标题： 可扩展的 noisy 量子计算机的量子算法 显示英文标题

标题： Scalable Quantum Algorithms for Noisy Quantum Computers

摘要： 量子计算不仅有望解决量子物理领域长期存在的问题，还可以在其他广泛领域提供加速。 然而，由于当前量子计算机存在噪声且规模有限，许多著名的量子算法目前对于实际感兴趣的计算规模来说是不可行的。 本博士论文开发了两种主要技术以减少量子计算资源需求，旨在扩展当前量子处理器上的应用规模。 第一种方法基于计算成本高昂量（如量子电路梯度或量子几何张量 QGT）的随机近似。 第二种方法从不同的角度看待 QGT，从而在当前量子计算机上实现时间演化的更高效描述。 虽然我们算法的主要应用方向是量子系统的模拟，但所开发的子程序还可用于优化或机器学习等领域。 我们的算法在一系列代表性模型上进行了基准测试，例如在数值模拟和硬件实验中的伊辛模型或海森堡自旋模型。 结合错误缓解技术，后者扩展到了 27 个量子比特；进入了变分量子算法在嘈杂量子计算机上难以扩展到的范围。 显示英文摘要

摘要： Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum computers, may prominent quantum algorithms are currently infeasible to run for problem sizes of practical interest. This doctoral thesis develops two main techniques to reduce the quantum computational resource requirements, with the goal of scaling up application sizes on current quantum processors. The first approach is based on stochastic approximations of computationally costly quantities, such as quantum circuit gradients or the quantum geometric tensor (QGT). The second method takes a different perspective on the QGT, leading to a potentially more efficient description of time evolution on current quantum computers. While the main focus of application for our algorithms is the simulation of quantum systems, the developed subroutines can further be utilized in the fields of optimization or machine learning. Our algorithms are benchmarked on a range of representative models, such as Ising or Heisenberg spin models, both in numerical simulations and experiments on the hardware. In combination with error mitigation techniques, the latter is scaled up to 27 qubits; into a regime that variational quantum algorithms are challenging to scale to on noisy quantum computers without our algorithms.