Randomized benchmarking with gate-dependent noise

We analyze randomized benchmarking for arbitrary gate-dependent noise and prove that the exact impact of gate-dependent noise can be described by a single perturbation term that decays exponentially with the sequence length. That is, the exact behavior of randomized benchmarking under general gate-dependent noise converges exponentially to a true exponential decay of exactly the same form as that predicted by previous analysis for gate-independent noise. Moreover, we show that the operational meaning of the decay parameter for gate-dependent noise is essentially unchanged, that is, we show that it quantifies the average fidelity of the noise between ideal gates. We numerically demonstrate that our analysis is valid for strongly gate-dependent noise models. We also show why alternative analyses do not provide a rigorous justification for the empirical success of randomized benchmarking with gate-dependent noise.Comment: It measures what you expect. Comments welcome. v2: removed an inconsistent assumption from theorem 3 and clarified discussion of prior work. Results unchanged. v3: further clarified discussion of prior work, numerics now available at https://github.com/jjwallman/numerics. v4: licence change as required by Quantu

Chronic fatigue syndrome; an approach combining self-management with graded exercise to avoid exacerbations.

Controversy regarding the aetiology and treatment of patients with chronic fatigue syndrome (CFS) continues to affect the medical professions. The Cochrane collaboration advises practitioners to implement graded exercise therapy for CFS sufferers using cognitive behavioural principles. In contrast there is evidence that exercise can induce symptom exacerbations in CFS where too vigorous exercise/activity promotes immune dysfunction, which in turn increases symptoms in patients with CFS. When designing and implementing an exercise programme it is important to be aware of both these seemingly opposing view points in order to deliver a programme without any detrimental effects on CFS pathophysiology. Using evidence from both the biological and clinical sciences, the present manuscript explains that graded exercise therapy for people with CFS can be safely undertaken without detrimental effects to the immune system. Exercise programs should be designed to cater for individual physical capabilities and should also account for the fluctuating nature of symptoms commonly reported by people with CFS. In line with cognitive behaviourally and graded exercise-based strategies, self-management for people with CFS involves encouraging the patients to pace their activities and respect their physical and mental limitations with the ultimate aim of improving their everyday function