Quantum Compilation Device Stochastic Gate Selection

The patent applies dynamics by transitioning from a deterministic gate sequence to a stochastic one, where the quantum circuit is represented as a probability distribution over multiple elementary gate sequences. This dynamic approach allows the system to achieve higher approximation accuracy without proportionally increasing the length of individual gate sequences, as the accuracy benefit comes from the distribution across multiple sequences rather than extending any single sequence.

The patent changes the parameter representation from a fixed deterministic gate sequence to a probabilistic distribution characterized by probabilities p(k) for each sequence Uk. This parameter transformation enables the system to encode more information and achieve higher approximation accuracy while maintaining comparable or reduced sequence lengths, as the probability distribution captures the essential quantum behavior more efficiently.

By introducing stochasticity and representing the quantum circuit as a distribution over gate sequences rather than a single deterministic sequence, the patent achieves faster convergence to high approximation accuracy. This dynamic representation allows compilation algorithms to explore the solution space more efficiently and find accurate approximations with shorter computational paths, thereby improving compilation efficiency without sacrificing accuracy.

The patent applies partial action by representing the quantum circuit with a truncated distribution over a finite number K of elementary gate sequences, where K is chosen to achieve the desired approximation accuracy. This approach avoids the excessive action of considering all possible gate sequences, which would be computationally intractable, while still achieving high accuracy through the probabilistic combination of a manageable number of sequences.