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：量子计算机有望极大增强机器学习能力，但当前量子比特数量的限制阻碍了这一前景的实现。为缓解此限制，可运用相关技术，在量子比特数少于电路原生需求的小型量子计算机上评估量子电路。这些技术通过在小规模量子计算机上评估多个更小的子电路，并将这些子电路以多项式形式组合，从而复现大规模量子计算机的输出。该方法所需的子电路评估次数通常远超通用电路的实际可行性。然而，我们探讨了在某些应用中大量子电路可能冗余的可能性，即仅需少量求和即可有效估计完整电路。我们构建了一种机器学习模型，该模型能够以显著更少的电路评估次数近似大规模电路的输出。我们成功将该模型应用于手写数字识别任务，其中使用的模拟量子计算机规模远小于数据维度。此外，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）的输出任务——通过模拟访问5量子比特计算机实现。即便仅使用相对适中的子电路数量，我们的模型仍能精确逼近10量子比特PQC的输出，其性能优于神经网络方法。该研究方法在NISQ时代可能有助于在更大规模数据上实现量子模型。