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Quantum reservoir computing is a computing approach which aims at utilisingthe complexity and high-dimensionality of small quantum systems, together withthe fast trainability of reservoir computing, in order to solve complex tasks.The suitability of quantum reservoir computing for solving temporal tasks ishindered by the collapse of the quantum system when measurements are made. Thisleads to the erasure of the memory of the reservoir. Hence, for every output,the entire input signal is needed to reinitialise the reservoir, leading toquadratic time complexity. Overcoming this issue is critical to the hardwareimplementation of quantum reservoir computing. We propose artificiallyrestricting the memory of the quantum reservoir by only using a small numberinputs to reinitialise the reservoir after measurements are performed, leadingto linear time complexity. This not only substantially reduces the number ofquantum operations needed to perform timeseries prediction tasks, it alsoprovides a means of tuning the nonlinearity of the response of the reservoir,which can lead to significant performance improvement. We numerically study thelinear and quadratic algorithms for a fully connected transverse Ising modeland a quantum processor model. We find that our proposed linear algorithm notonly significantly reduces the computational cost but also provides anexperimental accessible means to optimise the task specific reservoir computingperformance.

Solving the time-complexity problem and tuning the performance of quantum reservoir computing by artificial memory restriction