A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a memory/computational bottleneck on classical computers during exact diagonalization. We apply Grover’s search in the form of a minimization procedure to solve this problem. Our quantum solution provides an exponential reduction in memory, and a quadratic speedup in time over classical methods. We discuss explicitly the full circuit implementation of Grover minimization as applied to this problem, finding that the oracle only scales as polylog in the size of the group, which acts as the search space. Further, we design an error mitigation scheme that, with no additional qubits, reduces the impact of bit-flip errors on the computation, with the magnitude of mitigation directly correlated with the error rate, improving the utility of the algorithm in the Noisy Intermediate Scale Quantum era.

多体哈密顿量可以通过以对称适应的基态表示来进行块对角化。寻找这些基态及其相应对称性的群轨道代表，目前是精确对角线化过程中经典计算机上的存储/计算瓶颈。我们以最小化程序的形式应用格罗弗的搜索来解决此问题。与传统方法相比，我们的量子解决方案可显着减少内存，并在时间上实现二次加速。我们明确讨论了应用于该问题的Grover最小化的全电路实现，发现预言机仅按组大小扩展为polylog，而该组充当搜索空间。此外，我们设计了一个错误缓解方案，该方案无需额外的量子位，