# A Theory of Quantum Subspace Diagonalization

@article{Epperly2021ATO, title={A Theory of Quantum Subspace Diagonalization}, author={E.N. Epperly and Lin Lin and Yuji Nakatsukasa}, journal={ArXiv}, year={2021}, volume={abs/2110.07492} }

Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized eigenvalue problem, with a matrix pencil corrupted by a non-negligible amount of noise that is far above the machine precision. Despite pessimistic predictions from classical perturbation theories, these methods can perform reliably well if the generalized…

## 2 Citations

Quantum subspace expansion algorithm for Green's functions

- Computer Science, Physics
- 2022

An algorithm to compute Green’s functions on quantum computers for interacting electron systems, which is a challenging task on conventional computers is presented, and a two-level multigrid Trotter time evolution is proposed for an eﬃcient preparation of the basis states in a quantum circuit, which takes advantage of the robustness of the subspace expansion against TroTter errors.

Say NO to Optimization: A Non-Orthogonal Quantum Eigensolver

- Biology
- 2022

A quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wavefunction ans¨atze employing a non-orthogonal multireference basis that captures a signiﬁcant portion of the exact wavefunction in a highly compact manner, and that allows computation of the resulting energies and wavefunctions at polynomial cost with a quantum computer.

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