Online Scheduled Execution of Quantum Circuits Protected by Surface Codes

Quantum circuits are the preferred formalism for expressing quantum information processing tasks. Quantum circuit design automation methods mostly use a waterfall approach and consider that high level circuit descriptions are hardware agnostic. This assumption has lead to a static circuit perspective: the number of quantum bits and quantum gates is determined before circuit execution and everything is considered reliable with zero probability of failure. Many different schemes for achieving reliable fault-tolerant quantum computation exist, with different schemes suitable for different architectures. A number of large experimental groups are developing architectures well suited to being protected by surface quantum error correcting codes. Such circuits could include unreliable logical elements, such as state distillation, whose failure can be determined only after their actual execution. Therefore, practical logical circuits, as envisaged by many groups, are likely to have a dynamic structure. This requires an online scheduling of their execution: one knows for sure what needs to be executed only after previous elements have finished executing. This work shows that scheduling shares similarities with place and route methods. The work also introduces the first online schedulers of quantum circuits protected by surface codes. The work also highlights scheduling efficiency by comparing the new methods with state of the art static scheduling of surface code protected fault-tolerant circuits.Comment: accepted in QI

Step-wise multiple regression - Relationship between cognitive test performance and walking time.

<p>Step-wise multiple linear regression with the cognitive tests scores as explained variables and walking time, age, gender, education level, height and weight as explanatory variables:</p><p>a) First step, age and education level are forced into the model,</p><p>b) Second step, walking time enters the model as first explanatory variable,</p><p>c) Then, the other confounders (gender, height, weight) were added one by one, R-squared for the final model is given.</p><p>d) Delta multiple R-squared between second step and first step, all p<0.0001.</p

Age, walking time and cognitive test scores.

<p>Values are expressed as the mean ± standard deviation in the whole study population and in the two subsets of subjects by age range. Percentages correspond to the ratio of low performers for each item. P values denote highly significant differences between the two age subsets.</p><p>(1) Comparisons between subsets are performed by a Mann-Whitney <i>U</i>-test for the scores and walking time (non normal distributions) and by a chi-square test for the % of subjects with low scores.</p

Simple regression - Relationship between cognitive test performance and walking time.

<p>Simple linear regression with the cognitive tests scores as explained variables and walking time as explanatory variable.</p

Scatter plot: MMSE score and explaining variables (age, education and walking time).

<p>Dot plots and linear regression for MMSE score against the main explaining variables: age, education and walking time. Subjects <50 years old are represented by red crosses, subjects ≥ 50 years old are represented by blue circles.</p

Scatter plot: Total psychometric score and explaining variables (age, education and walking time).

<p>Dot plots and linear regression for total psychometric score against the main explaining variables: age, education and walking time. Subjects <50 years old are represented by red crosses, subjects ≥ 50 years old are represented by blue circles.</p

Total psychometric score and walking time.

<p>The relationship between the total psychometric score and walking time is visualized with a dot plot of the data and a linear regression of the total psychometric score and walking time in the whole study population (a) and in the subset of volunteers aged 50 years and over (b). The linear regression equations and R squared values are indicated in the figures.</p

Scatter plot: Benton score and explaining variables (age, education and walking time).

<p>Dot plots and linear regression for Benton score against the main explaining variables: age, education and walking time. Subjects <50 years old are represented by red crosses, subjects ≥ 50 years old are represented by blue circles.</p