Table 1 Large-scale experimental demonstrations of quantum algorithms for ground state energy estimation, to date

From: Krylov diagonalization of large many-body Hamiltonians on a quantum processor

Reference

Algorithm

System

Qubits

Used Hilbert space dimension

Caveats of algorithm

9

VQE

Li2O

12

12 choose 4 = 495

No proof of convergence

55

QC-QMC

Diamond

16

(8 choose 6)2 = 784

May not be scalable in general56,57

8

VQE

Fermi-Hubbard

16

(8 choose 4)2 = 4900

No proof of convergence

53

SQD

Fe4S4

77

(36 choose 27)2 ≈ 8.86 ⋅ 1015

Requires sparse ground state wavefunction

This work

KQD

Heisenberg model

43

42 choose 5 = 850668

Requires symmetry (e.g., U(1))

  1. QC-QMC refers to a hybrid quantum-classical quantum Monte Carlo algorithm.
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