No Arabic abstract
We extensively test a recent protocol to demonstrate quantum fault tolerance on three systems: (1) a real-time simulation of five spin qubits coupled to an environment with two-level defects, (2) a real-time simulation of transmon quantum computers, and (3) the 16-qubit processor of the IBM Q Experience. In the simulations, the dynamics of the full system is obtained by numerically solving the time-dependent Schrodinger equation. We find that the fault-tolerant scheme provides a systematic way to improve the results when the errors are dominated by the inherent control and measurement errors present in transmon systems. However, the scheme fails to satisfy the criterion for fault tolerance when decoherence effects are dominant.
We review an approach to fault-tolerant holonomic quantum computation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the information remains protected.
We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We provide equivalence transformations for these boundary conditions that can be used to simplify fault-tolerant circuits and to derive circuit identities in a topological manner. The spatial dimensionality of the scheme can be reduced to two by converting one spatial axis of the cluster into time. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors. The operational overhead is poly-logarithmic in the circuit size.
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest level of code concatenation in order to efficiently correct errors arising from the inherent nondeterminism of two-qubit linear-optical gates. When combined with teleported error-correction (using either a Steane or Golay code) at higher levels of concatenation, the parity-state scheme is found to achieve a saving of approximately three orders of magnitude in resources when compared to a previous scheme, at a cost of a somewhat reduced noise threshold.
In this paper we introduce a universal operator theoretic framework for quantum fault tolerance. This incorporates a top-down approach that implements a system-level criterion based on specification of the full system dynamics, applied at every level of error correction concatenation. This leads to more accurate determinations of error thresholds than could previously be obtained. This is demonstrated both formally and with an explicit numerical example. The basis for our approach is the Quantum Computer Condition (QCC), an inequality governing the evolution of a quantum computer. We show that all known coding schemes are actually special cases of the QCC. We demonstrate this by introducing a new, operator theoretic form of entanglement assisted quantum error correction, which incorporates as special cases all known error correcting protocols, and is itself a special case of the QCC.
Machine learning (ML) provides us with numerous opportunities, allowing ML systems to adapt to new situations and contexts. At the same time, this adaptability raises uncertainties concerning the run-time product quality or dependability, such as reliability and security, of these systems. Systems can be tested and monitored, but this does not provide protection against faults and failures in adapted ML systems themselves. We studied software designs that aim at introducing fault tolerance in ML systems so that possible problems in ML components of the systems can be avoided. The research was conducted as a case study, and its data was collected through five semi-structured interviews with experienced software architects. We present a conceptualisation of the misbehaviour of ML systems, the perceived role of fault tolerance, and the designs used. Common patterns to incorporating ML components in design in a fault tolerant fashion have started to emerge. ML models are, for example, guarded by monitoring the inputs and their distribution, and enforcing business rules on acceptable outputs. Multiple, specialised ML models are used to adapt to the variations and changes in the surrounding world, and simpler fall-over techniques like default outputs are put in place to have systems up and running in the face of problems. However, the general role of these patterns is not widely acknowledged. This is mainly due to the relative immaturity of using ML as part of a complete software system: the field still lacks established frameworks and practices beyond training to implement, operate, and maintain the software that utilises ML. ML software engineering needs further analysis and development on all fronts.