This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal evolutions which can be chosen variationally. No qubit overheads or controlled-unitary operations are needed but the method is recursive which makes the circuit depth grow exponentially with the number of recursion steps. To make near-term implementations viable, the proposal includes optimization of diagonal evolution generators and of recursion step durations. Indeed, thanks to this numerical examples show that the expressive power of double-bracket iterations suffices to approximate eigenstates of relevant quantum models with few recursion steps. Compared to brute-force optimization of unstructured circuits double-bracket iterations do not suffer from the same trainability limitations. Moreover, with an implementation cost lower than required for quantum phase estimation they are more suitable for near-term quantum computing experiments. More broadly, this work opens a pathway for constructing purposeful quantum algorithms based on so-called double-bracket flows also for tasks different from diagonalization and thus enlarges the quantum computing toolkit geared towards practical physics problems.

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对角化的双括号量子算法

这项工作提出了双括号迭代作为获得对角化量子电路的框架。它们在量子计算机上的实现包括由输入哈密顿量生成的交错演化与可以变化选择的对角演化。不需要量子位开销或受控单一操作，但该方法是递归的，这使得电路深度随着递归步骤的数量呈指数增长。为了使近期实现可行，该提案包括对角演化生成器和递归步骤持续时间的优化。事实上，由于这个数值例子表明，双括号迭代的表达能力足以用很少的递归步骤来近似相关量子模型的本征态。与非结构化电路的强力优化相比，双括号迭代不会受到相同的可训练性限制。此外，由于实施成本低于量子相位估计所需的成本，它们更适合近期的量子计算实验。更广泛地说，这项工作开辟了一条基于所谓的双括号流构建有目的的量子算法的途径，也适用于与对角化不同的任务，从而扩大了面向实际物理问题的量子计算工具包。