Improved sample-based quantum diagonalization via randomized Hamiltonian simulation

Approximating ground states of many-body systems is a central computational challenge in physics and chemistry, with wide-ranging scientific implications. While quantum computers hold promise for tackling this problem, commonly recognized strategies demand circuit depths that surpass the capabilities of today’s hardware.

As a result, researchers have recently turned to sampling-based quantum diagonalization methods, which offer a more practical alternative for the near-term and early-fault-tolerant quantum devices now being developed. In this framework, the quantum computer acts as a sampling engine, generating data that define subspaces where the Hamiltonian is subsequently diagonalized using high-performance classical computing.

A recent proposal (Sample-based Krylov Quantum Diagonalization, SKQD) makes use of quantum Krylov states as subspace constituents, with convergence guarantees under appropriate assumptions. Given the complexity of chemical Hamiltonians, however, this proposal remains limited on the application side by the depth of the circuits. In this work, we introduce a new variant of the algorithm that leverages a qDRIFT-inspired randomized compilation of the Hamiltonian propagator. This algorithm combines the convergence guarantees of SKQD with a more near-term friendly circuit complexity.

We show results on a range of quantum chemistry systems belonging to the class of the polycyclic aromatic hydrocarbons, demonstrating improvements in the quality of the energy solutions with respect to standard approaches based on local unitary cluster Jastrow ansatzes. We also show how our proposal is able to explore the relevant portion of Hilbert space more efficiently by collecting relevant samples more effectively. Our approach, as an example of synergistic integration of quantum and classical resources, constitutes a promising path toward quantum advantage.