Abstract: Variational hybrid quantum-classical algorithms are a class of quantum algorithms intended to run on noisy intermediate-scale quantum (NISQ) devices. These algorithms employ a parameterized quantum circuit (ansatz) and a quantum-classical feedback loop. A classical device is used to optimize the parameters in order to minimize a cost function that can be computed far more efficiently on a quantum device. The cost function is constructed such that finding the ansatz parameters that minimize its value, solves some problem of interest. We focus specifically on the variational quantum linear solver, and examine the effect of several gradient-free and gradient-based classical optimizers on performance. We focus on both the average rate of convergence of the classical optimizers studied, as well as the distribution of their average termination cost values, and how these are affected by noise. Our work demonstrates that realistic noise levels on NISQ devices present a challenge to the optimization process. All classical optimizers appear to be very negatively affected by the presence of realistic noise. If noise levels are significantly improved, there may be a good reason for preferring gradient-based methods in the future, which performed better than the gradient-free methods with only shot-noise present. The gradient-free optimizers, simultaneous perturbation stochastic approximation (SPSA) and Powell’s method, and the gradient-based optimizers, AMSGrad and BFGS performed the best in the noisy simulation, and appear to be less affected by noise than the rest of the methods. SPSA appears to be the best performing method. COBYLA, Nelder–Mead and Conjugate- Gradient methods appear to be the most heavily affected by noise, with even slight noise levels significantly impacting their performance.

https://link.springer.com/article/10.1007/s11128-021-03140-x

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I adapted the recipe slightly for the ingredients that we had at home. The recipe is very “stable”: it can be easily modified to accommodate whatever seeds and nuts you have in the pantry!

What you need is the following:

• 2 eggs
• 65g flax seeds
• 40g sunflower seeds
• 65g sesame seeds
• 50g almond flour
• 30g chia seeds

The procedure is very simple. Put the eggs in a glass Pyrex bowl and whip them with the electric beater. Gently add the other ingredients and keep mixing. Flatten the dough on a Silpat mat until it has the thickness of a biscuit, sprinkle it with sea salt. Gently cut the dough into squares. 4 times 5 should do the trick.

Bake for 10 minutes at 220 C degrees. Switch off the oven.

Leave in the still warm oven for another 10-15 minutes until dry. Monitor the biscuit as you do not want it to get very dark. Take then out of the oven again and let it cool.

Soon it will be ready to enjoy.