Quantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. In an attempt to placate this limitation techniques can be applied for evaluating a quantum circuit using a machine with fewer qubits than the circuit naively requires. These techniques work by evaluating many smaller circuits on the smaller machine, that are then combined in a polynomial to replicate the output of the larger machine. This scheme requires more circuit evaluations than are practical for general circuits. However, we investigate the possibility that for certain applications many of these subcircuits are superfluous, and that a much smaller sum is sufficient to estimate the full circuit. We construct a machine learning model that may be capable of approximating the outputs of the larger circuit with much fewer circuit evaluations. We successfully apply our model to the task of digit recognition, using simulated quantum computers much smaller than the data dimension. The model is also applied to the task of approximating a random 10 qubit PQC with simulated access to a 5 qubit computer, even with only relatively modest number of circuits our model provides an accurate approximation of the 10 qubit PQCs output, superior to a neural network attempt. The developed method might be useful for implementing quantum models on larger data throughout the NISQ era.

翻译：量子计算机在增强机器学习方面展现出巨大潜力，但当前量子比特数量有限，制约了这一潜力的实现。为缓解此限制，可采用相关技术，使用比电路所需量子比特数更少的计算机评估量子电路。这些技术通过在较小计算机上评估多个较小电路，再将其组合成多项式以模拟较大计算机的输出。该方案所需的电路评估次数对于通用电路而言并不实际。然而，我们研究了在某些应用中许多子电路可能是多余的可能性，即用更少的求和项足以估计完整电路。我们构建了一种机器学习模型，该模型能够以更少的电路评估逼近较大电路的输出。我们将该模型成功应用于数字识别任务，使用了远小于数据维度的模拟量子计算机。该模型还被应用于近似随机10量子比特参数化量子电路（PQC）的任务，模拟了仅能访问5量子比特计算机的场景——即便使用的电路数量相对适中，我们的模型仍能准确近似10量子比特PQC的输出，其性能优于神经网络方法。所提出的方法可能有助于在NISQ时代对更大规模数据实现量子模型。