Quantum Generative Modelling (QGM) relies on preparing quantum states and generating samples from these states as hidden - or known - probability distributions. As distributions from some classes of quantum states (circuits) are inherently hard to sample classically, QGM represents an excellent testbed for quantum supremacy experiments. Furthermore, generative tasks are increasingly relevant for industrial machine learning applications, and thus QGM is a strong candidate for demonstrating a practical quantum advantage. However, this requires that quantum circuits are trained to represent industrially relevant distributions, and the corresponding training stage has an extensive training cost for current quantum hardware in practice. In this work, we propose protocols for classical training of QGMs based on circuits of the specific type that admit an efficient gradient computation, while remaining hard to sample. In particular, we consider Instantaneous Quantum Polynomial (IQP) circuits and their extensions. Showing their classical simulability in terms of the time complexity, sparsity and anti-concentration properties, we develop a classically tractable way of simulating their output probability distributions, allowing classical training to a target probability distribution. The corresponding quantum sampling from IQPs can be performed efficiently, unlike when using classical sampling. We numerically demonstrate the end-to-end training of IQP circuits using probability distributions for up to 30 qubits on a regular desktop computer. When applied to industrially relevant distributions this combination of classical training with quantum sampling represents an avenue for reaching advantage in the NISQ era.
翻译:量子建模(QGM) 依靠量子建模(QGM) 来准备量子状态,并生成来自这些状态的样本,作为隐藏的(或已知的)概率分布。由于某些类别量子状态(电路)的分布本质上很难进行典型的抽样,因此QGM是量子实验的优劣测试台。此外,基因建模任务对于工业机器学习应用来说越来越具有相关性,因此QGM是展示实际量子优势的有力候选人。然而,这要求量子电路经过培训,能够代表与工业相关的分布,而相应的培训阶段对于当前量子硬件来说具有广泛的培训成本。在这项工作中,我们提出基于特定类型电路的典型的QGM培训协议,允许高效的梯度计算,而对于量子实验来说则是非常困难的。我们考虑的量子建模(QP) 快速的量子建模任务及其扩展。我们从时间复杂性、紧张性和反浓缩特性的角度,我们开发了模拟其输出概率分布的典型的路径, 允许将常规培训应用于常规的频率分布, QQQreal train train train train trememalial分布用于在进行。我们进行比例的取样中进行。