patterns of disease. The large number of possible combinations of defects gives rise to marked disease variation among patients. The higher frequency of some defects or combination of defects ces subsets. Inbred strains of animals have less polymorphism and thus some strains have a greater susceptibility to infections, LE and RA. Many of the phenomena that occur in LE and RA are secondary to the basic defect of inadequate tissue debridement. Rheumatoid factor (RF) is generally a normal beneficial phenomenon of increasing particle size so that immune complexes can more readily be removed by the reticuloendothelial system. In the presence of defective microdebridement the system is overloaded and no longer effective. This results in circulating RF. There are clearly multiple basic genetic defects. For example, the known multiple genetic defects in complement in LE are relevant to the systems involved. They are important ligands for defense and debridement mechanisms. A null allele is not likely to be a secondary phenomenon. It might be in a fault tolerant site and contribute to disease in one host, and yet not contribute to disease in another host. A host with an overloaded microdebridement system is more susceptable to infections, including low grade pathogens. Since a combination of defects may have to develop to present the clinical syndromes, lesser numbers (or less significant combinations) of defective genes would sometimes be present in relatives. Autoantibodies are an example of a physiologic response to accumulated tissue debris. They occur when tissue damage is greater than can rapidly be removed or when there is inadequate tissue microdebridement. They are a universal biologic phenomenon for speeding tissue debridement in persons with normal debridement mechanisms. They produce problems in a person with defective microdebridement.