Speaker
Description
Quantum subspace diagonalization methods have emerged as a promising application of quantum computers. For matrices $A$ of suitable structure, the unitary operation $U = e^{\imath A t}$ can be efficiently approximated on current quantum devices. This has motivated the use of Krylov subspaces
$$
\begin{equation}
\mathcal{K}_m=\text{span} \left\{\mathbf{x},U\mathbf{x}, ..., U^{m-1} \mathbf{x}\right\},
\end{equation}
$$
whose resulting Rayleigh-Ritz approximation admits rigorous convergence guarantees. In practice, however, one must contend with the noise inherent to quantum computation. In particular, the quantum subroutine for estimating the inner products $\langle U^j \mathbf{x}, U^k \mathbf{x}\rangle$ is both prohibitively noisy and computationally expensive, hindering the ability to obtain accurate Krylov overlap matrices.
We present a quantum-subspace protocol that circumvents the need to compute these inner products by exploiting symmetries of the matrix $A$. This approach uses only operations that can be efficiently performed on a quantum computer and that incur relatively small errors. The resulting algorithm retains the convergence guarantees while substantially reducing computational overhead. The method is demonstrated using large-scale tensor network simulations.